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alekssr [168]
2 years ago
9

A rectangular field with perimeter of 80m is to have an area of at least 380m² . Describe the possible lengths and of the field.

​
Mathematics
1 answer:
Kryger [21]2 years ago
6 0

let \: x \: be \: the \: length \\ let \: y \: be \: the \: width

perimeter = 2x + 2y \\ area = xy

2x + 2y = 80 \\ xy = 380 \\  \\ x + y = 40 \\ xy = 380 \\  \\ x = 40 - y \\ (40 - y)y = 380

40y - y {}^{2}  = 380 \\ y {}^{2}  - 40y + 380 = 0 \\  y {}^{2}  - 40y + 400 = 20 \\ (y - 20) {}^{2}  = 20 \\ y  - 20 =± \sqrt{20}  \\ y_{1}=20-√20≈15.52786\\ y_{2}=20+√20≈24.4721

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kiruha [24]

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Answer:

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Step-by-step explanation:

You are being asked to factor 4 from each of the terms of the expression and use the distributive property to show the result.

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  = 4(3x) +4(8)

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The numbers that go in the boxes, left to right, are ...

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8 0
3 years ago
A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off
GuDViN [60]

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

(B) How large a rebate should the company offer the buyer in order to maximize its revenue?

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

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R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

6 0
2 years ago
Find the volume of the cone use pi=3.14 Round to the nearest hundredth?
xenn [34]

Answer:

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I will give Brainiest if your right
Setler79 [48]

Answer:

I'm always right B-) SHEESH

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