Answer:
54.8 feet
Step-by-step explanation:
We assume that the distance of interest is the direct line distance from the observation point to the bottom of the monument, segment PH in the diagram below.
This can be found using the Law of Sines.
∠PMH is the complement of the angle of elevation to the top of the monument, so is 40°.
∠MPH is the difference in the angles of elevation, so is 28°.
__
The Law of Sines tells us the ratio of side lengths is the same as the ratio of the sines of the opposite angles, so ...
PH/MH = sin(∠PMH)/sin(∠MPH) = sin(40°)/sin(28°)
Multiplying by MH, we can find the length of PH:
PH = (40 ft)(sin(40°)/sin(28°)) ≈ 54.7669 ft
PH ≈ 54.8 ft . . . . the distance Pete must climb to reach the monument.
Answer:

Step-by-step explanation:
We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.
We know that standard form of cosine function is
, where,
|A| = Amplitude,
Period =
,
C = Phase shift,
D = Vertical shift.
Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is,
.
Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by
, therefore, we can write
, therefore,
.
We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero
.
Therefore, our function required function would be
.
3

x
You can put that on a number line. Be sure that the dot you use is closed.
Answer:
see explanation
Step-by-step explanation:
step 4 take the square root of both sides
= ± 
x + 4 = ± 
step 5 subtract 4 from both sides
x = - 4 ± 
step 6 solve for x
x = - 4 -
or x = - 4 + 
For the first month, the membership fee deducted = $15
So, -15(1) will represent this situation.
Similarly, for the second, third, fourth months, the expressions will be:
-15(2), -15(3), -15(4) and so on.
Hence, if t represents the number of months, then -15t will represent ash's art club membership being deducted every month for a year.