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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)

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Marginal Revenue

kvv77 [185]

Answer:

Step-by-step explanation:

a) Revenue function us derives by taking the product of the number of yachts and the demand function p given. Mathematically,

R(x) = xp(x)

Given p(x) = 700 − 0.01x ln(x)

R(x) = x{700 − 0.01x ln(x)}

R(x) = 700x - x(0.01x ln(x))

R(x) = 700x - 0.01x²lnx

Hence the revenue function R(x) is expressed as R(x) = 700x - 0.01x²lnx

Marginal revenue function is derived by finding the derivative of the revenue function R(x). On differentiating;

d{R(x)}/dx = 700 - 0.01{x²(1/x)+2xlnx} (note that product rule was used to differentiate the function in parenthesis).

d{R(x)}/dx = 700 - 0.01{x+2xlnx}

Open the parenthesis

d{R(x)}/dx = 700 - 0.01x-0.02xlnx

Hence the marginal revenue function R'(x) is expressed as 700 - 0.01x-0.02xlnx.

b) In order to estimate the revenue to be realized from the sale of the 375th 34 ft Sundancer yacht, we will simply substitute the variable x = 375 into the revenue function R(x)

Given R(x) = 700x - 0.01x²lnx

R(375) = 700(375) - 0.01(375)²ln(375)

R(375) = 262500-1406.25ln(375)

R(375) = 262500-8334.74

R(375) = 254,165.26

Hence the revenue realized from the sale is approximately $254,165

For the Marginal revenue Function,

R'(x) = 700−0.01x−0.02xln(x)

R'(375) = 700−0.01(375)−0.02(375)ln(375)

R'(375) = 700−3.75−0.02(375)ln(375)

R'(375) = 700-3.75-44.45

R'(375) = 651.8

The marginal revenue is approximately $652

6 0

1 year ago

Shelley receives supplies for her sno-cones business weekly. She usually works concession at four events a week and averages sal

My name is Ann [436]

Answer:

<u>Shelley did not budget enough. She will need additional US$ 16 for fulfilling the average sales of 760 sno-cones at the 4 events. With the budget she has, she just can supply 714 sno-cones (250 / 0.35).</u>

Step-by-step explanation:

1. Let's check all the information given for solving this question:

Cost of individual supply = US$ 0.35

Budget per week = US$ 250

Average sales of sno-cones per event = 190

Number of events per week = 4

2. Let's check if Shelley budgeted enough for the week events:

Total of sno-cones Shelley will sell = Average sales * Number of Events

Total of sno-cones Shelley will sell = 190 * 4 = 760

Cost of supplies for the week = Total of sno-cones * Cost of individual supply

Cost of supplies for the week = 760 * 0.35 = US$ 266

Budget per week = US$ 250

Budget per week - Cost of supplies for the week = 250 - 266 = - 16

4 0

2 years ago

Divide 169 mi in the ratio 5 : 8.

krek1111 [17]

The answer is 169/5:8 = 5. It helps me alot it could help you to.

3 0

2 years ago

On January 4, janelle ruskinoff deposited $2192.06 in a savings account that pays 5.5 percent interest compounded daily. How muc

Andru [333]

Answer:

$7.94

Step-by-step explanation:

We have been given that on January 4, Janelle Ruskinoff deposited $2192.06 in a savings account that pays 5.5 percent interest compounded daily. We are asked to find the amount of interest earned in 24 days.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,