Maths-
General
Easy
Question
The Population of cities A and B are
and 1560,000respectively. The population of city C is twice the population of city B. The population of city C is how many times the population of city A ?
Hint:
Write the population of cities as the same powers of base 10 and then
compare.
The correct answer is: 20
Complete step by step solution:
Population of city A = ![2.6 cross times 10 to the power of 5](data:image/png;base64,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)
Population of city B = 1560000 = ![15.6 cross times 10 to the power of 5](data:image/png;base64,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)
Population of city C = 2
1560000 = ![2 cross times 15.6 cross times 10 to the power of 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAARCAYAAADe84KWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAjZJREFUeNrtWNFHQ1EYv2ZmkkiS9BDJJD1EkkwSmUl6GJMkPcQeekqv2f+QHmIyPfQ2M0n2kmSSjEnSQ6LHHvbSQzIzl/oOv3Fd95zde7bjXLk/fg87Z2d3v/t93+/77jWMAH7BrwMD+DBIAYIgBehFkFrEZ+Ku0xfixCLx2/LFbcV/KkbM4lpuPdqtV88TC9DTJF4RlzXpYBggnhKrYA5rdoSIc8Rb4o59s0LcIvbj8zTxAWuqcEHMCG66bPlnEJSY5QaxhLvXpMPATd+wfF7HGg9DxFc3Fx8nvmj0YpkgseSq+aynpIknDuvHgiKIEN/dXrgp2DsCve6pDFJOovpV62BtJOGwvoI9J2vM8/qSHYuwPK8CvQjrdZDeiKMS51Tq+EJlOFVL3XbeJD66TbQoGlzco0CvwjoFqYXmXyYeWnqmqPJZLyoRGzhfczkEqdJhCs60ZL11kHjJKVGRwBsJYW4qJoyJJ4tKmerwW0/ENZwLIdGYv+9r0mFKthMuJhCgSQm7UBUkKxKYRHlgVTfmsD5L/NSko86xu6jN7lyBZegZsa8LP++lTchkXxnVI2MtqnSw4SDJSbiilwuM4OEv7KOG64QZ4odgn1naJicBq5p0pJD8dpx7nUSvO3i9jtG1hAkzBCYRoBTnzUR7YmJ2uGdJuAU8761q0sFwRzzAf4rgNysyfir7Cqabhz/RtdJo+CbG2AJe9xiCIDEMI3N/cJbdjCWNOtrDWB5W3cDzXL8R4P/gD7FwvN2EkYHgAAAAlnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj4yPC9tbj48bW8+JiN4RDc7PC9tbz48bW4+MTUuNjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1zdXA+PG1uPjEwPC9tbj48bW4+NTwvbW4+PC9tc3VwPjwvbWF0aD6A0vFKAAAAAElFTkSuQmCC)
On dividing population of city C by population of city A, we have ![fraction numerator 2 cross times 15.6 cross times 10 to the power of 5 over denominator 2.6 cross times 10 to the power of 5 end fraction](data:image/png;base64,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)
On cancelling on numerator and denominator, we have
![not stretchy rightwards double arrow fraction numerator 2 cross times 15.6 over denominator 2.6 end fraction equals 12](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAjCAYAAAC5BAWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnRJREFUeNrtmr9Lw0AUx49SRKQIDiLiIIgUEQdBioiIixRxFETEUejgKG7iKPgviDiJi0gRkS5OIg6FIuIkgoODq4OIlCLUd/gKKab3K7k0d7wPfIc2XELzvbu8fPsYS4Z50AXoE9QAPYI2LV8zD9rHa4XRFEhGAXSOv6cOugItMqKNW9AGKIefJ0H3+J0tTkElgYlNw/OW0OQ8fu7HCXxHNssZBT0lcJ04TeeTtUbWRaMuOLaH0j1m0/Qjy7uT98zhFs80jdcxPG7Tn0HDZJ0ZvaAqFnhMw3hdw2WmN7AYq4B2AjWHaGfiz/Iy6BvH1xIoSp1nAHQJKmqM4UbfGBiusqKzoBms9PlKnpCc6wG0guMyOHFfQNtkbThjaPi45jibpgcp4ptGJ/iuMBLy/TTonez9D19Bx6A+A8NtbO8mxWUFV3cYDbK4nSEMM7IRDI+7kAtjCvQqOM638PUOE7pKNrdzLXlWduOVrYxvEBnUMhq+GjK+dY4e3P63AhN4FvOGJbI5/MaZRJ5xXjPIGhZgP6AP3IkKgvO0GMTH1BeO5ZNgIcF7KYuXuxF5E5aRxcvdiLyJBHdPVSJF3rvs7w8Gwi3TZW8l0uLqjaklaYR+faNT5+iYLo28m4o6ELyzEulZ6TqRt5ATvOhZDJPHV6XBdOXIW/VHHdJKT/X2bhp50zPd0e3dNPLuWL3n6H6n2nTTyJtw2HSTyJtwsCZQrRmcJUq2TK3LjmKaLVPrsmfIsmVqXfYUUbZMrcseIsuWqXXZM1SyZWpd9gjVbJlalz1BJ1um1mUP0M2WqXXZcUyyZWpddhzVbJlalz1CNVtOW+tyavgFVQ08kXG66VoAAADEdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtZnJhYz48bXJvdz48bW4+MjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjE1LjY8L21uPjwvbXJvdz48bW4+Mi42PC9tbj48L21mcmFjPjxtbz49PC9tbz48bW4+MTI8L21uPjwvbWF0aD60bnTIAAAAAElFTkSuQmCC)
Hence the population of city C is 12 times the population of city A.
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Write the standard form for ![6.8 cross times 10 to the power of negative 8 end exponent](data:image/png;base64,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)
Write the standard form for ![6.8 cross times 10 to the power of negative 8 end exponent](data:image/png;base64,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)
Maths-General
Maths-
Simplify by combining similar terms: ![2 root index 8 of 4 plus 7 cube root of 32 minus cube root of 500](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKUAAAATCAYAAADxuM2yAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA89JREFUeNrtWkFoE0EUXUooRUQUFRGUiIgEkVLQolKL5BKKFCmlBUVEiiIiHsSTIAUvojdLFaGoiBeFEqsUqV5KCUUkIigiUhQR8SChUCEHDaVa/+hbmQ4zuzOzs9sE9sGjyczfTd7Pn///zNbzzLCVOEb8QZwnThM7JXYriYsRmDT8z2Wa3hALCruoupLWX2+6YtH/jniE2ASy17MSu8PEKa8xkSN+UcyluuoQLAC3c+83I1BFPCWebFCNbLHNKeZSXXWIbuJnYgdxB3EcJZ3HOuJ3/G00rCXeIA5I5lJdCYMFWZFY5fqPoxK79cQXxHvEUeIw+hEep4mPNAM87v7RpHfxx44p7qXSlSdOoM+uET8QhxAINj6Oywemukx6vlXEm8QyOIIxW7u/KKE/9AOMZcHnGOMxJjTLOQQnD9ab9IU4in3O+2Xa1DD0E28pnHaZeEoyp9LFxnuJzdxYG/GZpY/jgI0uk99mknhISDiTEeyUyBLfCmMLErsa93oL+s6WkHuzFXIiQlBGCeYNODUI+o414b2uLh5VSx/HCRNdiwYLfFgyPiQsOF07YxGs5Ozh3nfhB/ZxQZGBxDI2GTG4ogTlODKZCuyI65UwpqNLPDqbsfRxXDDVpevjouKoKY85U7tA7EN5EVf2BBxZQ+neyM2/RqCq0IzMkF2moGT902BA/1RD2c0K82G6+Cw8gL7yoKWP4+gnbXTp+nhOaF3437piYadECxrRDgMH7CR+I2YCbK4SzzoILpvrstCUMbxOR5e4ETgXk49dIkyXf+heRSI6L9nUqlo6H/MWdlKsIT6WpFrR8fuF+SvEawH3bZVkhUXDFR/lKUAJpcJzrEv0XQ+C7YCFj13qd6WLBe0uVJgZbG51g7JmYSfthZiztoV80a/El8IYO7/cHXBNWXLfpDJlP1a7F4Mu1elCOaKPXcKVrgIWN4+Koiy3CGVZ124Jcmh6V2h8uTPE3+ihGPYSPxqWuCjPO03sm7DC22LSZbL6TXzsEnHqKir60oJko6Njt6RBHzX8kuyw+D5eXydeSnDDYnJdj2R1x62rFZudqD52CRe6WB/6SRjrVezg7wpHPbp2//FE0iuE4TbxJ5w8a3F9UkH5wJM/XnOlq4T2IIOsnEdpPO7Axy5hqmsMpwP+P990ISB7JbZT2NxlUKIvKhKBrl1oaVVhNfEX8aH379Fjkkc7JqhgY6ELU12dCDj/mIw5vtuRj13CVFc/sv0CjnNYlm8P2LjdgX6WkUcUO3Vdu0iYNjgCaSSkuhoY7RC5KdWV6qon9KW6Ul0u8QeotLsdpX42OQAAANp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+MjwvbW4+PG1yb290Pjxtbj40PC9tbj48bW4+ODwvbW4+PC9tcm9vdD48bW8+KzwvbW8+PG1uPjc8L21uPjxtcm9vdD48bW4+MzI8L21uPjxtbj4zPC9tbj48L21yb290Pjxtbz4mI3gyMjEyOzwvbW8+PG1yb290Pjxtbj41MDA8L21uPjxtbj4zPC9tbj48L21yb290PjwvbWF0aD4wBuWyAAAAAElFTkSuQmCC)
Simplify by combining similar terms: ![2 root index 8 of 4 plus 7 cube root of 32 minus cube root of 500](data:image/png;base64,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)
Maths-General
Maths-
Evaluate ![x squared plus 1 over x squared text if end text x equals 3 plus square root of 8](data:image/png;base64,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)
Evaluate ![x squared plus 1 over x squared text if end text x equals 3 plus square root of 8](data:image/png;base64,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)
Maths-General
Maths-
Simplify 4√12+5√27 - 3√75 +√300
Simplify 4√12+5√27 - 3√75 +√300
Maths-General
Maths-
Simplify √45 - 3√20 +4√5
Simplify √45 - 3√20 +4√5
Maths-General
Maths-
Arrange in ascending order of magnitude
and ![2 root index 6 of 3](data:image/png;base64,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)
Arrange in ascending order of magnitude
and ![2 root index 6 of 3](data:image/png;base64,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)
Maths-General
Maths-
The Diagonals of a square ABCD meet at O. Prove that ![A B squared equals 2 A O squared](data:image/png;base64,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)
The Diagonals of a square ABCD meet at O. Prove that ![A B squared equals 2 A O squared](data:image/png;base64,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)
Maths-General
Maths-
△ PQR is a right triangle with ∠Q=90∘ M is the midpoint of QR. Prove that
△ PQR is a right triangle with ∠Q=90∘ M is the midpoint of QR. Prove that
Maths-General
Maths-
In Triangle
. Prove that![A B squared equals A C squared plus B C squared minus 2 B C times C D](data:image/png;base64,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)
![](data:image/png;base64,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)
In Triangle
. Prove that![A B squared equals A C squared plus B C squared minus 2 B C times C D](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
In
and
prove that ![QM squared equals PM cross times MR.](data:image/png;base64,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)
In
and
prove that ![QM squared equals PM cross times MR.](data:image/png;base64,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)
Maths-General