Sixty eight and nine plus eleven equals 12
P=2
3p-1=5p-5-14+4p
3p-1=9p-19
-1=6p-19
18=6p
p=2
Answer:
The equation of circle A with radius AC is , or in other words option d.
Step-by-step explanation:
If the radius of this circle is AC, then we can determine the distance between points A ( - 1, 4 ) and C ( - 5,1 ) to come to the length of the radius -
Distance between A and C =
=
= = = 5 units - Which is also the length of the radius of the circle.
So if the radius is given to be 5 in length, knowing that the general equation for a circle is ( where ( h, k ) is the center and r is the radius ) if the radius is 5, , and solution must be option b / option d.
Now if the radius is AC, the center point must be point A ( circle A ). Therefore point ( - 1, 4 ) is the center, and the equation of the circle must be the following -
= - and hence our solution is option d
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
Answer:
Step-by-step explanation:
<u>Volume formula will be:</u>
where V - volume, k - coefficient of proportion, r² - squared radius, h - height
<u>Substitute the known values to find the unknown:</u>
- 62.8 = k*4*5
- 62.8 = 20k
- k = 62.8/20
- k = 3.14
<u>Now find the volume of the taller can:</u>
- V = kr²h
- V = 3.14*4*9 = 113.04 ≈ 113 in³
Correct option is A