Two boats start their journey from the same point a and travel along directions ac and ad, as shown below: what is the distance, cd, between the boats? 461.9 ft 530.9 ft 646.4 ft 325.5 ft

  461.9 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

In the diagram, you are given angles and the side opposite those angles. You want to find the difference between the lengths of the adjacent sides.

Solving the above equation for "Adjacent", we get ...

  Adjacent = Opposite/Tan

For our two boats, this tells us ...

  BC = (400 ft)/tan(60°)

  BD = (400 ft)/tan(30°)

Then the difference BD -BC = CD is ...

  CD = BD -BC = (400 ft)/tan(30°) -(400 ft)/tan(60°)

  CD = (400 ft)(1/tan(30°) -1/tan(60°)) ≈ 461.9 ft

Comment on the solution

Of course, 1/tan(x) = cot(x) = tan(90° -x). So, our expression could be ...

  CD = (400 ft)(tan(60°) -tan(30°)) . . . . . a little easier to evaluate

x> 6

step-by-step explanation:

8x+8> 7x+14

8x-7x> 14-8

x> 6

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!