It looks like the given equation says
![xy^8 + e^{y/5} = e](https://tex.z-dn.net/?f=xy%5E8%20%2B%20e%5E%7By%2F5%7D%20%3D%20e)
When <em>x</em> = 0, you have
![0\cdot y^8 + e^{y/5} = e \\\\ e^{y/5} = e^1 \\\\ \dfrac y5 = 1 \\\\ y=5](https://tex.z-dn.net/?f=0%5Ccdot%20y%5E8%20%2B%20e%5E%7By%2F5%7D%20%3D%20e%20%5C%5C%5C%5C%20e%5E%7By%2F5%7D%20%3D%20e%5E1%20%5C%5C%5C%5C%20%5Cdfrac%20y5%20%3D%201%20%5C%5C%5C%5C%20y%3D5)
Differentiating both sides with respect to <em>x</em> gives
![\left(xy^8 + e^{y/5}\right)' = e' \\\\ \left(xy^8\right)' + \left(e^{y/5}\right)' = 0 \\\\ x\left(y^8\right)' + x'y^8 + e^{y/5}\left(\dfrac y5\right)' = 0 \\\\ 8xy^7y' + y^8 + \dfrac15e^{y/5}y' = 0](https://tex.z-dn.net/?f=%5Cleft%28xy%5E8%20%2B%20e%5E%7By%2F5%7D%5Cright%29%27%20%3D%20e%27%20%5C%5C%5C%5C%20%5Cleft%28xy%5E8%5Cright%29%27%20%2B%20%5Cleft%28e%5E%7By%2F5%7D%5Cright%29%27%20%3D%200%20%5C%5C%5C%5C%20x%5Cleft%28y%5E8%5Cright%29%27%20%2B%20x%27y%5E8%20%2B%20e%5E%7By%2F5%7D%5Cleft%28%5Cdfrac%20y5%5Cright%29%27%20%3D%200%20%5C%5C%5C%5C%208xy%5E7y%27%20%2B%20y%5E8%20%2B%20%5Cdfrac15e%5E%7By%2F5%7Dy%27%20%3D%200)
That is, the derivative operator distributes over sums, and the derivative of a constant is 0; apply the product rule on the first term and chain rule on the second; then use chain rule one more time.
Now plug in <em>x</em> = 0 and <em>y</em> = 5, and solve for <em>y'</em> :
![8\cdot0\cdot5^7y' + 5^8 + \dfrac15e^{5/5}y' = 0 \\\\ 5^8 + \dfrac15e y' = 0 \\\\ \dfrac15e y' = -5^8 \\\\ y' = \boxed{-\dfrac{5^9}e}](https://tex.z-dn.net/?f=8%5Ccdot0%5Ccdot5%5E7y%27%20%2B%205%5E8%20%2B%20%5Cdfrac15e%5E%7B5%2F5%7Dy%27%20%3D%200%20%5C%5C%5C%5C%205%5E8%20%2B%20%5Cdfrac15e%20y%27%20%3D%200%20%5C%5C%5C%5C%20%5Cdfrac15e%20y%27%20%3D%20-5%5E8%20%5C%5C%5C%5C%20y%27%20%3D%20%5Cboxed%7B-%5Cdfrac%7B5%5E9%7De%7D)
Answer:
A. 12/13
Step-by-step explanation:
Remember SOH, CAH, TOA.
In this situation, the function is sine so sine= opposite/hypotenuse.
The side opposite of K is 12.
The hypotenuse is the longest side so it will be 13.
Therefore, sineK= 12/13(a)
Answer:
4
Step-by-step explanation:
Simplifying
17 = 5k + -3
Reorder the terms:
17 = -3 + 5k
Solving
17 = -3 + 5k
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-5k' to each side of the equation.
17 + -5k = -3 + 5k + -5k
Combine like terms: 5k + -5k = 0
17 + -5k = -3 + 0
17 + -5k = -3
Add '-17' to each side of the equation.
17 + -17 + -5k = -3 + -17
Combine like terms: 17 + -17 = 0
0 + -5k = -3 + -17
-5k = -3 + -17
Combine like terms: -3 + -17 = -20
-5k = -20
Divide each side by '-5'.
k = 4
Simplifying
k = 4
Answer:yes
Step-by-step explanation:
5 shirts = $60
If all of the shirts are the same price, then you divide 60/5.
60/5=12
One shirt is $12.