Answer: He will have enough paint to put one coat of paint on all of the tables.
Answer:
h² = p² + b²
Step-by-step explanation:
324 = 289 + x²
x² = 35
x = 6 is your nearest ten answer
Answer:
60
Step-by-step explanation:
half of 120 is 60
<span>y=−13x+4
when x = ?, y = ?,
x = -2, y = 30
x = -1, y = 17
x = 0, y = 4
x = 1, y = - 9
x = 2, y = -22
x = 3, y = -35
these are a couple, connect the dots, and graph
hope this helps</span>
Answer:
(a) V = ∫₂⁵ π ((ln(x))² + 14 ln(x)) dx
(b) V = ∫₂⁵ 2π (x − 1) ln(x) dx
Step-by-step explanation:
We know the region is the area 0 ≤ y ≤ ln(x) from x=2 to x=5.
(a) Revolve around the line y=-7, and we get a hollow cylinder on its side. Slice vertically into thin washers. The thickness of each washer is dx. The inside radius is r = 0 − (-7) = 7. The outside radius is R = ln(x) − (-7) = ln(x) + 7. The volume of each washer is:
dV = π (R² − r²) t
dV = π ((ln(x) + 7)² − 7²) dx
dV = π ((ln(x))² + 14ln(x) + 49 − 49) dx
dV = π ((ln(x))² + 14 ln(x)) dx
The total volume is the sum of all the washers from x=2 to x=5:
V = ∫ dV
V = ∫₂⁵ π ((ln(x))² + 14 ln(x)) dx
(b) Rotate about x = 1, and we get a hollow cylinder standing upright. Slice into cylindrical shells. The thickness of each shell is dx. The radius of each shell is r = x − 1. The height of each shell is ln(x). The volume of each shell is:
dV = 2π r h t
dV = 2π (x − 1) ln(x) dx
The total volume is the sum of all the shells from x=2 to x=5.
V = ∫ dV
V = ∫₂⁵ 2π (x − 1) ln(x) dx