Answer:
c. 500 + 24 * 8
Step-by-step explanation:
if there is 500 gallons of water already in the swimming pool and we are trying to add more and we are adding 24 gallons for 8 minutes to the already existing pool of water.
Distribute the 3 to both x and 2
3(x + 2) = 3x + 6
3x + 6 + 2x = -4
Combine like terms
(3x + 2x) + 6 = -4
5x + 6 = -4
Isolate the x. Note the equal sign. What you do to one side, you do to the other. Subtract 6 from both sides
5x + 6 (-6) = -4 (-6)
5x = -4 - 6
5x = -10
Divide 5 from both sides
5x = -10
5x/5 = -10/5
x = -10/5
x = -2
-2 is your answer for x
hope this helps
Answer:
![\dfrac{dy}{dx} = \frac{2x-3}{\ln 16(x^2 - 3x)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2x-3%7D%7B%5Cln%2016%28x%5E2%20-%203x%29%7D)
Step-by-step explanation:
We are given the following in the question:
![y = \ln {16}(x^2 - 3x)](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%20%7B16%7D%28x%5E2%20-%203x%29)
We have to find the derivative of the given expression.
![y = \ln 16(x^2 - 3x)\\\text{Using the log propert}\\\\\log_a b = \dfrac{\log b}{\log a}\\\\dfrac{d(x^n)}{dx} = nx^{n-1}\\\\\dfrac{d(\log x)}{dx} = \dfrac{1}{x}\\\\\text{\bold{Differentiating we get}}\\\\\displaystyle\frac{dy}{dx} = \frac{d(\ln 16(x^2-3x))}{dx}\\\\= \frac{1}{16(x^2-3x)})\frac{d(x^2-3x)}{dx}\\\\=\frac{1}{\log 16(x^2-3x)}(2x - 3)\\\\= \frac{2x-3}{\ln 16(x^2 - 3x)}](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%2016%28x%5E2%20-%203x%29%5C%5C%5Ctext%7BUsing%20the%20log%20propert%7D%5C%5C%5C%5C%5Clog_a%20b%20%3D%20%5Cdfrac%7B%5Clog%20b%7D%7B%5Clog%20a%7D%5C%5C%5C%5Cdfrac%7Bd%28x%5En%29%7D%7Bdx%7D%20%3D%20nx%5E%7Bn-1%7D%5C%5C%5C%5C%5Cdfrac%7Bd%28%5Clog%20x%29%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5Ctext%7B%5Cbold%7BDifferentiating%20we%20get%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7Bd%28%5Cln%2016%28x%5E2-3x%29%29%7D%7Bdx%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B16%28x%5E2-3x%29%7D%29%5Cfrac%7Bd%28x%5E2-3x%29%7D%7Bdx%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B%5Clog%2016%28x%5E2-3x%29%7D%282x%20-%203%29%5C%5C%5C%5C%3D%20%5Cfrac%7B2x-3%7D%7B%5Cln%2016%28x%5E2%20-%203x%29%7D)
![\dfrac{dy}{dx} = \frac{2x-3}{\ln 16(x^2 - 3x)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2x-3%7D%7B%5Cln%2016%28x%5E2%20-%203x%29%7D)
Answer:
see explanation
Step-by-step explanation:
given a parabola in standard form : y = ax² + bx + c : a ≠ 0
• If a > 0 then parabola opens up
• If a < 0 then parabola opens down
given y = 4x² - 8x + 8 ← in standard form
with a = 4, b = - 8 and c = 8
here a > 0 then parabola opens up