$\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}$

$\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )$

8 0

3 years ago

A car travels along a straight stretch of road. It proceeds for 16.2 mi at 57 mi/h, then 24.6 mi at 44 mi/h, and finally 45.1 mi

LekaFEV [45]

Answer:

The average velocity the entire trip was 43.25 mi/h

Step-by-step explanation:

In this case we have to calculate an average based on the miles traveled. First we have to calculate the total of miles traveled, then calculate the portion of the total travel of each and with this calculate the average speed during the trip. First the total miles traveled:

$TotalMiles=16.2+24.6+45.1=85.9$

Now the percentages:

At 57 mi/h were $\frac{16.2}{85.9}=0.19$

At 44 mi/h were $\frac{24.6}{85.9}=0.29$

At 37.8 mi/h were $\frac{45.1}{85.9}=0.52$

Now multiplying the speed by the portion and summing them we can have the average velocity:

$57*0.19+44*0.29+37.8*0.52=43.25$

The average velocity the entire trip was 43.25 mi/h

5 0

2 years ago

Can somebody help me with this question

ArbitrLikvidat [17]

What you need to do is find the greatest amount (1) and the lowest amount (1/4) of sap collected and the find how many times the lowest can go into the greatest. (So how many times can 1/4 go into 1). I believe that this is how you would do that.

8 0

3 years ago