It’s A and B hope this helps :)
How do bonds generate income for investors?
Answer- <span>Bonds pay a specified amount at maturity.</span>
$12.50 is the correct answer
Step 1 he had to multiply the $22.75 times 3 weeks it should have been
($22.75 x 3) + $32.75 - $14.25
$68.25 + 32.75 - $14.25
$86.75
Let r = (t,t^2,t^3)
Then r' = (1, 2t, 3t^2)
General Line integral is:
![\int_a^b f(r) |r'| dt](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20f%28r%29%20%7Cr%27%7C%20dt)
The limits are 0 to 1
f(r) = 2x + 9z = 2t +9t^3
|r'| is magnitude of derivative vector
![\sqrt{(x')^2 + (y')^2 + (z')^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x%27%29%5E2%20%2B%20%28y%27%29%5E2%20%2B%20%28z%27%29%5E2%7D)
![\int_0^1 (2t+9t^3) \sqrt{1+4t^2 +9t^4} dt](https://tex.z-dn.net/?f=%5Cint_0%5E1%20%282t%2B9t%5E3%29%20%5Csqrt%7B1%2B4t%5E2%20%2B9t%5E4%7D%20dt%20)
Fortunately, this simplifies nicely with a 'u' substitution.
Let u = 1+4t^2 +9t^4
du = 8t + 36t^3 dt
![\int_0^1 \frac{2t+9t^3}{8t+36t^3} \sqrt{u} du \\ \\ \int_0^1 \frac{2t+9t^3}{4(2t+9t^3)} \sqrt{u} du \\ \\ \frac{1}{4} \int_0^1 \sqrt{u} du](https://tex.z-dn.net/?f=%5Cint_0%5E1%20%5Cfrac%7B2t%2B9t%5E3%7D%7B8t%2B36t%5E3%7D%20%5Csqrt%7Bu%7D%20%20du%20%5C%5C%20%20%5C%5C%20%5Cint_0%5E1%20%5Cfrac%7B2t%2B9t%5E3%7D%7B4%282t%2B9t%5E3%29%7D%20%5Csqrt%7Bu%7D%20%20du%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B1%7D%7B4%7D%20%5Cint_0%5E1%20%5Csqrt%7Bu%7D%20%20du)
After integrating using power rule, replace 'u' with function for 't' and evaluate limits: