It’s D, when lines are perpendicular, the slopes of the lines are opposite reciprocals.
It is quite simple actually since it is simple division with the negative rules.
Just simplify the problem and use the negatives to determine if it is positive or negative. (two negatives equal a positive and one negative equals a negative)
∫(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>.
A + R + J = 1925
A = 1/2R
J = 2R
1/2R + R + 2R = 1925
7/2R = 1925
R = 550
J = 2(550)
J = 1100
Joel collects 1100 cans.
Answer: if it's 18 times 29 then it's 522. If it's 18 to the power of 29 it's 2.52873108 times 10^36 (decimal form)
Step-by-step explanation:
