Answer:
(1 cm)cos3πt
Step-by-step explanation:
Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft
where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.
Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations = 2 s
So, f = 3/2 s =1.5 /s = 1.5 Hz
Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm
h = Acos2πft
= (1 cm)cos2π(1.5Hz)t
= (1 cm)cos3πt
Answer:
- 100
- 80
- 100
- 80
x = 10
y = 6
Step-by-step explanation:
We can use the vertical angle theorem to solve for most of this problem. We know that 1/3 will have the same measure and so will 4/2. We can create an equation to solve for 1 and 3.
10x = 100
x = 10
We aren't given angle 4 so we are going to have to solve that ourselves. We can create an equation knowing that 4 and 3 will create a supplementary angle.
100 + z = 180
z = 80
Now, that we have angle 4, we know that angle 2 will have the same measure because they are vertical angles. Now to find the value of y, we can take the angle measure and solve for it.
10y + 20 = 80
10y = 60
y = 6
Best of Luck!
Answer:
depends on the radius
Step-by-step explanation:
To find the area of a circle, use the formula A = π r²
To find the area, substitute r for the radius of your circle
For example:
If I had a circle with a radius of 2,
A = π 2²
A≈12.57
Hope this helps
Answer:
Step-by-step explanation:
The formula that is used to calculate the area of a rectangle is:
Where "l" is the lenght and "w" is the width.
You know that the area of that rectangle is:
And, according to the exercise, its lenght is 7 more than its width; then:
Then, you can make the corresponding substitution into the formula :
Simplify:
Factor the equation. Find two numbers whose sum is 7 and whose product is -744. These are 31 and -24.
Then, you get:
The width of the rectangle is the positive value:
Then, the lenght is:
B. Fiscal Policy. Hope that helps you.