if a pyramid and a rectangular prism have congruent bases and equal heights, what's the difference between their volumes?
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Step-by-step explanation:
6 and 7 was already answered so I'll do 5 and 8.
5. The point the curve crosses the x axis is the x intercept, to find the x intercept of a rational function, we set y=0, and solve for x.
Set the numerator equal to 0.
So the x intercept is (4,0).
Next, to find gradient, we take the derivative of the function.
We could use product rule, but for simplicity, serperate the function
Next using exponents rules,
Now we take the derivative,
Derivative of a constant is zero.
Derivative of a power function,
We move the exponent to the front, then we subtract the exponent by 1.
So, we get
Now, we plug in. 4,
The slope or gradient at the x intercept is 1/4
8. The derivative of ax^2+bx, with respect to x is
When x=2, we have a gradient of 8.
When x=-1, we have a gradient of -10.
We have two system of equations,
Let subtract the system to eliminate b.
Plug 3 for a, back in to solve for b.
So a is 3
b is -4