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Assertion: The period of <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals s i n invisible function application 2 x c o s invisible function application left square bracket 2 x right square bracket minus c o s invisible function application 2 x s i n invisible function application left square bracket 2 x right square bracket" width="267" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»⁡«/mo»«mn»2«/mn»«mi»x«/mi»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»⁡«/mo»«mo»[«/mo»«mn»2«/mn»«mi»x«/mi»«mo»]«/mo»«mo»-«/mo»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»⁡«/mo»«mn»2«/mn»«mi»x«/mi»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»⁡«/mo»«mo»[«/mo»«mn»2«/mn»«mi»x«/mi»«mo»]«/mo»«/math»'/> is 1/2. Reason: The period of x – [x] is 1.

Solution for the question - assertion: the period of f(x)=sin 2x cos[2x]-cos 2x sin[2x] is 1/2.reason: the period of x  [x] is 1. if (a) is false but (r) is true.

Assertion: the period of f(x)=sin 2x cos[2x]-cos 2x sin[2x] i-Turito

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Assertion : Fundamental period of <img src="data:image/png;base64,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" class="Wirisformula" alt="c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi" width="135" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»⁡«/mo»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«mi»o«/mi»«mi»t«/mi»«mo»⁡«/mo»«mi»x«/mi»«mtext» is «/mtext»«mn»2«/mn»«mi»π«/mi»«/math»'/>. Reason : If the period of f(x) is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAHVJREFUeNpjYIAAJiD+BcT/8eBfUHUkAzUgvsBAJRAExEupZVgjEJdQy7A1QOxHLcPuArEkNQxiAeIv1HKVJRDvp5ZhkUA8n4ikU0tM8pkExMkE1CwG4jRoYsYL1gGxF5G+IGjYOyDmoJZhpIBRw0gzBB0zAAC8NSH/ozxNHgAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+VDwvbWk+PG1uPjE8L21uPjwvbXN1Yj48L21hdGg+tf7ZZAAAAABJRU5ErkJggg==" class="Wirisformula" alt="T subscript 1 end subscript" width="19" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»T«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/> and the period of g(x) is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJhJREFUeNpjYIAAJiD+BcT/8eBfUHUkAzUgvsBAJRAExEupZVgjEJdQy7A1QOxHLcPuArEkNQxiAeIv1HKVJRDvp5ZhkUA8H488cro7CsQq+AybBMTJRFgKSsBZQHwOn6J1QOxFgk9+4JN8B8QcRBpkD8QHqRG2ktAwU6LUIFDe3UKNtAgyYBsQ81HDeyCDNKiVDrGVdWAAAO0hI0uYXuHxAAAAYHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5UPC9taT48bW4+MjwvbW4+PC9tc3ViPjwvbWF0aD4aV5SuAAAAAElFTkSuQmCC" class="Wirisformula" alt="T subscript 2 end subscript" width="19" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»T«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/math»'/>, then the fundamental period of f(x) + g(x) is the L.C.M. of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAHVJREFUeNpjYIAAJiD+BcT/8eBfUHUkAzUgvsBAJRAExEupZVgjEJdQy7A1QOxHLcPuArEkNQxiAeIv1HKVJRDvp5ZhkUA8n4ikU0tM8pkExMkE1CwG4jRoYsYL1gGxF5G+IGjYOyDmoJZhpIBRw0gzBB0zAAC8NSH/ozxNHgAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+VDwvbWk+PG1uPjE8L21uPjwvbXN1Yj48L21hdGg+tf7ZZAAAAABJRU5ErkJggg==" class="Wirisformula" alt="T subscript 1 end subscript" width="19" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»T«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/> and T

Solution for the question - assertion : fundamental period of cos x+cot x52 pi . reason : if theperiod of f(x) is t_(1) and the period of g(x) is t_(2) , then t

Assertion : fundamental period of cos x+cot x52 pi . reason-Turito

Assertion: The function defined by <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK4AAAATCAYAAAAJWDZFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA2BJREFUeNrtWk9kXEEYfypWVZSKqIoIVVU9VIiqquolqqIqcttDDytUVVRU6SFWVYWVQ1T00lNVRYjaQ1WUqoiIXGJF9FClhx5WRMghKiKW9Pv4rY7XmXkz7+1kZ5r34yeb9/bN/vab733/3kbR8cEheEBcJ94OTPMK8UKU41jjEvFXQHpPEB8Ra/nWpQMbr2J5TQXX+eYIOwHafz93weSNPRs7doW4mnK9FVzvA7qIr4mlwPbkFnEpd0017iAaMb8ROwTn60+55gBx2aOa8X5ge3IO9j/v8DP2ELCCBDtpXXDQy/jbD8NlwTIcuN04TZwkPghkTy4SP8F5XYGbvo2Qo+0IcU5yfIo4lnHtxynqY1/qxcM2RtoF3GxpsosphhX77irrtRzPic8kxz8Tb0qOjyqc8SXOibhO/OpAs42GJvi7rDkyNqfbF8St6O/orS+l5gVMQFw7CO/7BHRv4qZelET5NLbO6ridCJx12LNKPCO+oSrUgMyicG6XWFAsXIs1ciU0P3EUsI6u9tRRBxMNzXX2cSP2OXICTuszMC478TwiWhbNpnZIq5k1/kTQauqeVkRh0/1uha5OfN4ksg770FPi3fgbvxN7JQs0Epq5abweTIiqBw4bSlMNLqNXEU4g4h1xyGPNjB9CPyP2ArsOdNvoqiAIJKa4PcW5RsK1XzCu4bTY1QbHtdFgM32wzQCLKIlELGmiuw+aVft+UpMhbXRn0bUdLwtkuAbDy6ArFRjjcErdrNZlqWCqwXX0io+U+PVvzzWr9l3Xk2TRbarramQ4QuU091Zzh91QnOPjH5A+ipr1XTVnNhpcO8G2RFfNc82qfX9CLDvQbaprCH1XIriWUM02VeMwHoh/JJ5CIb2mSR1jWKfVsNHg2gnqSLFNlLHJPmueif59isjZcUMyVWiFblNdA+i5ElFVNBEM2QOIboxrROHc7b1XrOHiAYStBtdOwGOhNygRuK6dhT6fNVfRnA3i/x4cKznSbdOcrWOi0IFmcVyW+Xdi0SKOVaGmKeDL9UjeN4fOM373tPqRr62Go8IEJgtl2HNLGIf5qJn13YPzNuAsw57YuhfNbQMZYFQWuTYTFvlffmRz1OiOcjjBK9QSJo9jH0b2j22nonB+F5AjIHAaH8nNkCMk/AENCBgSHjgcVwAAAPl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPig8L21vPjxtaT54PC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtc3VwPjxtaT54PC9taT48bW4+MzwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bWk+YTwvbWk+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5iPC9taT48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5jPC9taT48L21hdGg+Ias2RwAAAABJRU5ErkJggg==" class="Wirisformula" alt="f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c" width="174" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»a«/mi»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math»'/> is invertible if and only if <img src="data:image/png;base64,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" class="Wirisformula" alt="a to the power of 2 end exponent less or equal than 3 b" width="55" height="16" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»a«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»≤«/mo»«mn»3«/mn»«mi»b«/mi»«/math»'/>. Reason: A function is invertible if and only if it is one-to-one and onto function.

Solution for the question - assertion: the function defined by is invertible if and only if. reason:a function is invertible if and only if it is one-to-one and

Assertion: the function defined by is invertible if and only if-Turito

Assertion : <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals s g n left parenthesis x minus vertical line x vertical line right parenthesis" width="138" height="18" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»s«/mi»«mi»g«/mi»«mi»n«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«mo»)«/mo»«/math»'/>can never become positive. Reason : f(x) = sgn x is always a positive function.

Solution for the question - assertion : f(x)=sgn(x-|x|) can never become positive. reason : f(x) = sgnx is always a positive function. if (a) is true but (r) is false.

Assertion : f(x)=sgn(x-|x|) can never become positive. reason -Turito

If f (x) = <img src="data:image/png;base64,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" class="Wirisformula" alt="open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for  end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then  end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f ​ left parenthesis x right parenthesis d x equals close" width="316" height="45" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced open=¨{¨ close=¨¨ separators=¨|¨»«mrow»«mtable»«mtr»«mtd»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/msup»«/mtd»«mtd»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mtext»for «/mtext»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«mo»≤«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mtext»2,«/mtext»«/mtd»«mtd»«mtext»otherwise«/mtext»«/mtd»«/mtr»«/mtable»«mo»,«/mo»«mtext»then «/mtext»«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mtext»-2«/mtext»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msubsup»«mrow»«mi»f«/mi»«mi»​«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«/mrow»«/mrow»«/mrow»«/mfenced»«/math»'/>

Solution for the question - if f (x) = 321-1

If f (x) = -Turito

The value of the integral <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 2 end exponent end superscript open vertical bar fraction numerator log subscript e end subscript invisible function application blank x over denominator x end fraction close vertical bar" width="90" height="45" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/msubsup»«mrow»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mfrac»«mrow»«mrow»«mrow»«msub»«mrow»«mi»log«/mi»«/mrow»«mrow»«mi»e«/mi»«/mrow»«/msub»«/mrow»«mo»⁡«/mo»«mrow/»«/mrow»«mi»x«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mrow»«/math»'/> dx is :

Solution for the question - the value of the integral dx is : 535/23/2

The value of the integral dx is : -Turito

Assertion : Let <img src="data:image/png;base64,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" class="Wirisformula" alt="f colon R minus left curly bracket 1 , 2 comma 3 right curly bracket rightwards arrow R" width="123" height="16" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»:«/mo»«mi»R«/mi»«mo»-«/mo»«mo»{«/mo»«mn»1,2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»}«/mo»«mo»§#8594;«/mo»«mi»R«/mi»«/math»'/> be a function defined by f(x) = <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 1 over denominator x minus 1 end fraction plus fraction numerator 2 over denominator x minus 2 end fraction plus fraction numerator 3 over denominator x minus 3 end fraction" width="172" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mn»3«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/>. Then f is many-one function. Reason : If either <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis x right parenthesis greater than 0" width="59" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/math»'/> or <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of apostrophe left parenthesis x right parenthesis less than 0 comma for all x element of" width="105" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#60;«/mo»«mn»0«/mn»«mo»,«/mo»«mo»§#8704;«/mo»«mi»x«/mi»«mo»§#8712;«/mo»«/math»'/>domain of f, then y = f(x) is one-one function.&lt;/span

Solution for the question - assertion : let f:r-{1,2,3}rarr r be a function defined by f(x) =(1)/(x-1)+(2)/(x-2)+(3)/(x-3) . then f is many-one function. reason

Assertion : let f:r-{1,2,3}rarr r be a function defined by f(-Turito

Solution for the question - assertion : fundamental period of cos x+cot x i5 2pi . reason : if theperiod of f(x) is t_(1) and the period of g(x) is t_(2) , then

Assertion : fundamental period of cos x+cot x i5 2pi . reason -Turito

Function<img src="data:image/png;base64,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" class="Wirisformula" alt="f colon Z rightwards arrow Z comma" width="61" height="16" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»:«/mo»«mi»Z«/mi»«mo»§#8594;«/mo»«mi»Z«/mi»«mo»,«/mo»«/math»'/> f(x) = 2x + 1 is-

Solution for the question - function f:z rarr z f(x) = 2x + 1 is- many one intomany one ontoone-one into

Function f:z rarr z f(x) = 2x + 1 is- -Turito

that the range of x – [x] is [0 , 1) then of [x] – x is (–1 , 0]

If f(x) is an even function and <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of apostrophe left parenthesis x right parenthesis" width="33" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/> Exist for all 'X' then f'(1)+f'(-1) is-

Solution for the question - if f(x) is an even function and f^(')(x) exist for all 'x' thenf'(1)+f'(-1)is- zerosome times positive and some times negative

If f(x) is an even function and f^(')(x) exist for all 'x' th-Turito

In two separate collisions, the coefficient of restitutions  and  are in the ratio 3:1.In the first collision the relative velocity of approach is twice the relative velocity of separation ,then the ratio between relative velocity of approach and the relative velocity of separation in the second collision is

Solution for the question - in two separate collisions, the coefficient of restitutions and are inthe ratio 3:1.in the first collision the relative velocity of

In two separate collisions, the coefficient of restitutions a-Turito

Suppose <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared" width="102" height="18" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»'/> for<img src="data:image/png;base64,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" class="Wirisformula" alt="x greater or equal than negative 1" width="54" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8805;«/mo»«mo»-«/mo»«mn»1«/mn»«/math»'/>. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals–

Solution for the question - suppose for. if g(x) is the function whose graph is the reflection of thegraph of f(x) with respect to the line y = x, then g(x) equ

Suppose for. if g(x) is the function whose graph is the refle-Turito

Solution for the question - a spotlight installed in the ground shines on a wall. a woman standsbetween the light and the wall casting a shadow on the wall. how

A spotlight installed in the ground shines on a wall. a woman s-Turito

<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/481438/1/903671/Picture5.png" alt="" width="157" height="" /> As shown a block of mass <img src="data:image/png;base64,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" class="Wirisformula" alt="M blank" width="19" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«mi» «/mi»«/math»'/>is lying over rough horizontal surface. Let<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAMCAYAAAC9QufkAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAIFJREFUeNpjYMAN6oG4nARxFLAKiANIEEcBt4BYmgRxOGAC4m9YxFlwiKMAcyDej0XcEoc4CogE4oVYxBOBeD4hzZOAOA9NzA+IPwFxMiHN64B4BxBzALEa1La5QLwJiL0IaX4H9dsPKO2IJM6FTyMbEH9gIBN4QZ1NFoiHBhhBAAC7rRmQpdufawAAAF50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4QTA7PC9taT48bWk+JiN4M0JDOzwvbWk+PC9tYXRoPteBU1AAAAAASUVORK5CYII=" class="Wirisformula" alt="blank mu" width="15" height="12" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi» «/mi»«mi»μ«/mi»«/math»'/> be the coeeficient of kinetic friction between the two surfaces in contact. The force Of friction between the block and horizontal surface is given by <img src="data:image/png;base64,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" class="Wirisformula" alt="F equals mu R equals mu M g" width="100" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»F«/mi»«mo»=«/mo»«mi»μ«/mi»«mi»R«/mi»«mo»=«/mo»«mi»μ«/mi»«mi»M«/mi»«mi»g«/mi»«/math»'/> (<img src="data:image/png;base64,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" class="Wirisformula" alt="because R equals M g right parenthesis" width="75" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∵«/mo»«mi»R«/mi»«mo»=«/mo»«mi»M«/mi»«mi»g«/mi»«mo»)«/mo»«/math»'/> To move the block without acceleration, the force (P)required will be just equal to the force of friction , ie , <img src="data:image/png;base64,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" class="Wirisformula" alt="P equals F equals mu R" width="75" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«mo»=«/mo»«mi»F«/mi»«mo»=«/mo»«mi»μ«/mi»«mi»R«/mi»«/math»'/> If d is the distance moved , then work done is given by <img src="data:image/png;base64,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" class="Wirisformula" alt="W equals P cross times d equals mu R d" width="118" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»W«/mi»«mo»=«/mo»«mi»P«/mi»«mo»×«/mo»«mi»d«/mi»«mo»=«/mo»«mi»μ«/mi»«mi»R«/mi»«mi»d«/mi»«/math»'/>

If reaction is R and coefficient of friction is<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAMCAYAAAC9QufkAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAIFJREFUeNpjYMAN6oG4nARxFLAKiANIEEcBt4BYmgRxOGAC4m9YxFlwiKMAcyDej0XcEoc4CogE4oVYxBOBeD4hzZOAOA9NzA+IPwFxMiHN64B4BxBzALEa1La5QLwJiL0IaX4H9dsPKO2IJM6FTyMbEH9gIBN4QZ1NFoiHBhhBAAC7rRmQpdufawAAAF50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4QTA7PC9taT48bWk+JiN4M0JDOzwvbWk+PC9tYXRoPteBU1AAAAAASUVORK5CYII=" class="Wirisformula" alt="blank mu" width="15" height="12" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi» «/mi»«mi»μ«/mi»«/math»'/>, what is work done against friction in moving a body by distance d? <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN4AAAB2CAYAAACnKC00AAAgAElEQVR4nO2d51dbWbL2f8o5gACRc8bkaJx6zdwv8+n+vXfNzH3d021jbILBBNsEE02WhHLW+6FX7T6ocU/P7cZh5jxreYGFdHTCfnbVrnqqtqFYLJbQ8R+DUqmEwWD40qfxHw/jlz4BHTr+E6ETT4eOLwDzlz4BHb8NpdJPK4L/i5son5XfdVfzy0Mn3jcALXHKX7+NSAaD4cZnisWieo/8riWyTsTPD93V/IpxG7HktXLIe26zjCaTSRFM+7uWdJ86ro67gUGPan7dEDKUk6KcNIJisaj+rv1sPp8HwGg0qs8ajUaMRuMN0ukW8PNAdzW/AfwaKYrFIoVCAZPJhNH4swOTy+VIJBJks1kARTybzYbZbMblcmEymZTrqZPt80K3eF8xxBIJoQqFArlcjnw+j9FoxG63K8umJU6hUGB/f5+lpSXOz8/JZDJkMhlsNhterxePx0NLSwttbW1UVlYq0hoMhhsWU8fdQbd43wDE4mWzWU5PT7m6usJsNtPW1obH41GEKRaLmM1m8vk8+/v7PH36lIODA1wuFxaLBbvdjsPhoFgssrOzw5MnTxgbG8NkMt34Hh13D514Xzm0ViibzbK0tMTy8jKBQACHw4HNZsNqtd4gTT6f5+zsjL29PTKZDFNTUzQ1NeFwOEilUjx79owff/wRp9NJT08PNpvtRiBHt3Z3D514XzkkEplOp7m4uODVq1f87W9/o6amhtbWVqqrq7FarQCYzWaKxaIKpoRCIbq7u3n8+DHt7e2YzWYikQgnJyfs7OxwcnJCLBajoqJCEe735At1/HboxPvKUSqVKBaLRCIRNjc32dzc5ODggHA4zNLSEp2dnXi9XkWUQqGAwWBQwZV0Ok0mk1Frw2g0SjKZxG63qwCLTrbPD514XzlKpRLpdJrd3V2ePn3K27dvicVipFIpFhYW6O/vp7W1FafTqawd/Jwo393d5a9//Svv3r3DYrEQjUZ5+/YtVVVVdHV14ff7lTsrOT59rXf30In3FUMs0MXFBQsLCzx79ozz83NFjg8fPrC0tMS9e/fo6enBYrFgMpmUdcvn81xfX7OwsMD79++pqKjA6XSSTqfp6+ujra0Nq9V6w83URlF13B104n3FKBQKZLNZtre3WV5e5uTkBJvNhs1mw2g0kslkWF9f5/Xr11RXVxMIBNRnzWYzdrsdm83G4OAg9fX1VFZWKoIlEgmi0agK3ICuXvmc0In3leA26VY+n+fk5IQXL16ws7NDVVUVLpeLVCqlyHd+fs7Tp09pbW3FZrPh8/kwGo24XC48Hg91dXX893//N93d3djtdi4vL8lkMszNzbG7u8vMzMwNS/cp/aeOPxY68b5ixONx1tfXefnyJZlMhvHxcaxWKx8/fsTtdtPU1MTq6qpyN4PBIG63G4PBgNVqxWKxUFlZSU1NDVVVVZjNZoxGI42NjZRKJSKRCKlU6hdBFh13D92Z/4qRTqe5urrCaDTS09PDkydPaG9vx+VyUVVVxfT0NDMzM/h8Pq6vr0kmkxQKBUqlEj6fj6amJurq6nA4HCpwYjabqaqqIhgMYrPZyGQyNyycKFh03C10i/cVw+Fw0NbWxp/+9Ceqq6sZHR3l+fPnGI1GzGYzTU1NBAIBnE4nbW1tVFRUYLFYKBQKtLW18Ze//IVAIEBFRYUinsPhoLW1lf/6r//C5XLhdDpVMEWPaH4+6MT7iuH1ehkZGaGxsRGbzYbL5QJ+CroUi0WsViuNjY3U1NTg8/lwuVwqQllbW8uTJ0+wWq04nU5FKpPJRCAQYHx8HIvFgs/no1QqKaG1TrzPA514XxHKB73RaMTj8eB0OoGfXM98Pk8ul8NgMGCxWPB6vfj9/l9UGgjhtDIw+d3hcGC1WpVbKZULoCfRPxd04n0l0JJOBr/2p4T9pZLAaDSq3y0WixJIA+qn9hjlv4swWvt+3dp9PujE+8pRTr5cLkcul1PuplatouPbgR7V/MqhTXALJNem1VjqapNvC/rT+opRTjCtewm/rEjX12ffDnRX8ytGeamOvCbEKyemjm8HusX7BqBd54msS9Z2n2qGpOPrhk68bwTl7fjgpsrkn7mZeiexrws68b5ylLfxk1yd6C51ide3CZ143xCEeNoUgu5ifpvQifeNQBtI0RJQ/qbj24JOvK8c5VFLCbCYTKYb7dh1fFvQ0wl/EO6qYZDWwsn/y/dA0PHtQSfeb8Q/29zjNq3l70V5nq5UKim5mLZHio5vDzrxfgc+h2xLjivRTJvNphrZShmPTr5vD/oa73dA6ti0+CPdv/LuXxaLBb/fj8/nw2q13tjzQHc5vy3oxPudKLc4f7QF0uo0tc2IynWboGs1vyXoxPsDoLU4f2SZTnkKIZvNEg6HiUQiZLPZG5UL2vSCjq8fOvH+BZRHLsvXdX90W7xyQkufzWw2Sy6X04n2DUMPrvxG3LYjK/xSL3nbLq2/B58K2ty29bLuan470Il3B7iLNR6guouJTlMn27cLnXi/E3dh5QS3VZqbzWbVL0VLOr3787cFnXi/A7cN9D9SwVKetBfFiuT19H4r3y704MpXjttq8G6rUtDxbUG3eHcAbSRS/v9/sYC/lqK4rQL9t7qbnyKrvkHl54NOvN+JTw1SbZuG2/ae+9TnypPxwI3PCOGEzCKW/r8EW25L9uuk+zzQiXcHEFdQyFC+B135z0+tFeVv2uNoXUxtV2ltF+nbjgW3N8rVifZloBPvDnDbgP5U9PPX2vNpraaQOZ/Pqx2BynOInxJp/5p11R6nPIKq4+6gB1fuACKeFoL8FjnZp14XayldpJPJJMlkkmw2qzYh0VrDfxV6X84vA93i3QGkbu7q6opEIvGLCKRYP62lKV+7yd8lb5fJZIjFYqTTaUwmE+l0mv39fQqFAh6Ph3Q6/YtKCS20xyxfZwqBHQ4HLpcLi8Vy9zfpPxyGYrGox6P/YORyOS4vL/l//+//sb+/TzqdvkE8qSzQ7mWezWaV5bJYLFitVqxWKzabjXw+TyqVIpPJsLW1xd7eHi6Xi+HhYYLBIBUVFWQyGbUxZTmJ4We3UvKA0jpCtuey2WzU1NQwMzNDVVUVVqv1S97Cf3voFu8OkM1mOT8/53//939ZXV1VlQRikZxOJ3a7HafTST6fJ5FIkE6nyeVywE/74nm9XlXomkgklOXMZDKk02kATk9P8Xq9eDwecrmcEk/HYjHy+TxWq/VGJFQCMMViURFQG5xpamrC5XIxMTFBIBD4YvfvPwE68e4A4mqmUimcTie9vb1UV1crS+Z2u9Ue5cVikVQqRTKZJB6PYzKZ8Pl8N96TSCQIhUJkMhlFpkKhcMM1FDmZuLiFQgGr1UoqlVLWFH5eK4r7mkgkiEajbG9vEw6HlQXUcbfQiXcHkD3rLBYLDoeD6upq2tra8Hq9uFwuzGYz2WwW+GlvOgnGaItdzWYzNptNuZrX19ekUilsNhtmsxmDwYDb7cZisSirZbVayefzJJNJdR4SiAGUxcxmsyook8vlODk5IRKJEAqFyOfzuhrmM0An3h1AeqN4PB4ymQzV1dXKjZMBL0SS/9tsNrVXeTgcVoM/k8mo9ZfRaFQ7uQJqv/N0Oq30m/l8HpvNps4lEAgoMieTSaLR6I1NTyQ9IU2U5Px13C104t0BxNWULY5tNpsKlIiVslgsxGIxFUFMpVJEIhGMRiOpVAqLxYLJZFKFr16vF7fbjcHw09bJ+XxeEc5qtSoX8+rq6sa5eDweHA4HpVKJWCxGJBIhmUySTqfVd8jaUhvx1HG30Il3R5CARTabJZPJkMvlVMMip9OplC3iKqZSKaLRqMr/AVitVuWKwk8EdjqdqsNYJBJR7xPrJ+tFWcfJOtNgMKjcn6wJ5TPadoE6Pg904t0BtIoTiWZKCF8gqYRUKkUqlSKfz98IgCQSCUqlEjabDYPBQCKRIJ/PU1NTg9/vx+PxKDdR1pJVVVUkEgmurq5UIEbcSavVisPhIBAIYLFY1LlFo1Gurq5wuVwquKO7mncPnXh3AAliFAoFbDYbfr8ft9uN3W6nWCySTCYVWdLptIouZjKZGzk+yck5HA7MZjPxeFz1Xamurlaup9lsxuFw4HA41PfncjnS6TRVVVX4fD48Hg9OpxOHw4HRaCSfz5PJZDAYDASDQfx+P9fX18qa6rhb6MS7AxSLRdLptFKT5PN5YrGYiiY6HA6cTidms1klzE0mk2rrIFUHYpUkEhoOh4nH4yqK6XA4lDsqkc90Oq2OGw6HsVgsVFdX43K5cLlcZLNZZdnEdb28vKRQKKjJQsfdQyfeHUC7tstkMkSjUc7PzzGZTFitVmprazGbzUSjUdLpNKVSCZfLpaxSPp8nGo0q91OIJetEIYmQNJ/PE4/HCYVCSlLmdruVmxmPxzEajXg8HpLJpCK7BFJEjiYur06+u4dOvDuEVrhss9lUMENcvGg0yvX1tVoHVlRUKMWKyL3sdjtms1klwv1+P5WVlXg8HhUkKZVKOBwOvF4vmUxGRUVbW1uVdZUUg7R/TyQSXF5ekk6nub6+BsDtdqs1pY67hU6834nb6um0NXgmkwm73X4jcS6pACGJWBqbzUYul8NqtSqZl91uJ5lMKjdSIqTaRLeoWZxOJ36/n3Q6zeXlpXIzReEi0c1CoaBkaplMRn2XBF103D104v0OfKquTgIgQkqtCkWCJloxs/yTJLbZbKZQKKhk9+XlJaenp8pdlHWa5Acl3weodIXVar2Rysjn85jNZpxOp3KB4ee+oHI+ss7UcbfQ7/DvwG25L23RqugwLy8v8Xg82O32G4WrsraTZHosFuPi4uLGVlyS3NbuDiQBFBFQh0IhlZq4uLhQ0VSv14vdbleBF0krSPRUUgjpdBqDwaDOUU+i3z104v0BKO9vKUGNYrGI3W7H4XCoKgTJ8UlZjtlsxmKxKFe0VCqpwEqxWOTw8JAPHz5QLBZpaWnBZrMpwl1dXXFwcMDHjx/xer04nU4SiQQul4u6ujplNWUSMJlM5PN5LBYLbrf7hmWWKKdu7T4P9Lv8O1FOOkAJlQuFApWVldTV1am1mrZfivxuNpuprKzEYDAoPaUEQBYWFlheXqayslIlzyWn9/HjR+bn53n9+jXBYJCenh6qq6uprKzE5XJhNBpVZYJYWFlLSuRV3GA5d0lt6Lhb6MT7nbgtAijBi1QqRTqdVr/HYrEb3aClLk/SBWItJQIqBbWRSASTyUQ0GlWfu76+5vDwkOPjY66vr7FarcRiMZqamggEAni9XpUaMBgMqpBWjhOLxdT5SmV7ZWUldrv9c96+/1jozvwfBO1aL5fLqShkIpEgmUyq6KasxZLJpMrNCUGlSsFisShlSSaTIZ/PE4lE2N7e5uzsjFgsxunpKTs7O2pNl8/nMRqNOBwOta6TqGkikVBJd4l8SgI/kUhwfn5OPp8nGAz+Ys89HXcD3eL9gdC6c7FYTEUvC4UCbrcbt9utgi0CSaBL0aq2L4q2d2YqlWJvb4+9vT0KhQKnp6ecn5+r2juLxYLX68Xn8ynlislkUrk+KYx1OBy43W6VWL+4uFB5vGAwqDSkOu4WOvH+QEg0U6yYuI0S9oefrKHX61VEAVTLBqnPE9WJRDcdDociXzgcxuPxcHV1RTabVdZRcoWSC4SfkuVCxHg8rtaPUgsoVQ2SwwsEAjdIq+PuoBPvD4K4mhIplOoCWccJKc1mMz6f70aARaoXZNdXIZwktyVBnsvliEQi2Gw2Dg8PyeVyuN1u1S5C2xhJ5GaiRBG3U3KD0WhUWWipbPf7/eq7dNwtdOL9TmiVK1qLJ0WqYq2ERKLXFDWK1M2JgFkijVoSSlsHIfTZ2Rmnp6eYzWbsdruyipJ4l6S5VhDtcDiU6ypV7NLHJZlM4vP5VJ5RJ97dQyfeHwht/Z1YKqPRSCKRuNG2QXJ4YuWkisFisai8XyQSIRKJkEgksNvteDweLi8v2dvbw2KxkEqlqKysVJFLt9uNy+VSomkhuURRpUeLw+FQDY1EAyr5Rilb0vfau3t8tlW0uGLlMqny/wNKHS9/137+a4ZYC7mmpqYmgsEgbrcbp9OJy+VSaz2tVEs6Tksxq8/nU2qTTCZDIBCgsrISi8XC6ekpR0dH2O12Ghoa8Hg8ACpiqr2Hsq6TtWEymVTBGikpklIg7Ws66e4en93iaQko7pioN8p7P2rf/7XOwrc1js1msySTSdxuN7W1tUpxImstsVIS6pcUgpBTW7JjMBhUXu7y8pLz83MsFgs1NTXU19crzaWkD4TE2WxWRTIlTyiWV6Rn0gBJqiW0jZR03C0+G/GkCxagSmI2NzeJx+N0dnbS0NDA2dkZ4XAYn89HXV2dGghfI+EE5XsPSENZ6RQmFQKy9gMUEUS65fF4VERS3ERtvs3j8RAIBHC5XMDPqQNxHeXzwI3muS6XSyldstksRqNR5QulAl4+IxZPu7WYjrvDZyOeuF8yo4bDYV69esXHjx+x2+1UVFSwsbHB+/fvaWlpubWN+LcwIGRjERngsuaS8h8pZJWaObF0EoSRtaDf76e+vp6WlhYCgQB+v59AIEAwGMTr9VJfX69q8+rr6wkEAjfWkPLduVxOBXDsdruyuFVVVbjdbvb391WQRq/F+3z4rMSDn7cSjsVibGxscHV1RTweJ5VKsbW1xdra2o2Wc9/C2k4LSSfAT63apRN0PB5XVk7IKROJlO1I3Zwk26WUp7KyEqPRSHt7uwrAVFVVYbFY8Pl8NDc3U1tbq/Zb0Obt4vE48HORq1hUIbrL5VI5QFnf6eS7e3zWNV75/mtS3iKulwQCtLVqgFr3fa2Qtal2LzupONBaESkTks9I0yMhm7RulxYQtbW1NDc3q0CLy+UiGAySyWTUOs7hcFBfX091dbUinrjnQjrZnCQWi6loqwi2E4kEgKrr+9pd+38XfDbiaWdSGaTa/ePi8fiN7srikomCQuumfm0onyCkmFWqvrXlPtJIVoTTElgSKZfH41HJcNF1np2dKWmZtHGQRrjaJLukBIxGI7FYTFU+iCXL5/OKXFIkK2s/sc7/iaTTGgPBXfcZ/SLEE1Ll8/kbSeHj42M1OKVO7Gt3NeUBaX8ajUbVwUssidTCJRIJLBaL2rpLWrAnEgncbjcVFRWqbEeaG2mT7SKClvYQ8XhcEUyOJZuhiAWU5Lt83u/3K7fTZrOpDmQmk0nP430mfLEEuigrrq6uePPmDW63m7OzM6LRKO/evWNhYYHp6WmqqqrUoP4ad7Ipny0leptOp4nFYoRCIeXS5XI5RTbphSlt+OLxuNJews+NkuR4sViMeDxOQ0ODalwkx5cIplg3cS39fr9yg2XtJ5FQaUEhyXmRnv0nrvG0e0nIz7uefD77Gg9+bn8HEI1GWV9fJxgMqg02Li4uOD4+Vnk+wbcwIGSgSyQzFoup7bMA5YrKe7Xt3c1mMx6PR+XfZPcf7Y6ysv6VyUhcR7GyXq9X1eDJbkHS3k9kZVIcK1XnQlYdP+PfhnjaC5EuWyaTidbWVoLBIK2trdy/f5+LiwsikQhtbW2qU7KIiL9m4sksKUoUcaETiQROp/PGe6UOTzqOiSg6Go0SCoVU/xMp3ZGIp9wDybvZbDaqq6uV/EuqEaTeT85LmuuKckUUK9lsVuUcI5GI2mTlP93V/BzX/lktnnYjj0QigclkYnR0lJmZGVU5LXsEyP4AMqt/7Ws9QLmR2WxWWTvZQARQFQLabbGsVqtqu+d0OhWJhIixWEzl3pLJJMlk8kYnakkLaJVAUkArFRBms1klz6VgVoItsneCbEr5n0g4rbBDfn724Ip84af83F97MLe9XyupkguRdYvsG9fe3k59fb0qmZHvuS2KqQ1kyPvk/+KCaYM45e/9v+K2h1D+PdpCWO0/rasog14+I4ENSWJL4ARQ60QhrxBHyosk/ydtHoTY0u5Pa1UlzSDnJMJpQOVNyweg9jrLU0GfE7/2vb/2XH7tWLe9V/s37TMq//xvOX752CjHP7V44uqJ5RFoxc3a17QuYfmFyMWYzWYaGhqYmZmhs7OTyspKFcmTNIN2d9RyPaT2WLdd1G3ELL85t2lAfy2w8KmHrs03lou/5XpkXSX9UiTKmEwmVfJatmmWLl8S8RXFi2gvZXIRskhJkKwpxYqKYkXe43a7VTWD1OJJ5Fh7r8uvT/ssyyeyT90j7f3QPg/txPNH4FPn8Smilovxy69Fe33agIv291+zguVGQPt6ORTxbrtZ2sH9qRuuFfNK9bLWsmlPWE7AYrHQ19dHa2urCmeXkwu4YSnEApaTrVyKVn6Dy92n8nMrvynaG1aO8uNoz7mcvFrxtzZIIhIxg8FwI9IpOTRRtYhLLmtAIZBMXNIZTOu2ivhaSCqTprbpkZyjrPMknyh/104Yn7rW8nt52326zbrLa/+qC1c+/n7L539t8i8//08RUs77NhJ9yisAblzjp3jzC4t326wnPyUap01+a62gPCyZmcuJp12rSUsE+HltpHUvZaGvPY/ywSO/a8n5qRlMex7ymXK39J/NZp+6kdprFUsls564e9LQSApX5dxkTScpACFCqfRT70xZ42m9iVKppNZx4nYKUUulkkpJaKsQ0uk0V1dX6j5KLjEajapWhNp78alyrF+zMv/sb/8KYX7rvf+tx7jNCpaf022f06qmyj/7KRJqx1v5JCb45BpPBrPkkKLRqFI5aDcvlIcsuSmr1Uo6nVbC3HLyiVujrUOTwSMkLl+zlc++8rp20w4tybTfI+vJ22a0cuJ96uZrP6Od1eTz4hrDT+Jv2ZJLNgS5vLxUhLJYLEqnKZIvsVKZTEZpLGVNpy2ileuSIItMhFLWI3I0qSQXxYwcS9oASmOlSCRCLpe7kSuU1EK5WyiTxG0Tn5BZnqd2E06tp1I+2ZXjU8qk3+Oaaklf7r1pG/2Wp63kuZa/pn293NO5bdL/VINg9Wr5xclgODg44OXLl7x584ZkMqluosiP3G63esDyU9qCi2IDfg6hGwwGFUCQi5AEsOSwxD2SGV3cNZE6yWCRzsfaC9TuASB1bdqtp2QwSa5NSCORv18jXvkaS75DLLasn5aWlri6ulK7A52eniohuGy/LPdFlCQVFRUUiz/t0CrklSoHiWLKg5WBonU95RzEkyh3SbVtJSwWiyofkg0xd3d3+Z//+R8V6JHvkfshk6rcb20nNLHy2jWjPF+5T9pnox0XWnzq/pdbln/mpZT/XUs6rdcg96x8F9zbEuraa9ZOMOVLDbnuYrGIx+Ohrq5O7QB14xxLP0GZRAk3J5NJRbrV1VUuLi5wOBzkcjnOzs64vLzE4XDQ0NBAdXW1kkOdnZ0p+ZPf71c3/OTkhFQqhcvlora2Fp/PRzKZJBQKEYvFCAQCdHd3q0idJNFLpRJVVVVUVVVRKBSIRCKcnZ2pXVErKirUjYpEIqTTabX7qihDLi4uSCaTVFRU4PF4cDgcpFIpzs/PiUajat0lEVUZ8CL7kpsej8eJRqOUSiWl9hcLLwWlJpNJuXAyUMVTEHIXi0Vl3dxuN8FgkPr6emw2G6FQiOPjY2X1pC2D0Wjk6uoKo9GoavEkQplMJlVBrd/vv7Gppbi30tZBCo5DoZAaWNlslpqaGqqqqlQ5kwi8ZSBrd6uVSgZJY0igSCZj7doSUF3VhOzi+rrdbvXsZEDH43FVCS/jsVj8aRdd2T9CdKxCdplotcXG8hzFwgNqbEtzJ23BcS6XIx6PY7fbsVgsarIQQyIaWYkmizyvVCqpbm0S5JKUTn19PX/5y1/o7+9X5yb33Fzuokm07ODggMXFRba2tmhsbGRqagqfz8fJyQlra2vs7u7S1tZGX18fTU1NRKNRdnd3icfjNDY20tHRQWtrK9lslo8fP5JKpaiqquLevXv09PRgtVq5urpiYWEBg8FAX18fjx49UgPs9evXJBIJPB4PIyMjtLS0kM1mWVxcJBKJ4HQ66e/vp6urC7PZzNHREW/evKFUKtHT00NTUxMWi4VQKEQ8HieTydDW1kZvby9Wq5Xz83Pm5+e5vr6mubmZ/v5+vF4viUSCN2/eqP3Gu7u7cTqd6vpE2Nzb20swGMRgMHB0dMT79+8xmUz09vYqWVcoFFJNZ9va2qivr6eyspLLy0vW1tY4ODigoaGB7u5uWlpasFgsfPjwgaurK6qrq2lvb8fn85HJZNjZ2SEWi2G32+nr66O7u5tiscj5+TkrKysUi0Wam5vV+abTad6/f8/u7i6BQIChoSHl1kajUVZWVjAajXR2dlJRUUGpVCIcDnN6eko6naa7u1uVGuVyOZaXl7m+vqahoYHKykolbri4uCAcDmM0GnG73colPjk54eDgAJvNRnd3tyJyPB7n6OiISCSi7ofD4SCTybC/v8/5+Tn19fU0NDTgcDhIJBLs7Oyo1xsbG7Hb7eRyOU5PTzk+PsZut1NXV0cgEAAgFApxeHhIMpmksbGR2tpaLBaL+o6rqyvq6+upr69XG7ccHh4SCoWora2ltrYWt9tNLpfj8PCQg4MDamtr6ejoULs1XVxcsLm5iclkoru7G7/fr7SzR0dHhEIhJicnbywJtDBr1ywyE79//56lpSUODw9pb29naGiI2tpawuEw5+fn2O12njx5wujoKB0dHRQKBUWU3t5eRkdHuXfvHj6fj83NTY6Pj+nq6mJgYIDR0VECgQDHx8dEIhHcbjdPnjzh/v37tLe3E4/HVTnLyMgIExMTjI2NEY/H2djYUASamJjgwYMHeDweDg4OODo6IhgMMjAwwOPHj/H5fIRCIebn52lubmZqaorvvvuO+vp6Li4uePbsGQ0NDQwNDXH//n1aW1sV6U5OTlS6o7e3F5PJxPv379XWWCMjI0xPT+PxeDg+PubVq1cqRXL//n2qq6sJh8Osra1RLBbp6enh4cOHNDQ0UCgUWFpaIhqN0tTUxMMrFhoAABSrSURBVKNHj+jt7cVut7O1taW+e2pqitHRUfx+PwcHB2oNNjo6yv3792lrayORSPDy5UvOz88ZGRlhdnaW4eFhkskka2trXF5e4vf7mZ6e5uHDh1itVra3t3nx4gXt7e309/czMzNDMBjk6OiI77//nlwuR1tbG48fP6a5uVnVTV5eXqrXu7q6MBqNHBwc8OzZM5xOJ729vQwMDGCxWPj48SPPnz/H7XbT0tLC/fv3qampIRKJ8PLlSwwGAwMDA4yNjdHY2EihUFCTZmtrK2NjY3R3d2O1WllaWiKbzVJZWcnk5CRjY2P4fD6Ojo54/fo1NpuNzs5ORkZG1Bh9+fIl6XSaiooKHj58SH9/P9lslrdv31IsFqmrq2NycpKRkRGMRiOLi4uk02nq6+uZnJxkcHAQm83Gzs4Oz549w2QyMTY2xpMnT3A6nRwfH/PixQsSiQTt7e08ePCA1tZWIpEIq6urxGIxamtrefz4sZpQtSiVSj+v8aRW7Pj4mMXFRY6Pj6mqqmJ8fJza2loSiQTr6+vqdRmsACsrK7x7945SqcTExATDw8NUVFSwtbXF9vY2mUyGoaEhZmZmqKio4PDwkPX1dba2tmhubmZmZoa2tjaKxSKbm5usra3h8/kYHx9nYGAAq9XK/v4+GxsbGI1GpqenefDgATU1Nezu7rK2tkYkEqGjo0OpYK6urjg8POTk5ITGxkYmJiZoa2vj+vpazawtLS3Mzs7S3t7O9fU1x8fH7O7u4nQ6GRwcZGxsDLPZzOHhIXt7exgMBoaGhnjy5Ak+n4/j42O2traIRqP09/ffuFd7e3scHR1RW1vL4OAgPT09lEoltra2OD4+JhAIcO/ePUZHR3E4HOzt7bG5uUkmk+HBgwfMzs5SVVWlZGRGo5Hx8XH+9Kc/0dPTQ7FY5Pj4mFgsRnt7O7OzswwNDeH1enn9+jWXl5dqIpqenqaxsZHj42O1h/r4+DiPHz+mvb1dKWRk4pRjFQoFzs7OuLq6or29na6uLqanp7HZbOzt7XF4eKgs2vDwME1NTRwdHfHx40fMZjNTU1PKw4nH4+zs7JDJZGhvb2dkZITBwUFKpRJv377l+vqa6upq+vv7mZiYwOl0sre3RyKRoKKigpGRETUZRKNRtra2MBqNasLp6OigVCqpHXa7urqYnJxkcnISn8/HxsYGsVhMeRiTk5PU1dXx9u1bcrkcdXV1jIyMcP/+faqqqvj48SPZbJZAIEBPTw+zs7N0d3dzfHys3PSJiQmePHlCd3e3srSZTIb+/n5GR0cZHR2lsrLy1vWsWSJSuVyOnZ0dFhYW2NraUoOyra2N8/NzXr16xfz8PI2NjTx+/JiOjg4ymQyrq6s8ffoUq9XK6OgoY2NjeDwe9vb2+Otf/0oqlaKzs5MHDx5QVVXFxcUFCwsLvH37Fp/Px8OHD2lvbyeVSrG0tMTc3Bxms5lHjx4xMjJCoVBgYWGB58+fEwqFGB8f58mTJ4p0//jHP9jd3eXevXv86U9/orm5mXQ6rQjpcDh49OgRnZ2dZLNZNjY2WF5exm63c//+ffr6+tTrCwsLpNNpJiYmmJqaoqKiguXlZRUsGRoaYnR0lJaWFt6+fcvLly/Z2Nigo6ODkZERurq6CIVC7O7u8ubNGwwGA/39/UxNTZFKpW58hwwkg8HAzs4OL1684Pj4mHv37imLHYlEeP36NZubm1RXV/PgwQN1Hevr6ywuLlIqlfjzn//MyMgIZrOZd+/e8Y9//INEIsHIyAhPnjzB7/dzcXHBmzdvuLq6YmBggJmZGVpaWjCZTCwsLLC5uUllZSWPHj2iv78fh8PB/Pw8y8vLlEolHj16RFdXF263m/X1df7xj3/w7t07pqenldU8PT3l+fPnvHr1isHBQe7fv09HRwepVIrV1VUWFhaoqqpiYmKCkZERTCYT6+vrrKyskEwmGRwcZHZ2VnlKz58/Z39/n87OTmVpQ6EQr1+/Znl5mWAwyKNHj7h37566v8vLyxgMBiYnJ3n06BEOh4Pt7W1evnzJ5eUlfX19PHnyRJFrcXGRZDLJ0NAQ3333HTU1NXz8+JG1tTXOzs6Uhri9vZ1wOMzr169ZXFykrq6O2dlZxsbGMBgMzM3NMT8/j9Fo5M9//jPDw8N4PJ4bARitxTOk0+lSOp3m3bt3LC4ucnBwQHd3N+Pj49TV1REOh1lYWGBlZQWfz8fs7CxdXV0Ui0WWl5d58eIF+XyeyclJRkdHcTqdvH//nuXlZc7Ozujp6WF8fJzGxkb29vZ4+fIlOzs71NXVKUuXSCRYW1tjYWGByspK+vr6mJiYoFQq8f79e77//nuSySQDAwPcv38fh8OhXI29vT11rKamJlKpFB8+fGBvb49SqUR/fz+NjY0kEglevXrF1tYWHo+HyclJOjs7SafTbG5u8vr1a/L5vLKyBoOB7e1tVldXiUaj6pz8fj9nZ2fMz8+zt7enBqt0/FpeXmZ3dxez2czw8DAdHR0YDAZWVlaU63nv3j16e3sJBAKKQKenp/T09DAxMUFdXR37+/usra3x9u1bAoEAU1NT9PX1EQ6H2dzc5NWrVzgcDsbGxhgeHiafz7OxscH3338PoCx2RUUFu7u7zM3Nkcvl6O7uZnBwkJqaGmKxGEdHRywvLwNw79492traSKfTrK+vMz8/j9PpZHR0lKGhIUwmE1tbWzx//pzLy0taWlqU53F2dsbc3ByHh4f4/X4ePXpEW1sb2WyWhYUF1tfXMRqNPHz4kJ6eHux2O+vr66yurnJ5ecng4CBDQ0NUVlby/v175ufn2dnZoaurSz3bWCzGmzdvWF5exu12Mz4+zvDwMLFYjLW1NVZXVzGZTAwMDNDb24vb7ebt27fMz8+TSqXo6elhZGREkWtpaYnd3V06OzuZmpqisrKSvb093rx5w/n5OW1tbWqZFQqFWFxcZGVlBZfLxfT0NMPDw6RSKdbW1vjhhx8wGo3MzMwwOzuLw+G4EaTRRkqLxSLmTCbDwcEB33//PeFwmNraWiYmJqiurlbBj+3tbeVeNjc3K/dyfn6edDqtXAq/38/79+958eIFoVBIPfzKykq1l9vm5iYNDQ3Mzs6qddXy8jKbm5t4vV5GR0fp6+vDZDKxvb3N4uIihUKB6elpBgcHqaioYGdnh6WlJY6Pj2lvb1czrqwDDw8Pqampob29ncbGRuLxOOvr62xublJVVcXY2Bg9PT0kk0nevXvHixcvsFqt6kEajUbW19f58ccfyeVyDAwMMD4+TiAQIBKJKNeopaWFwcFBFVyam5vj7du3yjXq6Oggl8uxsbHB3NwcBoNBueJms5nNzU3m5+eJRCLKjZP179zcHB8+fKC2tpbZ2Vk1qchsLx5GT08PJpOJ5eVlnj9/zsXFBU+ePGF8fBy/38/Ozg5zc3McHR0xNjbGwMAAwWBQuWtv377FbrfT399Pa2urCrz8+OOPOJ1OhoaGlLu/u7vL3/72N+LxuLonwWCQjx8/8sMPP7Czs0NLSwuPHz+moaGBeDzOysoKS0tLeL1eJiYm6O3txWKxsLOzw9raGvF4XLlmTqeTw8NDXrx4wfn5OYODg0xOTqr1ocQdampq1PownU6zurrK8vIyxWKR+/fv09PTg8PhUPf3+vqae/fuMTY2ht/v5/z8nKWlJUKhEF1dXYyNjeH1ejk8PGRubo7T01P6+voYGRlR6/W5uTk2NjYIBAI8ePCA5uZmCoUCa2trvHjxQk0qfX19eL3eG2mLcrWOwWDAmEgklF9eXV3NzMwMHR0dKtCwurqKx+NhdHSU/v5+5c7Mz89TLBYZHh5Wa7ejoyOePn1KLBaju7ubmZkZGhoaiMVi/Pjjj8o6PXz4kM7OTkXglZUVLBYLs7Oz6jt2dnZ49eoVkUiE/v5+hoaGqK6uJhKJsLy8zN7engpmSF+S9fV1tre3sdls9PT00NXVpQb+/v6+er/45CsrK8zNzSnXb3R0FLfbzbt373j27Jmy2NPT01RXVxMKhXj37h1nZ2e0tLQwMzNDT08PsViM+fl5FhcXsdvt3Lt3j8HBQUwmk3ow+XyegYEBhoeHsVqtHB8fq+9oa2tT9yoUCvH8+XPevn2Ly+VifHyc3t5eisUi8/PzvHr1ikKhwPDwMMPDwzgcDtbX13n16hWxWIyxsTGmp6fxer3s7e3x7NkzDg8PaWtrY3x8XFk6ebYmk4nx8XHlxSwuLt54tjKQjo+PWVlZIRwO09XVxcTEBM3NzYRCIZaWlvjw4YNaS8v4efXqFa9fv8bhcDA8PMzg4CB2u52TkxN2d3cxGo0MDg4yPT2Nz+fj48ePvHr1itPTU1pbW5mdnaWuro5IJML8/Dxv3rzBbrczMjJCT08PFotFXYfFYlHeisPhYG1tje+//14FhUZGRqiqquL09FRFaCVI5/f71eSxv79Pa2srExMTBINBLi8v+fHHH1lbW8Pr9fL48WO6u7ux2+28fv2apaUljEajWhfX1dWpPO2vCQLMRuNPe2FPTU3R2dlJb28vhUKBo6Mj9vb2qKioYGpqSkXe9vf3WV1dxel00tfXx+DgILW1ter1ZDKpAg2NjY2Ew2E+fPjA5eUlHR0d6sEAXFxcsLOzQ3V1NaOjo3R3d+P1elVEMJPJMDw8zNTUFH6/n2QyyerqKqFQiOHhYcbGxmhoaCCZTLKyssKHDx+oqKhQC+dMJsPh4SGbm5sYDAYVDcxms2xvb7O3t4fZbOa7775jdHQUu93OwcGB+u7Z2Vmmpqaora0lm82yu7vL8fEx1dXVDAwMUFdXRz6fZ3V1lY2NDaqqqnj48CG9vb3YbDY2NjZYX1/HYDAwOzvLyMgIfr+f/f19lpeXCYVCDA0NqXsVjUbZ2Nhge3ub1tZWRkdH1fPY2Nhgfn5eeQWyhlhfX+fp06dkMhnGxsaYmZmhpqaG/f19/v73v3N4eMjAwACPHj1SgYlnz56xt7dHdXU1w8PDytLNzc2xuLiI2WxW6xe73a6sZiaT4bvvvuPevXsEg0FCoRA//PCDin7Pzs7S0tJCJpNhaWmJ1dVV7HY709PTDA0N4XQ6WVlZYWtri2KxSH9/P52dnWqSWFhY4MOHD/T29qp7cnJywosXL1hbW6O5uVlZTYDXr1+rqOr4+DgjIyNYrVYVd4hGowwNDfHo0SOCwSB7e3s8ffqU09NTtV4PBAJsb2/zww8/sLe3d8O1DYVCvHz5kvn5eRoaGpTByOVyrKys8Pe//11xR8ao5FBlXfcp8pk9Hg+dnZ20t7ertgCZTIaqqioGBwdxuVx0d3crZYXX66Wrqwuv10t7e7tqLS6J8YqKCrq7u2lublYqisrKSoaGhujo6FBdlXO5HC6Xi76+PgKBAB0dHfh8PpU0DQQCdHV10dbWRk1NjVKMeDwe+vr6GBgYoKam5oYQubGxkaamJpqampQsymKx0NjYSDAYpL29Xe14arPZaG5uxuVyqSisVBD4/X5qa2sZHR2ltrZWqT/kmhsaGmhoaFB9VOx2O+3t7bS3t9PX16fqCEulEo2NjSp/WVFRoWZCm83G0NAQk5OTBINBHA4H4XAYk8lEV1cXw8PDdHV13diSq7a2lqGhIeXWi17T4XCoaGBDQ4Oq37NarQwODqpooCSxo9GocrnlXhUKBa6vr/F6vQwNDSlLEI/HOT09JZvN0t7ezuTkJIFAQMnESqUSnZ2dDA0N0dnZqdrMy/n29vYyNDSEz+cjnU5zcXFBPp+ntbVVjaN8Pk84HFapovv371NbW6uaNoXDYYLBoKpmcbvdHB8fc3Z2htPpZGJiQqWvIpEIR0dHAIyPjzMxMaHc9LOzM5U/HBoaoqamhkKhwMePH2+sWVtbWzGbzWo3XiGd5EI/fvzI/v4+TqeTmZkZ9d2SkgN+IX/8hdUrFAolWfSJPwo/1YLJHmqSmTcYDOp1UXsIJPNfKpXweDw31PPSQk4KPWVGSCaTZLNZbDab6mqslZyJQkJkSrLhY7FYVNIms9lMJpNRhZyi6hDZTjgcJpVKUVFRgcPhUN99fX1NMpnE4/EoooiEKhwOqya7IvES9YSU4UiiuFAocHFxQTqdVt2eRYUhg0l6msgseHZ2xvX1teoQLQqReDzO+fk5xWKR2tpaVeQaj8c5OTkhnU7T0NCAz+dT9+Pi4oKjoyPq6+upra1VrRLPzs44OzsjEAhQU1OD3W7HZDIRCoWUZ1BbW6u2EAuHw+zv71MoFGhsbFSDMpvNsrW1RSqVUglsrcpke3sbt9tNW1ubUsdEIhH29/cplUq0tLSo5HIul1NpJ2lJKNfx/v17wuEwVVVVtLW1KbmdJLDdbjfd3d3qPp6cnHB4eEg+n6e7u1tNBpFIhPX1dVKpFH19fQSDQbXz7fb2NoeHh3R0dNDV1YXNZiOZTLKxsaHSTjLZiVzy+PgYt9utDIM8PwmyiJcmKhgth7RC6luJV74AlEGrVWZrNY5asatW9aLVxIluE1D6S5FNyee1zXxEfiRia9nfrbwuT/4ON0t4tMob7bVoBa1yQ7SiaW37QLlW2Y9cJo9yIbZ2FjMYDKp/jDaCJdIh+S6RasmkJhpGKUrVnpdco5ybyK/kONq8kKSC5LpzuZxSm2SzWWXhRVSey+XIZDJKfiXfJe/XWmTRVoqmVVsvKPdJ2x5QKhzkddFkamsMRWcrml3t61I1odVySsc58WpknGi/W9szRiZIkXKJYFxkbbIxqMFgUJZeWmNIEygxDiJJky7cMj7S6TSZTEZ1epNdmsqDKb/WnMtQLBZLv8bMT6n2/9XXtWU/5e+5TdWtHeTl75HXhHjlotbbrkV73E/hU8fVfv626yz/XftTjndbZEv+pj1u+fHKr738fdrPamvpys+l/Hjlv5ffm9uu67fct9vO67Z7qB2gWivxqev91HF+7by11/ZrdZ1arfJtxym/d+XHva1OtPw8f3HPisXi19/MRIeOfzN8na2Zdej4N4dOPB06vgB04unQ8QWgE0+Hji8AnXg6dHwB6MTToeMLQCeeDh1fADrxdOj4AtCJp0PHF4BOPB06vgB04unQ8QXw/wFjvHfyCGhIEwAAAABJRU5ErkJggg==" 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Solution for the question - if reaction is r and coefficient of friction is alpha , what is work doneagainst friction in moving a body by distance d? (mu rd)/(2)

If reaction is r and coefficient of friction is alpha , what is-Turito

Work done <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses W close parentheses equals" width="42" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mi»W«/mi»«/mrow»«/mfenced»«mo»=«/mo»«/math»'/> Area under curve of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAFlJREFUeNpjYMAEP4D4Pxr+BcRM6ApVgPgCA5EgAIiXEqu4HojLiVW8Cmo6UeAWFs9JY1MI8u0XYk01B+K9xCqOBOL5xCqeBMTJxCpeB8RexCp+B8QcDNQCAG0iFICd+m2LAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5GPC9taT48L21hdGg+PJEFugAAAABJRU5ErkJggg==" class="Wirisformula" alt="F" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»F«/mi»«/math»'/>-<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAKCAYAAABi8KSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHFJREFUeNpjYECAZCDuYMAEzVA5DHAOiMWR+IlAPIUBB/AA4j4o2wWI9zIQALuB2B6ILwCxMCHFBUD8C4j1CCm0BuI1UKdE4lOoBMSbgJgLiHmA+AwuZ4gC8TY0SR8gXoyukA2I1wGxNBZDlkNDiHQAAJxHEBolHuC4AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48L21hdGg+wQ7kJQAAAABJRU5ErkJggg==" class="Wirisformula" alt="x" width="11" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«/math»'/> graph = Area of triangle <img src="data:image/png;base64,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" class="Wirisformula" alt="O A B equals fraction numerator 1 over denominator 2 end fraction cross times 5 cross times 1 equals 2.5 blank J" width="172" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»O«/mi»«mi»A«/mi»«mi»B«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»×«/mo»«mn»5«/mn»«mo»×«/mo»«mn»1«/mn»«mo»=«/mo»«mn»2.5«/mn»«mi» «/mi»«mi»J«/mi»«/math»'/>

The force <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAFlJREFUeNpjYMAEP4D4Pxr+BcRM6ApVgPgCA5EgAIiXEqu4HojLiVW8Cmo6UeAWFs9JY1MI8u0XYk01B+K9xCqOBOL5xCqeBMTJxCpeB8RexCp+B8QcDNQCAG0iFICd+m2LAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5GPC9taT48L21hdGg+PJEFugAAAABJRU5ErkJggg==" class="Wirisformula" alt="F" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»F«/mi»«/math»'/> acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory <img 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" 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Solution for the question - the force f acting on a particle moving in a straight line is shown infigure. what is the work done by the force on the particle in

The force f acting on a particle moving in a straight line is s-Turito

Spring constant <img src="data:image/png;base64,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" class="Wirisformula" alt="k equals fraction numerator F over denominator x end fraction equals" width="63" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»k«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»F«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«/math»'/> Slope of curve <img src="data:image/png;base64,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" class="Wirisformula" alt="therefore k equals fraction numerator 4 minus 1 over denominator 30 end fraction equals fraction numerator 3 over denominator 30 end fraction equals 0.1 blank k g divided by c m" width="233" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∴«/mo»«mi»k«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»4«/mn»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mn»30«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«/mrow»«mrow»«mn»30«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»0.1«/mn»«mi» «/mi»«mi»k«/mi»«mi»g«/mi»«mo»/«/mo»«mi»c«/mi»«mi»m«/mi»«/math»'/>

The pointer reading <img src="data:image/png;base64,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" class="Wirisformula" alt="v divided by s" width="29" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»v«/mi»«mo»/«/mo»«mi»s«/mi»«/math»'/> load graph for a spring balance is as given in the figure. The spring constant is <img src="data:image/png;base64,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" alt="" />

Solution for the question - the pointer reading 1//5 load graph for a spring balance is as given in thefigure. the spring constant is 1" "kg//cm   0.3" "kg//cm