An angle next to another interior angle
Answer:
x = 2.36603 or 0.633975
Step-by-step explanation:
Here we want to solve the quadratic equation using the completing the square method.
2x^2-6x + 3 = 0
divide through by 2 first;
x^2 -3x + 3/2 = 0
x*2 -3x = -3/2
Half the x term will be -3/2 and squaring it is 9/4
we add this to both sides
x^2-3x/2 + 9/4 = -3/2 + 9/4
(x-3/2)^2 = 3/4
Finding square root of both sides
x-3/2 = √(3/4)
x = 3/2 ± √(3/4)
x = 3/2 + √(3/4) or x = 3/2-√(3/4)
which becomes
x = 2.36603 or 0.633975
Answer:
26
Step-by-step explanation:
Answer: 350 adult tickets
Step-by-step explanation:
(omg I remember this question!)
- a stands for the number of adult tickets sold
student tickets : a + 65
<em>the equation for the prob: </em>
765 = a + (a + 65)
<em>solve:</em>
combine 'like terms'
1.) 765 = a + a + 65
2.) 765 = 2a + 65
<u>- 65 - 65 </u>
700= 2a
divide by 2
700/2 = 2a/2
<em>(700/2 = 350) </em>
<em>(the "2" in 2a is cancelled out by the other 2)</em>
<u>350 = a </u>
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
