Answer:
D
Step-by-step explanation:
She only cut the 15% extra and no the other 75%
Answer:
1/16
Step-by-step explanation:
The answer to the question
Answer:
; ![y^7](https://tex.z-dn.net/?f=y%5E7)
Step-by-step explanation:
![(w^4)^5=\\w^{4*5}=\\w^{20}\\\\\frac{y^9}{y^2}=\\ y^{9-2}=\\y^7](https://tex.z-dn.net/?f=%28w%5E4%29%5E5%3D%5C%5Cw%5E%7B4%2A5%7D%3D%5C%5Cw%5E%7B20%7D%5C%5C%5C%5C%5Cfrac%7By%5E9%7D%7By%5E2%7D%3D%5C%5C%20y%5E%7B9-2%7D%3D%5C%5Cy%5E7)
Answer:
The rate increases at 398mi/h
Step-by-step explanation:
Given
--- rate when
--- distance
<em>The given parameters is represented with the attached figure</em>
Using Pythagoras theorem [take the attached image as a point of reference]
![y^2 = x^2 + 1^2](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%5E2%20%2B%201%5E2)
![y^2 = x^2 + 1](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%5E2%20%2B%201)
Differentiate with respect to time (t):
![2y \frac{dy}{dt} = 2x \frac{dx}{dt}](https://tex.z-dn.net/?f=2y%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%202x%20%5Cfrac%7Bdx%7D%7Bdt%7D)
Divide both sides by 2
--- (1)
When y = 2:
--- Pythagoras Theorem
![2^2 = x^2 + 1](https://tex.z-dn.net/?f=2%5E2%20%3D%20x%5E2%20%2B%201)
![4 = x^2 + 1](https://tex.z-dn.net/?f=4%20%3D%20x%5E2%20%2B%201)
Collect like terms
![x^2 = 4 -1](https://tex.z-dn.net/?f=x%5E2%20%3D%204%20-1)
![x^2 = 3](https://tex.z-dn.net/?f=x%5E2%20%3D%203)
Solve for x
![x = \sqrt 3](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%203)
So:
![y \frac{dy}{dt} = x \frac{dx}{dt}](https://tex.z-dn.net/?f=y%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20x%20%5Cfrac%7Bdx%7D%7Bdt%7D)
Substitute:
,
and
![2 * \frac{dy}{dt} = \sqrt 3 * 460](https://tex.z-dn.net/?f=2%20%2A%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Csqrt%203%20%2A%20460)
![2 * \frac{dy}{dt} = 460\sqrt 3](https://tex.z-dn.net/?f=2%20%2A%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20460%5Csqrt%203)
Divide by 2
![\frac{dy}{dt} = 230\sqrt 3](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20230%5Csqrt%203)
![\frac{dy}{dt} = 230*1.7321](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20230%2A1.7321)
![\frac{dy}{dt} = 398.383](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20398.383)