Answer:
30
Step-by-step explanation:
if its asking for inches
∫(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:
x = 8
Step-by-step explanation:
Step 1: Write an equation
2x - 9 = 7
Step 2: Use the Addition Property of Equality
2x = 16
Step 3: Use the Division Property of Equality
x = 8
Answer:
1500 pot holders
Step-by-step explanation:
32×48=1536 so it's about 1500 pot holders because 1536 it's closet to 1500
The total ratio is 5
The number of comedy movies watched is 12
The number of other movies watched is 18
<h3>What is a ratio?</h3>
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. Therefore,
He has watched 2 comedy movies for every 3 other movies. The total movies he has watched is 30. Therefore,
Ratio of comedy to total movies is as follows:
number of comedy movies watched = 2 / 5 × 30 = 60 / 5 = 12
number of other movies watched = 3 / 5 × 30 = 90 / 5 = 18
Therefore,
total ratio = 5
number of comedy movies watched = 12
number of other movies watched = 18
learn more on ratios here: brainly.com/question/10080852
