Answer:
14449 inches^3
Step-by-step explanation:
length+girth=116 inches
w + 4x= 116
volume=x^2*w
w=116-4x
V=x^2* (116-4x)
for max value, dv/dx=0
dv/dx= 232x-12x^2
232x-12x^2=0
x=19.3333
w=116-4(19.33)
=38.67
V=19.33^2*38.67=14449 inches^3
The missing exponent of 1/169=(1/13)
Answer:
D
Step-by-step explanation:
Any ellipse has the following equ
ation:
![\frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B%20%7Ba%7D%5E%7B2%7D%20%7D%20%20%2B%20%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%7D%7B%20%7Bb%7D%5E%7B2%7D%20%7D%20%20%3D%201)
where
- 2b = vertical axis length
- 2a = horizontal axis length
(as in the picture)
So it should be like:
![\frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B%20%7B%20%28%5Cfrac%7B6%7D%7B2%7D%20%29%7D%5E%7B2%7D%20%7D%20%20%2B%20%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%7D%7B%20%7B%28%20%5Cfrac%7B4%7D%7B2%7D%20%29%7D%5E%7B2%7D%20%7D%20%20%3D%201%20%5C%5C%20%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B%209%7D%20%20%2B%20%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%7D%7B%204%20%7D%20%20%3D%201)
Since it should be moved to the right and up, the answer would be:
![\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%20%7B%28x%20-%205%29%7D%5E%7B2%7D%20%7D%7B%209%7D%20%20%2B%20%20%5Cfrac%7B%20%7B%28y%20-%201%29%7D%5E%7B2%7D%20%7D%7B%204%20%7D%20%20%3D%201)
Answer:
36 degrees
Step-by-step explanation:
There's 180 degrees in a triangle.
Since they're supplementary angles, we do 180-142=38.
We now know that 106+38+x=180.
Solve for x: x=36
Answer:
The graph should be stretched rather than become narrower.
Step-by-step explanation:
To figure this out, just create some example points.
At x = 0, your y-value will always be 0. But if you were to plug in the value 1, you would get a y-value of 1 in y=x^2, but a value of 0.5 in y=0.5x^2. If you were to plug in a value of 2, you would get a value of 4 in y=x^2, but a value of 2 in y=0.5x^2.
If you continue this pattern for a few more points, then plot them, you will see that adding a coefficient of 0.5 simply stretches the graph