∫(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:
The vector joining the ship to the rock is t= 7 i + 5 j
The direction is 0.9505 radians east of north.
Step-by-step explanation:
The position vector of the ship:
r= 1 i + 0 j
The position vector of the ship:
s= 6 i + 5 j
The vector joining the ship to the rock is:
t = r + s
t = (1 i + 0 j) + (6 i + 5 j)
t = 7 i + 5 j
The bearing of the rock to the ship is:
Θ=
= 0.9505 radians
Answer:
1,3,5
Step-by-step explanation:
81 is a perfect square so it can be written as an integer
11.8 is rational because it can be written as a fraction (107/9)
sqrt(6) isn't a perfect square so it is irrational
3/7 is a fraction so it is rational
8.57 is a terminating decimal so it is rational
Answer: 64% of the variability in weight can be explained by the relationship with height.
Step-by-step explanation:
- In statistics, Correlation coefficient is denoted by 'r' is a measure of the strength of the relationship between two variables.
- Coefficient of determination,
, is a measure of variability in one variable can be explained variation in the other.
Here, r= 0.80

That means 64% of the variability in weight can be explained by the relationship with height.
Answer:
Step-by-step explanation:
7.5