If you are looking for how to turn that worded problem into an equation...
Heres the answer you're looking for
3x-11
The answer is: (z - 6)(z + 15)
z² + 9z - 90 = z*z + 15z - 6z - 6*15 =
= (z*z + 15z) - (6z + 6*15) =
= z(z + 15) - 6(z + 15) =
= (z - 6)(z + 15)
first speed --- x mph
return speed -- x+16 mph
6/x + 6/(x+16) = 1
times each term by x(x+16)
6(x+16) + 6x = x(x+16)
x^2 + 4x - 96 = 0
(x-8)(x+12) = 0
x = 8 or x is a negative
her first speed was 8 mph
her return speed was 24 mph
check:
6/8 + 6/24 = 1 , that's good!
Answer:
Multiplying the mass of ice by the specific latent heat of fusion of ice
Step-by-step explanation:
The heat energy required to completely melt 100 grams can be calculated by multiplying the mass of ice (100g) by the specific latent heat of fusion of ice (336J/g)
Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
