The average rate of change over the interval
is 2.17
Explanation:
Given that the cost of a floral bouquet after a discount is given by the function 
We need to determine the average rate of change over the interval 
The average rate of change can be determined using the formula,

where
and 
Substituting the value of a and b in the function, we get,






Hence, substituting these values in the formula, we get,

Simplifying, we get,

Dividing, we have,

Thus, the average rate of change over the interval
is 2.17
30x-12-8x+40
22x-12+40
22x +28
Answer:
Step-by-step explanation:
The graph is sketched in the attachment. It's easy to sketch the same graph using the given information. Let's say h is the height. For time t=0 you put a dot on 3 feet since it's the lowest point of the ferris wheel (you get that by substracting the diameter of 40 feet from the highest point given (43 feet).
Second dot is your highest point 43 feet at t=4 sec since it is the half of the circle.
The third dot is your lowest point again at t=8 sec. If you connect the dots like a sine you get the sketched graph.
To find out what is the equation for the graph you need to look at the amplitude which in this case is 20 feet. Then you need to find out the frequency at which the wheel is turning. Since you are given the period (8 sec for a full cycle) you get the frequency:

Now you need to find out the phase of the wave. Since we want to be at 0 feet at t=0 you need to shift the wave 90° degrees forward or
in radians.
Finally it's important to shift the whole wave up. You do that by adding the appropriate amount that is in this case the half of the diameter plus the 3 feet to the ground.
The equation you get is:

where A is amplitude,
is the phase shift and
is the frequency.
Finally you can get the height at
sec:

Answer:
Step-by-step explanation:
<u>Sum of internal angles of a regular polygon is:</u>
<u>We have here 5-sided polygon:</u>
- S = 180*(5 - 2) = 180°*3 = 540°
<u>Now sum the given angles measures and solve for x:</u>
- 3x + 1 + 2x + 15 + 3x - 10 + 3x - 8 + 5x - 2 = 540
- 16x - 4 = 540
- 16x = 544
- x = 544/16
- x = 34°
<u>Find the measure of angle R:</u>
- m∠R = 3x - 10 = 3*34 - 10 = 102 - 10 = 92
- m∠R = 92°
Answer:
x = 28.8
Step-by-step explanation:
Using the Sine rule in the triangle then
=
( cross- multiply )
x × sin87° = 43 × sin42° ( divide both sides by sin87° )
x =
= 28.8