∫(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: What percentage to save for retirement?
Saving 15% of income per year (including any employer contributions) is an appropriate savings level for many people. Having one to one-and-a-half times your income saved for retirement by age 35 is an attainable target for someone who starts saving at age 25.
Step-by-step explanation: That's the answer I got it right! lol!
Exponential equation is
y=a(b)ˣ
when b>1, it is growth
when 0>b>1, it is decay
so
we want the 2nd number to be more than 1
that would be the 3rd one, y=3(8)ˣ
4500 is the answer to this question.
Answer:
The man traveled 20km by train.
Step-by-step explanation:
If x is the distance he traveled by train, you can write this equation to represent the situation:
Then, you can simply solve for x:
The man traveled 20km by train.
