Answer:
it depends how good the food is lol
Step-by-step explanation:
Answer:
-336/527
Step-by-step explanation:
Trig identities are involved.
tan(2x) = 2tan(x)/(1 -tan(x)²)
Using tan = sin/cos, we can write this in terms of sine and cosine as ...
tan(2x) = (2sin(x)/cos(x))/(1 -sin(x)²/cos(x)²) = 2sin(x)cos(x)/(cos(x)² -sin(x)²)
= 2sin(x)cos(x)/(1 -2sin(x)²)
Now, the cosine can be found from ...
cos(x) = √(1 -sin(x)²)
for sin(θ) = 24/25, cos(θ) = √(1 -(24/25)²) = 7/25 . . . . 1st quadrant angle
Filling in the values in the above identity, we have ...
tan(2θ) = 2(24/25)(7/25)/(1 -2(24/25)²) = 336/-527
tan(2θ) = -336/527
_____
You can use a calculator or estimate that the angle for sin(θ) = 24/25 will be greater than 67.5°, so double the angle will be greater than 135°. (θ ≈ 74°) This means ...
- 2θ > 135°, so the magnitude of tan(2θ) will be less than 1
- 2θ is in the 2nd quadrant, so the sign of tan(2θ) will be negative
These observations will help you choose the correct answer without any further math.
Answer:
We find the length of each subinterval dividing the distance between the endpoints of the interval by the quantity of subintervals that we want.
Then
Δx= 
Now, each
is found by adding Δx iteratively from the left end of the interval.
So

Each subinterval is
![s_1=[-2,-3/2]\\s_2=[-3/2,-1]\\s_3=[-1,-1/2]\\s_4=[-1/2,0]](https://tex.z-dn.net/?f=s_1%3D%5B-2%2C-3%2F2%5D%5C%5Cs_2%3D%5B-3%2F2%2C-1%5D%5C%5Cs_3%3D%5B-1%2C-1%2F2%5D%5C%5Cs_4%3D%5B-1%2F2%2C0%5D)
The midpoints of the subintervals are

The points used for the
1. left Riemann sums are the left endpoints of the subintervals, that is

2. right Riemann sums are the right endpoints of the subinterval,

3. midpoint Riemann sums are the midpoints of each subinterval
