A rational number is a number that can be made by dividing two integers (whole numbers). Since 5 and 4 are integers, then the answer will be a rational number.
Answer:
Step-by-step explanation:
![\frac{x^3}{a^3} +\frac{a^3}{x^3} =p\\\frac{x^3}{a^3} -\frac{a^3}{x^3} =q\\adding\\2\frac{x^3}{a^3} =p+q\\\frac{x^3}{a^3} =\frac{p+q}{2} \\substitute~in~first\\\frac{p+q}{2} +\frac{2}{p+q} =p\\\frac{(p+q)^2+4}{2(p+q)} =p\\(p+q)^2+4=2p(p+q)\\p^2+q^2+2pq+4-2p^2-2pq=0\\q^2-p^2+4=0\\q^2=p^2-4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%7D%7Ba%5E3%7D%20%2B%5Cfrac%7Ba%5E3%7D%7Bx%5E3%7D%20%3Dp%5C%5C%5Cfrac%7Bx%5E3%7D%7Ba%5E3%7D%20-%5Cfrac%7Ba%5E3%7D%7Bx%5E3%7D%20%3Dq%5C%5Cadding%5C%5C2%5Cfrac%7Bx%5E3%7D%7Ba%5E3%7D%20%3Dp%2Bq%5C%5C%5Cfrac%7Bx%5E3%7D%7Ba%5E3%7D%20%3D%5Cfrac%7Bp%2Bq%7D%7B2%7D%20%5C%5Csubstitute~in~first%5C%5C%5Cfrac%7Bp%2Bq%7D%7B2%7D%20%2B%5Cfrac%7B2%7D%7Bp%2Bq%7D%20%3Dp%5C%5C%5Cfrac%7B%28p%2Bq%29%5E2%2B4%7D%7B2%28p%2Bq%29%7D%20%3Dp%5C%5C%28p%2Bq%29%5E2%2B4%3D2p%28p%2Bq%29%5C%5Cp%5E2%2Bq%5E2%2B2pq%2B4-2p%5E2-2pq%3D0%5C%5Cq%5E2-p%5E2%2B4%3D0%5C%5Cq%5E2%3Dp%5E2-4)
Answer:
7 and 13
Step-by-step explanation:
x+y=20
x-y=6
2x=26, x=13, 13+7=20, 13-7=6.
<span>we are asked to determine the integral tan^(-1)(8 x) dx. we use the inverse property of trigonometric equation in integral calculus such that the answer is </span><span>integral tan^(-1)(8 x) dx. = </span>x tan^(-1)(8 x)-1/16 log(64 x^2+1)+ C where C is a constant.
Answer:
125 times larger
Step-by-step explanation:
Let's say the radius is 3, just as an example.
The formula of a sphere is V=4/3 pi r^3
Then we can just substitute and test it out.
V=4/3 pi (3)^3
V=4/3 pi (27)
V=36 pi
Then multiple the previous radius by 5 to test it out.
V=4/3 pi (15)^3
V=4/3 pi (3375)
V=4500 pi
Then divide the bigger one by the smaller one
You will get 125, therefore it is 125 times larger
hope this helps :D