Answer: 5 seconds
<u>Step-by-step explanation:</u>
Maximum height is the y-value of the vertex. The number of seconds at maximum height is the x-value (aka axis of symmetry).
h(x) = -2x² + 20x + 48
a=-2 b=20 c=48
Axis of symmetry: x =
=
=
= 5
Answer:
f'(x) = -1/(1 - Cos(x))
Step-by-step explanation:
The quotient rule for derivation is:
For f(x) = h(x)/k(x)
In this case, the function is:
f(x) = Sin(x)/(1 + Cos(x))
Then we have:
h(x) = Sin(x)
h'(x) = Cos(x)
And for the denominator:
k(x) = 1 - Cos(x)
k'(x) = -( -Sin(x)) = Sin(x)
Replacing these in the rule, we get:
Now we can simplify that:
And we know that:
cos^2(x) + sin^2(x) = 1
then: