The answer to the questions
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
----
For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
Answer: 703.3125 in cubed
Step-by-step explanation:
The formula to find the volume of something is to…
1. Find the area of the base! Remember, area is length x width. In this case we would have 15.5 x 8.25 = 127.875
2. Multiply the base area we just found by the height! In this case, we take 127.875 x 5.5 and this gives us 703.3125 as our final answer!
Answer:
angle of depression ≈ 53.8°
Step-by-step explanation:
the angle of depression is the measure of the angle from the horizontal downwards from the top of the flag pole.
this angle is alternate to ∠ A and is congruent to ∠ A
using the sine ratio in the right triangle
sin A = 
= 
, then
∠ A = 
( ) ≈ 53.8° ( to 1 d.p )
Angle of depression ≈ 53.8°
Answer:
- 56
Step-by-step explanation:
The opposite of a number is its negative value
Then the opposite of 56 is - 56
