Answer:
4x + y = 13
Step-by-step explanation:
1. Change 4x + y -2=0 into slope intercept form to find the slope:
y = -4x +2 The slope is -4
2. Plug in x, y and m into y = mx + b
-3 = -4 (4) + b
-3 = -16 + b
13 + b
3. Plug m and b into equation y = mx + b
y = -4x + 13
4. Change equation into standard form:
4x - y = 13
The first one! Also I love the name.
Answer:
The height of the water is ![60.5\ ft](https://tex.z-dn.net/?f=60.5%5C%20ft)
Step-by-step explanation:
step 1
Find the volume of the tank
The volume of the inverted right circular cone is equal to
![V=\frac{1}{3}\pi r^{2} h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7D%20h)
we have
![r=16\ ft](https://tex.z-dn.net/?f=r%3D16%5C%20ft)
![h=96\ ft](https://tex.z-dn.net/?f=h%3D96%5C%20ft)
substitute
![V=\frac{1}{3}\pi (16)^{2} (96)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%2816%29%5E%7B2%7D%20%2896%29)
![V=8,192\pi\ ft^{3}](https://tex.z-dn.net/?f=V%3D8%2C192%5Cpi%5C%20ft%5E%7B3%7D)
step 2
Find the 25% of the tank’s capacity
![V=(0.25)*8,192\pi=2,048\pi\ ft^{3}](https://tex.z-dn.net/?f=V%3D%280.25%29%2A8%2C192%5Cpi%3D2%2C048%5Cpi%5C%20ft%5E%7B3%7D)
step 3
Find the height, of the water in the tank
Let
h ----> the height of the water
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
![\frac{R}{H}=\frac{r}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BR%7D%7BH%7D%3D%5Cfrac%7Br%7D%7Bh%7D)
substitute
![\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B96%7D%3D%5Cfrac%7Br%7D%7Bh%7D%5C%5C%20%5C%5Cr%3D%20%5Cfrac%7Bh%7D%7B6%7D)
where
r is the radius of the smaller cone of the figure
h is the height of the smaller cone of the figure
R is the radius of the circular base of tank
H is the height of the tank
we have
-----> volume of the smaller cone
substitute
![2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h](https://tex.z-dn.net/?f=2%2C048%5Cpi%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7Bh%7D%7B6%7D%29%5E%7B2%7Dh)
Simplify
![221,184=h^{3}](https://tex.z-dn.net/?f=221%2C184%3Dh%5E%7B3%7D)
![h=60.5\ ft](https://tex.z-dn.net/?f=h%3D60.5%5C%20ft)
Answer:
slopes is the ratio of the change in the y value over the change in the x value
Answer:
x = 7
Step-by-step explanation:
4x−12=16
Step 1: Add 12 to both sides.
4x−12+12=16+12
4x=28
Step 2: Divide both sides by 4.
4x/4 = 28/4 = 7
x=7