The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t=0 and that the windmill turns counterclockwise at a constant rate.

Answers

Answer 1

Answer: The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.

Answer 2

Answer:

The sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) is; y = 30sin(πt/15) + 30

How to solve Sine Functions?

The period of a sine function is represnted as;

b = 2π

This period is usually repeated after each 2π units.

The sine model is expressed as;

y = a(sin (bt)) + k

We are told that the blades are 10 feet long and complete 2 rotations every minute. Thus the period is;

b = (2π/60) * 2

b = π/15

The blades of a windmill turn on an axis that is 30 feet from the ground and the blades are 10 ft long. Thus,

k = 30 and a = 10

Plugging the relevant values into the given formula gives;

y = 30sin(πt/15) + 30

Thus, the sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) is;

y = 30sin(πt/15) + 30

Read more about sine functions at; brainly.com/question/9565966

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Emily is three years older than twice her sister mary’s age. the sum of their ages is less than 30. let x represent mary's age. which inequality represents mary’s possible age? responses •0

Answers

x < 9

Step-by-step explanation:

Let's use the information given to create an inequality for Mary's age (represented as x):

↪ Emily is three years older than twice Mary's age, so Emily's age is 2x + 3.

↪ The sum of their ages is less than 30, so we can write an inequality:

x (Mary's age) + 2x + 3 (Emily's age) < 30

Now, We can simplify the inequality:

3x + 3 < 30

Subtract 3 from both sides of the inequality:

3x < 27

Now, divide both sides by 3 to isolate x:

x < 9

So, Mary's possible age (represented by x) is less than 9. The inequality that represents Mary's possible age is: x < 9.

Anthony earned $131 in tips last night while working at the restaurant. If his tipsconsisted of $1 bills and $5 bills only and he counted 47 bills in total, then how
many $5 bills did Anthony receive?

Answers

Answer:21 5 dollar bills

Step-by-step explanation:

Find the volume of a sphere with a radius of 5m. Remember that the volume of a sphere is 4/3pir^3

Answers

(4/3)*π*125 = 523,(3);

Answer:

523,(3) m³

Step-by-step explanation:

$V=(4)/(3)\pi*r^(3)=(4)/(3)\pi*5^(3)=(4*125)/(3)\pi=(500)/(3)\pi=523,(3)~m^(3)$

(Picture Attached)20 Pts:

Which of the following completes the proof? (6 points)

By the midpoint formula

By definition of congruence

Given

By construction