Answer:
The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.
Step-by-step explanation:
The initial state of the battery on Sanchez's phone is 30% so in time t equals zero the battery should be at that value and as time progresses the battery should lose battery charge at a rate of 3% for each hour. We can write this in an equation form by taking the initial state and subtract it by the rate multiplied by the value of time. We have:
B(t) = 30 - 3*t
The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.
Answer:
5.24, 21/4, or 5 and 1/4
Step-by-step explanation:
78+139+14 = 231
231/44 = 5.25
Or 21/4 (improper fraction)
Or 5 and 1/4 (mixed number)
I'm not exactly sure what you were asking I hope that helps!
Substitute
and
. Then the integral transforms to
![\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bx%5C%2Cdx%7D%7B%28x%5E2%2B4%29%5E3%7D%20%3D%20%5Cfrac12%20%5Cint%20%5Cfrac%7Bdu%7D%7Bu%5E3%7D)
Apply the power rule.
![\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bdu%7D%7Bu%5E3%7D%20%3D%20-%5Cdfrac1%7B2u%5E2%7D%20%2B%20C)
Now put the result back in terms of
.
![\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bx%5C%2Cdx%7D%7B%28x%5E2%2B4%29%5E3%7D%20%3D%20%5Cfrac12%20%5Cleft%28-%5Cdfrac1%7B2u%5E2%7D%20%2B%20C%5Cright%29%20%3D%20-%5Cdfrac1%7B4u%5E2%7D%20%2B%20C%20%3D%20%5Cboxed%7B-%5Cdfrac1%7B4%28x%5E2%2B4%29%5E2%7D%20%2B%20C%7D)
Answer:
225
Step-by-step explanation:
30*750/100
225 is answer
2 cups was our starting point and we were left with 3/8 cups left after he spilled it, we are looking to find how much he spilled.
We could start by making 2 into a fraction so we could minus 3/8 easily.
2 = 16/8 (Two wholes is 16 eights.)
Now solve like a regular subtraction equation.
16/8 - 3/8 = 13/8
Our answer is 13/8 which simplified as a mixed fraction is 1 5/8
We lost 1 and 5/8 cups.