Answer:
Angle BPQ = 64°
Step-by-step explanation:
4x + 12 +2x = 90
6x + 12 = 90
- 12 -12
6x = 78
x = 13°
BPQ = ((4(13) + 12)°
(52 + 12)°
64°
A
Volume of the Cylinder
Givens
H = 60 yards.
Diameter = 20 yards
pi = 3.14
Formula
V = pi * r^2 * h
Calculations
r = d/2
r = 32/2
r = 16
V = 3.14 * 16^2 * 60
V = 48230 cubic yards [Cylinder's Volume]
Cone
<em>Formula</em>
V = 1/3 pi r^2 H
<em>Givens</em>
pi = 3.14
r = 16 yards
h = 20 yards
<em>Sub and solve</em>
V = 1/3 3.14 * 16^2 * 20
V = 5359 cubic yards.
<em>Total Volume of the structure</em>
48230 + 5359 = 53589 Cubic Yards
<em>Water Content</em>
The answer to this part requires a proportion.
1 Cubic yard will hold 201.97 gallons.
53589 yd^3 = x
1/201.97 = 53589 /x [ You should get a pretty big answer]
x = 201.87 * 53589
x = 10 819 092 gallons can be held by the tank.
10 819 092 gallons <<<< answer
B
If the height of both the cylinder and the cone remain the same. If the radius doubles in both the cylinder and the cone then the tank will hold 4 times as much.
Total volume before doubling the radius = pi * r^2 h + 1/3 pi r^2 h
New Total Volume = pi * (2*r)^2 h + 1/3 pi * (2r)^2 h
New Total volume = pi * 4r^2 h + 1/3 pi *4 r^2 h
New Total Volume = 4 [pi r^2 h + 1/3 pi r^2 h]
but pi r^2 h + 1/3 pi r^2 h is the total volume before doubling the radius
New volume = 4 original volume. <<<<< answer to part B
Answer:
A triangle
Step-by-step explanation: The two squares lean against each other
Answer:
x=11, y=8/3
Step-by-step explanation:
Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then
LM=NO
and
LO=MN
Thus,
![\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D4x%2B4%3D5x-7%5C%5C%20%5C%5Cx-7%3D3y-4%5Cend%7Barray%7D%5Cright.)
Solve this system of two equations. From the first equation:
![4x-5x=-7-4\\ \\-x=-11\\ \\x=11](https://tex.z-dn.net/?f=4x-5x%3D-7-4%5C%5C%20%5C%5C-x%3D-11%5C%5C%20%5C%5Cx%3D11)
Substitute it into the second equation:
![11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}](https://tex.z-dn.net/?f=11-7%3D3y-4%5C%5C%20%5C%5C3y-4%3D4%5C%5C%20%5C%5C3y%3D4%2B4%5C%5C%20%5C%5C3y%3D8%5C%5C%20%5C%5Cy%3D%5Cdfrac%7B8%7D%7B3%7D)