Answer:
3.67 hours
Step-by-step explanation:
Speed is the ratio of distance to time, it is given by the formula:
Speed = Distance / time
For annike her average speed was 11 miles per hour and she started at 7 am.
At 8 am (time = 1 hr i.e 7 am to 8 am) the distance she would have covered is given as:
11 miles/hr = distance / 1 hr
Distance = 11 miles per hr × 1 hr = 11 miles
After 8 am, the distance traveled at time t is:
11 = distance/t
distance = 11t
Total distance = 11t + 11
For Celia she started at 8 am at 14 miles per hour, at time t, the distance traveled is:
14 = distance/t
Distance = 14t
Given that both bikers traveled the same distance, hence:
14t = 11t + 11
3t = 11
t = 11/3
t = 3.67 hours
Answer:
60%
Step-by-step explanation:
First subtract Maria's answer by the actual, 40-25= 15
Next you would divide 15 by the actual. 15÷25= .6
times that by 100 to get .60×100= 60%
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Product to Sum Identity: cos A · cos B = [cos (A - B) + cos (A + B)]/2
Use the Odd Function Identity: cos (-A) = - cos (A)
<u>Proof LHS → RHS:</u>
![\text{LHS:}\qquad \qquad 2\cos \bigg(\dfrac{11\pi}{16}\bigg)\cdot \cos \bigg(\dfrac{\pi}{16}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BLHS%3A%7D%5Cqquad%20%5Cqquad%202%5Ccos%20%5Cbigg%28%5Cdfrac%7B11%5Cpi%7D%7B16%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B16%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
![\text{Prod to Sum:}\quad \dfrac{2\bigg[\cos \bigg(\frac{(11\pi -\pi)}{16}\bigg)+\cos \bigg(\frac{(11\pi+\pi}{16}\bigg)\bigg]}{2}+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BProd%20to%20Sum%3A%7D%5Cquad%20%5Cdfrac%7B2%5Cbigg%5B%5Ccos%20%5Cbigg%28%5Cfrac%7B%2811%5Cpi%20-%5Cpi%29%7D%7B16%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cfrac%7B%2811%5Cpi%2B%5Cpi%7D%7B16%7D%5Cbigg%29%5Cbigg%5D%7D%7B2%7D%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
![=\cos \bigg(\dfrac{10\pi}{16}\bigg)+\cos \bigg(\dfrac{12\pi}{16}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%3D%5Ccos%20%5Cbigg%28%5Cdfrac%7B10%5Cpi%7D%7B16%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B12%5Cpi%7D%7B16%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
![=\cos \bigg(\dfrac{5\pi}{8}\bigg)+\cos \bigg(\dfrac{3\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%3D%5Ccos%20%5Cbigg%28%5Cdfrac%7B5%5Cpi%7D%7B8%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
![=\cos \bigg(\dfrac{-3\pi}{8}\bigg)+\cos \bigg(\dfrac{-\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%3D%5Ccos%20%5Cbigg%28%5Cdfrac%7B-3%5Cpi%7D%7B8%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B-%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
![\text{Odd Functions:}\quad -\cos \bigg(\dfrac{3\pi}{8}\bigg)-\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{\pi}{4}\bigg)+\cos \bigg(\dfrac{3\pi}{8}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BOdd%20Functions%3A%7D%5Cquad%20-%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29-%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cbigg%29%2B%5Ccos%20%5Cbigg%28%5Cdfrac%7B3%5Cpi%7D%7B8%7D%5Cbigg%29)
= 0
LHS = RHS ![\checkmark](https://tex.z-dn.net/?f=%5Ccheckmark)
Answer:
33.3
Step-by-step explanation:
Answer:
46,288
Step-by-step explanation:
40,000 + 6,000 + 200 + 80 + 8
46,288
Hope this helps :D