2.49/6 = 0.415
3.32/8 = 0.415
unit rates are equal :)
This is a quadratic formula, which is (-b+-sqrt(b^2-4ac))/2a.
Parabolic graphs are quadratic formulas.
So this is not too hard, as with any math problem we write what we know.
Starting speed: 80km/h
Time from P to Q: 2.5h
Increase in speed: 20km/h (25% is dividing by 4)
Distance from Q to R: 150 kilometers
So let's find the speed and distance for both legs of the trip.
Speed for P to Q: 80km/h
Distance from PtoQ: 200km (2.5h * 80km/h)
Speed from Q to R: 100km/h (80 +20)
Distance from QtoR: 150km.
Now we multiply the speeds by their respective distances add them and then divide by the total distance.
((80 *200) + (100 * 150))/350 = ~88.57143
Answer:
See below.
Step-by-step explanation:
First, use the co-function identity:
We can turn the second term into cosine:
Substitute:
Now, use the sum to product formulas. We will use the following:
Substitute:
Use the even-odd identity:
Therefore:
Replace the second term with the original term:
Proof complete.