Answer: 7/24
Step-by-step explanation:
The polynomial is a third degree polynomial with x and y terms so when written in standard form x comes before y and the x^3 is going to be the first term. The first term of this polynomial is 8x^3, aka the second answer choice.
I'm afraid it's not 11 (unless you can round the result up, but there is no mention about it).
8 + 13 + 11 + 9 + 13 = 54
54 / 5 = 10,8
Firstly you sum all the numbers and then you divide the result by the amount of the summed up numbers.
The price increase was $12.
60
x 0.2
---------
12
Hope this helped!
∫(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>.
