Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
![\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac12%20%5Csin%282%28t%2Bh%29%29%20-%20%5Cfrac12%20%5Csin%282t%29%7Dh%20%3D%20%5Cdfrac%7B%5Csin%282t%2B2h%29%20-%20%5Csin%282t%29%7D%7B2h%7D)
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
![\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%282t%29%5Ccos%282h%29%20%2B%20%5Ccos%282t%29%5Csin%282h%29%20-%20%5Csin%282t%29%7D%7B2h%7D)
or
![\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csin%282t%29%5Cdfrac%7B%5Ccos%282h%29-1%7D%7B2h%7D%20%2B%20%5Ccos%282t%29%5Cdfrac%7B%5Csin%282h%29%7D%7B2h%7D%7D)
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)
She had to make a 90 flat
hope this helps (;
The mean is the same thing as the average. To find the average, add all the numbers up (aka find the sum of the numbers) and divide by how many numbers there is:
![average = \frac{sum \: of \: numbers}{\# \: of \: numbers}](https://tex.z-dn.net/?f=average%20%3D%20%20%5Cfrac%7Bsum%20%5C%3A%20of%20%20%5C%3A%20numbers%7D%7B%5C%23%20%5C%3A%20%20of%20%20%5C%3A%20numbers%7D%20)
So the sum of your numbers is: -6 + 2 + 5 + -7 + -11 + -6 = -23. And there are 6 numbers total.
That means average =
![\frac{-23}{6} = -3.833333](https://tex.z-dn.net/?f=%20%5Cfrac%7B-23%7D%7B6%7D%20%3D%20-3.833333)
≈ -3.8
Your final answer is -3.8
Circumference of a circle is the distance around the circle. This can be found by using the equation below
2*pi*radius
Our diameter, as shown, is 9cm. Since radius is half of the diameter, our radius is 4.5cm.
Therefore, our circumference is...
2 * pi * 4.5 = 9pi cm total
Answer: 105 miles?
I am not sure but that"s what I got
Step-by-step explanation: