Answer:
7. (4x +10)/(x^3 +3x^2 -16x -48)
9. -320/93
Step-by-step explanation:
7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.
6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))
= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator
= (6x +18 -2x -8)/((x -4)(x +3)(x +4))
= (4x +10)/((x^2 -16)(x +3))
= (4x +10)/(x^3 +3x^2 -16x -48)
_____
9. First you simplify the denominator:
2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400
Then you perform the division. This can be done by multiplying by the inverse of the denominator.
(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93
The range is the output, which would be the Y value.
The Y value would be calculated based on the input value for x.
any positive number raised to any value of x would be a positive number so 0.5^x would always be positive.
That would be multiplied by 4, which is a positive value, so the output ( Y value) would always be positive.
The range for this would be (0,∞)
Answer:
Option D. 
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
In this problem we have
substitute
-----> exact value of the volume
This question has extraneous info to trick you.
f(x) = g(x)h(x) ⇒ f'(x) = g'(x)h'(x) . Letting x = 10, we get f'(10) = g'(10)h'(10). then just plug in the values provided. g(10) and h(10) are there to throw you off, just use g'(10) and h'(10).
So f'(10), pronounced "eff prime of ten", = 0 * 35 = 0.
If the question were asking for f(10) instead of f'(10) then you would use g(10) and h(10), ⇒-4*560=90.
