Answer:
200π
Step-by-step explanation:
Graph: desmos.com/calculator/pwa9vqzmpy
The region is inside a horizontal parabola y = (5x)^½, starting at its vertex at x=0 and ending at x=5. Cut a thin vertical slice with thickness dx and position x.
Revolving this thin slice about the y-axis, we get a cylindrical shell with radius x, thickness dx, and height 2y. The volume of the shell is:
dV = 2π (x) (2y) (dx)
dV = 4π xy dx
dV = 4π x (5x)^½ dx
dV = 4π√5 (x^³/₂) dx
The total volume is the sum of all the shell volumes from x=0 to x=5.
V = ∫₀⁵ dV
V = ∫₀⁵ 4π√5 (x^³/₂) dx
Evaluating the integral:
V = 4π√5 ∫₀⁵ (x^³/₂) dx
V = 4π√5 (⅖ x^⁵/₂) |₀⁵
V = 4π√5 [(⅖ 5^⁵/₂) − (⅖ 0^⁵/₂)]
V = 200π
The volume of the solid is 200π cubic units.
They will have the same slope.
D. √5 <span>
Let's first simplify the equation
sqrt(75)/sqrt(15)
Factor it
(sqrt(3)sqrt(5)sqrt(5)) / (sqrt(3)sqrt(5))
Now cancel the sqrt(3) and sqrt(5) on both top and bottom, giving
sqrt(5) / 1
sqrt(5)
So we're just left with the square root of 5. Checking the available options, you see that D. </span><span>√5 </span> is an exact match. So that's your answer.
Answer: 10 cups of flour
Step-by-step explanation:
15 1/2 cups of flour = 7 1/2 cups
7 1/2 ÷ 3 = 2 1/2
So, it takes 2 1/2 cups of flour to make one loaf of bread
If you want to make 4 loaves of bread, you multiply 2 1/2 × 4
2 1/2 × 4 = 10
It will take 10 cups of flour to make 4 loaves of bread.
Refer to attachment for your answer