Answer:
X = 1/4k
Step-by-step explanation:
24kx = 6
kx = 6/24
kx = 1/4
x = 1/4/k
x = 1/4k
Answer:
Step-by-step explanation:
Just divide the larger mass by the smaller.
0.5 / 0.005 = 0.5 / 0.5 * 10^-2 = 1 * 10^2 = 100
It take 100 ants to equal the mass of a grasshopper.
Answer with Step-by-step explanation:
Let x and y are two numbers
According to question
....(1)
Suppose x is larger than y
![x^2=x(4y+8x)](https://tex.z-dn.net/?f=x%5E2%3Dx%284y%2B8x%29)
![x=4y+8x](https://tex.z-dn.net/?f=x%3D4y%2B8x)
![x-8x=4y](https://tex.z-dn.net/?f=x-8x%3D4y)
![-7x=4y](https://tex.z-dn.net/?f=-7x%3D4y)
![y=-\frac{7}{4}x](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B4%7Dx)
Substitute the value of y
![x^2+(-\frac{7}{4}x)^2=100](https://tex.z-dn.net/?f=x%5E2%2B%28-%5Cfrac%7B7%7D%7B4%7Dx%29%5E2%3D100)
![x^2+\frac{49}{16}x^2=100](https://tex.z-dn.net/?f=x%5E2%2B%5Cfrac%7B49%7D%7B16%7Dx%5E2%3D100)
![\frac{16x^2+49x^2}{16}=100](https://tex.z-dn.net/?f=%5Cfrac%7B16x%5E2%2B49x%5E2%7D%7B16%7D%3D100)
![\frac{65}{16}x^2=100](https://tex.z-dn.net/?f=%5Cfrac%7B65%7D%7B16%7Dx%5E2%3D100)
![x^2=\frac{16\times 100}{65}](https://tex.z-dn.net/?f=x%5E2%3D%5Cfrac%7B16%5Ctimes%20100%7D%7B65%7D)
![x=\sqrt{\frac{1600}{65}}=\frac{40}{\sqrt{65}}=\frac{40}{65}\sqrt{65}=\frac{8}{13}\sqrt{65}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B%5Cfrac%7B1600%7D%7B65%7D%7D%3D%5Cfrac%7B40%7D%7B%5Csqrt%7B65%7D%7D%3D%5Cfrac%7B40%7D%7B65%7D%5Csqrt%7B65%7D%3D%5Cfrac%7B8%7D%7B13%7D%5Csqrt%7B65%7D)
![y=-\frac{7}{4}\times \frac{8}{13}\sqrt{65}=-\frac{14}{13}\sqrt{65}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B4%7D%5Ctimes%20%5Cfrac%7B8%7D%7B13%7D%5Csqrt%7B65%7D%3D-%5Cfrac%7B14%7D%7B13%7D%5Csqrt%7B65%7D)
Answer:
m = 9, n = 2
Step-by-step explanation:
Find
(x) by letting y = f(x) and rearranging making x the subject, that is
y = mx + n ( subtract n from both sides )
y - n = mx ( divide both sides by m )
= x
Change y back into terms of x with x =
(x) , then
(x) = ![\frac{x-n}{m}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-n%7D%7Bm%7D)
Given
(x) = g(x) , then
= ![\frac{x-2}{9}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-2%7D%7B9%7D)
By comparison of the 2 sides
m = 9 and n = 2
12.57 * 4.11 = 51.6627...rounds to 51.66