I can't see the next photo but I'm assuming that's what you're asking
Answer:
1. x = 67.5
2. x = 2.5
3. x = 35.2
4. x = 2.0
5. x = 17.0
Step-by-step explanation:
Question 1
The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:
2x/9 = 15
2x = 9(15)
Next solve for x:
2x = 135
x = 67.5
Question 2
The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:
20x/8.7 = 5.8
20x = 8.7(5.8)
Next, solve for x:
20x = 50.46
x = 2.523
Round to the nearest tenth:
x = 2.5
Question 3
The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:
5x/16 = 11
5x = 11(16)
Next, solve for x:
5x = 176
x = 35.2
Question 4
The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:
0.5x/0.06 = 17
0.5x = 17(0.06)
Next, solve for x:
0.5x = 1.02
x = 2.04
Round to the nearest tenth:
x = 2.0
Question 5
The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:
29(44)/x = 75
29(44) = 75x
Next, solve for x:
1276 = 75x
x = 17.0133
Round to the nearest tenth:
x = 17.0
Answer:
radius x = 3 ft
height h = 23,8 ft
Step-by-step explanation:
From problem statement
V(t) = V(cylinder) + V(hemisphere)
let x be radius of base of cylinder (at the same time radius of the hemisphere)
and h the height of the cylinder, then:
V(c) = π*x²*h area of cylinder = area of base + lateral area
A(c) = π*x² + 2*π*x*h
V(h) = (2/3)*π*x³ area of hemisphere A(h) = (2/3)*π*x²
A(t) = π*x² + 2*π*x*h + (2/3)*π*x²
Now A as fuction of x
total volume 505 = π*x²*h + (2/3)*π*x³
h = [505 - (2/3)* π*x³ ] /2* π*x
Now we have the expression for A as function of x
A(x) = 3π*x² + 2π*x*h A(x) = 3π*x² + 505 - (2/3)π*x³
Taking derivatives both sides
A´(x) = 6πx - 2πx² A´(x) = 0 6x - 2x² = 0
x₁ = 0 we dismiss
6 - 2x = 0
x = 3 and h = [505 - (2/3)* π*x³]/2* π*x
h = (505 - 18.84) / 6.28*3
h = 23,8 ft
