All categories

2 years ago

At 11:55 p.m., Thomas ties a weight to the minute hand of a clock. The clockwise torque applied by the

Mathematics

1 answer:

ryzh [129]2 years ago

7 0

Answer:

T(t) = 3sin((t-5)π/30)

Step-by-step explanation:

5 minutes after Thomas ties it on, the torque is zero and increasing. So, the sine function is shifted right 5 minutes. The maximum value is 3, so that is the multiplier of the sine function. The period is 60 minutes, so the coefficient of t is (2π/60) = π/30. The function you want is ...

T(t) = 3sin((t-5)π/30)

You might be interested in

The graph of a sinusoidal function has a maximum point at (0,5)(0,5)left parenthesis, 0, comma, 5, right parenthesis and then ha

Ksivusya [100]

Answer:

sinusoidal functions have the standard form of Asin(Bx - C) + D

Where A is the amplitude, 2pi/B gives us our period, C gives us our horizontal shifts in the opposite direction of the sign (because it's inside the parenthesis), and D gives us our vertical shifts in the same direction as the sign of D (positive or negative).

The easiest part is assigning the amplitude which is 3 as stated in the problem. This means that all of the max/mins of the graph will be multiplied by a factor of 3. However, this could be a positive or negative 3 depending on other info in the problem. We'll come back to this in a second.

We know 2pi/B = 8 in our problem. Solving for B gives us B = pi/4.

Now we need to find the corresponding maximum and minimums for a sin/cos function with a period of 8 by taking x values 0, pi/2, pi, 3pi/2, and 2pi (these are all values where normal sin/cos functions are either at their max/min or zero) and then divide each by pi/4. This will give us our new max/mins for a function with period 8. These values are 0, 2, 4, 6, and 8.

Since 2 is a minimum, then we know that there are no horizontal shifts. So C = o

Now we need to figure out if this is a sin or cos graph. A normal cos graph has a value of 0 at x = pi/2 which corresponds x = 2 in our problem. Your problem says that x = 2 will give us a minimum value so this tells us that our function must be a sin graph, not a cos graph. However, a sin graph has a maximum at 2 (which is pi/2 in a normal sin graph) while your problem calls for a minimum. This means that the amplitude we found earlier of 3 must actually be a -3 (I told you we'd get back to this!). The negative sign flips all of the maximums to minimums and vice versa of the sinusoidal graph.

Ok, let's put together what we know so far. A = -3, B = pi/4, and C = 0. So f(x) = -3sin((pi/4)x) + d

......But what about D?

Well, your problem says that one minimum of the graph is (2,1). In a graph without vertical shifts, we would expect the minimum to be at (2,-3). The difference between -3 and 1 is 4. This means in order to get from -3 to 1 we have to shift upwards of 4 units. In other words, D = 4.

Answer: -3sin((pi/4)x) + 4

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her

CaHeK987 [17]

Answer:

Her expenses are $25 per week.

Step-by-step explanation:

Given :Jessica earns a commission on each sale but has to pay for her own expenses.

She writes the equation of the function like this: $E(x) = 7x - 25$ , where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.

To Find: Which of the following are reasonable interpretations of the y-intercept of Jessica's function?

Solution:

$E(x) = 7x - 25$

x is the number of doors she knocks on during the week

E(x) is her earnings for the week in dollars.

Calculate y intercept

Substitute x = 0

$y= - 25$

Since E(x) is her total earning after clearing the payment of all her expenses.

So, 25 is her expenses per week.

Since we are given that she need to pay her expenses .

So, if there is no sale , still she need to pay expenses.

Thus the reasonable interpretations of the y-intercept of Jessica's function is Her expenses are $25 per week.

4 0

2 years ago

Read 2 more answers

Choose which statements are true about Pi. Check all that apply. Piis a whole number. Piis double the radius. Piis approximately

Ludmilka [50]

Answer:

Answer in explanation

Step-by-step explanation:

In this question, we would be examining the validity of some statements on the number π(pi)

π Is a whole number?

This is wrong, π is a fraction of 22 to 7 parts I.e 22/7

π Is double the radius?

This is wrong. It is the diameter that is double the radius

π Is approximately 3.14?

This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct

π represents the ratio of the circumference of the circle to the diameter?

This is correct.

Mathematically, circumference C = π * diameter D

Hence C/D = π

π Is approximately 22/7?

This is correct. This is the ratio used for π

7 0

2 years ago

Read 2 more answers

A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the c

Alchen [17]

Answer:

A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of π?

The expression which represents the value of π is option C from the attachment that is π = 43.96/14

Step-by-step explanation:

Given:

Circumference of the circle = 43.96 feet

Diameter f the circle = 14 feet

So,

We know that :

Circumference of the circle = $2(\pi )r$ or $(\pi)d$