Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 24: 104

Answer

$1.496037119 \times 10^{11}$ (meters)

Work Step by Step

Given the formula: $D = \left(\dfrac{GM}{4\pi^{2}} \right)^{1/3} T^{2/3}$ Given the values: $G = 6.67 \times 10^{-11}$ (the gravitational constant). $M = 1.99 \times 10^{30}$ (the mass of the sun). $T = 365.25 \times 24 \times 60 \times 60$ ($1$ year on earth assuming the length of it is $365.25$ days in seconds). We now just fill the given data with their respective variables forming this equation: $D=((6.67 \times 10^{-11} \times 1.99 \times 10^{30})\div(4 \times \pi^{2}) )^{1\div3} \times (365.25 \times 24 \times 60 \times 60)^{2\div3}$ which in the end will result to $1.496037119 \times 10^{11}$ (meters).
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