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8090 [49]
3 years ago
14

Jacqueline is checking her bicycle’s wheel. The wheel has a radius of 20 cm, and its center is 51 cm above the ground. Jacquelin

e is rotating the wheel at a constant speed of 225°/s. The height of a point on the tire as a function of time is given by h = 51 + 20 sin(225t), where h is the height in centimeters and t is the time in seconds. Find h when t = 19 s. Find your answer to the nearest tenth of a centimeter.
Mathematics
1 answer:
Alex777 [14]3 years ago
6 0

Answer:

h = 36.9 cm

Step-by-step explanation:

The function given to us is:

h(t) = 51 + 20 sin(225t)

Where h(t) is the function of the height in centimeters while t represents the time in seconds.

We have to find the height h(t) when the time is equal to 19 seconds.

Substitute t=19 into the given function

h(19) = 51 + 20 sin(225(19))

h(19) = 51 + 20 sin(4275)

h(19) = 51 + 20 (-0.7071)

h(19) = 51 + (-14,1421)

h(19) = 36.8579 cm

Rounding off to nearest 10th

h = 36.9 cm

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3 years ago
Find two numbers whose sum<br> is 37 and difference is 9.
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Answer:

23 and 14

Step-by-step explanation:

The sum of x and y is 37. In other words, x plus y equals 37 and can be written as equation A:

x + y = 37

The difference between x and y is 9. In other words, x minus y equals 9 and can be written as equation B:

x - y = 9

Now solve equation B for x to get the revised equation B:

x - y = 9

x = 9 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 37

9 + y + y = 37

9 + 2y = 37

2y = 28

y = 14

Now we know y is 14. Which means that we can substitute y for 14 in equation A and solve for x:

x + y = 37

x + 14 = 37

X = 23

Summary: The sum of two numbers is 37 and their difference is 9. What are the two numbers? Answer: 23 and 14 as proven here:

Sum: 23 + 14 = 37

Difference: 23 - 14 = 9

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