Answer: 
Step-by-step explanation:
Given
Length of the pipe 
Inside diameter of the pipe 
Outside diameter of the pipe 
Volume of the pipe
![\Rightarrow V=\dfrac{\pi }{4}[d_o^2-d_i^2]\\\\\text{Insert the values}\\\\\Rightarrow V=\dfrac{\pi}{4}[5^2-4^2]\times 10^{-4}\times 4\\\\\Rightarrow V=28.278\times 10^{-4}\ m^3\\\\\Rightarrow V=0.0028278\ m^3](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%5Bd_o%5E2-d_i%5E2%5D%5C%5C%5C%5C%5Ctext%7BInsert%20the%20values%7D%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D%5B5%5E2-4%5E2%5D%5Ctimes%2010%5E%7B-4%7D%5Ctimes%204%5C%5C%5C%5C%5CRightarrow%20V%3D28.278%5Ctimes%2010%5E%7B-4%7D%5C%20m%5E3%5C%5C%5C%5C%5CRightarrow%20V%3D0.0028278%5C%20m%5E3)
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If you are writing in slope-intercept form:
You first find the slope.
Put the slope in the equation.
Substitute any point into the equation and find the y-intercept.
Here is our profit as a function of # of posters
p(x) =-10x² + 200x - 250
Here is our price per poster, as a function of the # of posters:
pr(x) = 20 - x
Since we want to find the optimum price and # of posters, let's plug our price function into our profit function, to find the optimum x, and then use that to find the optimum price:
p(x) = -10 (20-x)² + 200 (20 - x) - 250
p(x) = -10 (400 -40x + x²) + 4000 - 200x - 250
Take a look at our profit function. It is a normal trinomial square, with a negative sign on the squared term. This means the curve is a downward facing parabola, so our profit maximum will be the top of the curve.
By taking the derivative, we can find where p'(x) = 0 (where the slope of p(x) equals 0), to see where the top of profit function is.
p(x) = -4000 +400x -10x² + 4000 -200x -250
p'(x) = 400 - 20x -200
0 = 200 - 20x
20x = 200
x = 10
p'(x) = 0 at x=10. This is the peak of our profit function. To find the price per poster, plug x=10 into our price function:
price = 20 - x
price = 10
Now plug x=10 into our original profit function in order to find our maximum profit:
<span>p(x)= -10x^2 +200x -250
p(x) = -10 (10)</span>² +200 (10) - 250
<span>p(x) = -1000 + 2000 - 250
p(x) = 750
Correct answer is C)</span>
Answer:
<h2>x < - 3</h2>
Step-by-step explanation:
Move 7 to the other side of the inequality
Divide both sides by - 5
Reverse the sign
We have the final answer as
<h3>x < - 3</h3>
Hope this helps you
