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:
interest rate = 2.9%
Step-by-step explanation:
the principal is $25,000, the interest is $10,875
Number of years = 15
We use simple interest formula
I = P*r*t
Where I is the interest amount=10,875
P is the principal amount= 25000
r is the interest rate = r
t is the number of years = 15
Plug in all the value in the formula
I = P*r*t
10875 = 25000 * r * 15
10875 = 375000 * r
Divide both sides by 375000
r=0.029
We always write rate of interest in percentage so we multiply by 100
0.029 * 100= 2.9%
So interest rate = 2.9%
Answer:
Step 1: Identify a, h, and k.
a=0.5, h= -2, k= -4
Step 3: The axis of symmetry is the line x= -2
Step 4: h(-4)= -2 h(-6)= 4
The graph should have points plotted at (-6, 4), (-4, -2), (-2, -4), (0, -2), and (2, 4)
Step-by-step explanation: The answers were already there, just here to repeat for others who are confused.
Answer:
0.411^5 times 0.599
Step-by-step explanation:
0.599 chance of landing on heads.
0.411 chance of not landing on heads.
0.411 times 0.411 times 0.411 times 0.411 times 0.411 (for the 5 flips that do not land on heads) times 0.599 (for the time that it does land on heads).
Answer:
The total volume of the whole figure is 576m³.
Step-by-step explanation:
First find the volume for the first figure.
Volume of a Rectangular Prism (formula): L•W•H
V = (15m)(12m)(2m)
V = 360m³
Now, find the volume for the second figure.
V = (6m)(12m)(3m)
V = 216m³
Finally, just add both volumes to find the total volume of the entire figure.
Vt = 216m³ + 360m³
Vt = 576m³
