Does not exist extreme values; cos x+sin^(4)x in -Turito

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Easy

Maths-

does not exist Extreme Values; $cos space invisible function application x plus sin to the power of 4 space x element of$

Maths-General

$[\frac{3}{4}, 1]$
$[1, \frac{3}{2}]$
$[\frac{1}{2}, 1]$
$[\frac{3}{2}, 2]$

Answer:The correct answer is: $open square brackets 3 over 4 comma 1 close square brackets$

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A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is $350 m s to the power of negative 1 end exponent$ is

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at

lambda divided by 4

and second resonance occurs at

3 lambda divided by 4.

Thus, at first resonance

fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses

And a second resonance

fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses

Subtracting Eq.(i) from Eq.(ii), we have

fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13

⟹ fraction numerator lambda over denominator 2 end fraction equals 28

therefore blank lambda equals 56 blank c m

Hence, frequency of tuning fork

v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is $350 m s to the power of negative 1 end exponent$ is

physics-General

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at

lambda divided by 4

and second resonance occurs at

3 lambda divided by 4.

Thus, at first resonance

fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses

And a second resonance

fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses

Subtracting Eq.(i) from Eq.(ii), we have

fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13

⟹ fraction numerator lambda over denominator 2 end fraction equals 28

therefore blank lambda equals 56 blank c m

Hence, frequency of tuning fork

v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z

In a sine wave, position of different particles at time $t equals 0$ is shown in figure. The equation for this wave travelling along positive $x minus a x i s$ can be

As is clear from figure, at

t equals 0 comma x equals 0

y equals 0

. Therefore, option (a)or (d)may be correct.
In case of (d);

y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis

fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets

fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets

fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v

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x equals 0

t equals 0

is positive, in figure. Therefore, particle velocity is in negative y-direction.

In a sine wave, position of different particles at time $t equals 0$ is shown in figure. The equation for this wave travelling along positive $x minus a x i s$ can be

physics-General

As is clear from figure, at

t equals 0 comma x equals 0

y equals 0

. Therefore, option (a)or (d)may be correct.
In case of (d);

y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis

fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets

fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets

fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v

fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses

i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e

x equals 0

t equals 0

is positive, in figure. Therefore, particle velocity is in negative y-direction.

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