I believe the answer is 13 ways to make 27 cents using Quarters, dimes, nickels, and pennies.
Step-by-step explanation:
Answer:
1) ![y =4x^2 +7](https://tex.z-dn.net/?f=%20y%20%3D4x%5E2%20%2B7)
2) ![y =7s^2 -3s^4 +181](https://tex.z-dn.net/?f=%20y%20%3D7s%5E2%20-3s%5E4%20%2B181)
Step-by-step explanation:
Assuming that our function is
for the first case and
for the second case.
Part 1
We can rewrite the expression like this:
![\frac{dy}{dx} =8x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D8x)
And we can reorder the terms like this:
![dy = 8 x dx](https://tex.z-dn.net/?f=%20dy%20%3D%208%20x%20dx)
Now if we apply integral in both sides we got:
![\int dy = 8 \int x dx](https://tex.z-dn.net/?f=%20%5Cint%20dy%20%3D%208%20%5Cint%20x%20dx)
And after do the integrals we got:
![y = 4x^2 +c](https://tex.z-dn.net/?f=%20y%20%3D%204x%5E2%20%2Bc)
Now we can use the initial condition ![y(0) =7](https://tex.z-dn.net/?f=%20y%280%29%20%3D7)
![7 = 4(0)^2 +c, c=7](https://tex.z-dn.net/?f=%207%20%3D%204%280%29%5E2%20%2Bc%2C%20c%3D7)
And the final solution would be:
![y =4x^2 +7](https://tex.z-dn.net/?f=%20y%20%3D4x%5E2%20%2B7)
Part 2
We can rewrite the expression like this:
![\frac{dy}{ds} =14s -12s^3](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bds%7D%20%3D14s%20-12s%5E3)
And we can reorder the terms like this:
![dy = 14s -12s^3 dx](https://tex.z-dn.net/?f=%20dy%20%3D%2014s%20-12s%5E3%20dx)
Now if we apply integral in both sides we got:
![\int dy = \int 14s -12s^3 ds](https://tex.z-dn.net/?f=%20%5Cint%20dy%20%3D%20%5Cint%2014s%20-12s%5E3%20ds)
And after do the integrals we got:
![y = 7s^2 -3s^4 +c](https://tex.z-dn.net/?f=%20y%20%3D%207s%5E2%20-3s%5E4%20%2Bc)
Now we can use the initial condition ![y(3) =1](https://tex.z-dn.net/?f=%20y%283%29%20%3D1)
![1 = 7(3)^2 -3(3)^4 +c, c=1-63+243=181](https://tex.z-dn.net/?f=%201%20%3D%207%283%29%5E2%20-3%283%29%5E4%20%2Bc%2C%20c%3D1-63%2B243%3D181)
And the final solution would be:
![y =7s^2 -3s^4 +181](https://tex.z-dn.net/?f=%20y%20%3D7s%5E2%20-3s%5E4%20%2B181)
Answer: taking the bus to work takes 13 minutes longer.
Step-by-step explanation:
It usually took josh 2/5 of an hour to ride his bike to work. This means that the number of hours that it took Josh to ride his bike to work is
2/5 × 60 = 24 minutes
But on Monday, his bike was broken, so he took the bus to work which took 5/8 of an hour. This means that the amount of time that it took Josh spent on the bus to work is
5/8 × 60 = 37.5 minutes
The difference between the time spent riding the bike and time spent on the bus is
37.5 - 24 = 13 minutes
F(10)=300+35(10)
f(10)=300+350
650(10)=300+350
6500
Answer:
10.4kg or 10kg 400 g
Step-by-step explanation:
1kg-1000 grams
600grams-0.6 kg
800 grams=0.8kg
6.6 kg +3.8kg
=10.4kg
or convert it back to the question
so the answer will be 10kg 400g