By definition of the derivative,
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{(s + h)^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cleft%28%5Cfrac%7B%28s%20%2B%20h%29%5E3%7D2%20%2B%201%5Cright%29%20-%20%5Cleft%28%5Cfrac%7Bs%5E3%7D2%20%2B%201%5Cright%29%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{s^3+3s^2h+3sh^2+h^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cleft%28%5Cfrac%7Bs%5E3%2B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D2%20%2B%201%5Cright%29%20-%20%5Cleft%28%5Cfrac%7Bs%5E3%7D2%20%2B%201%5Cright%29%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\frac{3s^2h+3sh^2+h^3}2}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cfrac%7B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D2%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 \frac{3s^2h+3sh^2+h^3}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac12%20%5Cfrac%7B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 (3s^2+3sh+h^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac12%20%283s%5E2%2B3sh%2Bh%5E2%29)
![\displaystyle\frac{dr}{ds} = \frac{3s^2}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Cfrac%7B3s%5E2%7D2)
Answer:
1. .43 m/s or 26.08 meters per min
5. The total displacement is 0
Step-by-step explanation:
Given:
<span>Face value $4,530,
discount rate 7.2%,
time 125 days
Discount on Simple Discount note:
Discount = Maturity Value * discount rate * term
Discount = 4,530 * 0.072 * 125/360
Discount = 113.25
Proceeds for the simple discount note
Proceeds = Maturity Value - Discount
Proceeds = 4,530 - 113.25
Proceeds = 4,416.75
The proceeds for the simple discount note is $4,416.75</span>
Answer:
3.25 cups
Step-by-step explanation:
To keep the proportions the same line up cups with cups and pancakes with pancakes
1 cup of milk for 8 pancakes
x cups of milk for 26 pancakes
x*8 = 1*26, cross multiply and solve for x
x = 26/8, divide both sides by 8
x = 3.25 cups of milk OR 3 cups and 1/4 of another cup
Answer: 1/3
Step-by-step explanation:
the card is not being replaced, so it is a dependent event.
Event A: picking an odd number
There are 4 cards total, and 2 odd numbered cards.
P(A) = 2/4 = 1/2
Event B: picking an even number.
There are now three cards total, because the card from Event A was not replaced. There are two even numbered cards.
P(B) = 2/3
P(A+B) = P(A) x P(B)
P(A+B) = 1/2 x 2/3 = 2/6 = 1/3