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cestrela7 [59]
3 years ago
14

A rectangular price tag has an area of 36 square centimeters. Its perimeter is 26 centimeters. What are the dimensions of the pr

ice tag?
Mathematics
1 answer:
marishachu [46]3 years ago
5 0

Answer:

4 cm by 9 cm

Step-by-step explanation:

The formula for area of a rectangle is A = LW, where L and W are the dimensions of the rectangle.  We have

36 = LW

The formula for perimeter of a rectangle is P = 2L + 2W.  We have

26 = 2L + 2W

Solve the area formula for any variable..

36/L = W

Plug that into the perimeter equation..

26 = 2L + 2(36/L)

Now simplify...

26 = 2L + 72/L

Multiply all 3 terms by L to get rid of the fraction...

26L = 2L² + 72

Now this is a quadratic equation, get all terms to one side and solve...

2L² - 26L + 72 = 0

Divide both sides by 2

L² - 13L + 36 = 0

Factor the left side

(L - 9)(L - 4) = 0

So L = 4, or 9

If L = 4, then W = 36/4 = 9

If L = 9. then W = 36/9 = 4

either way, the dimensions are 4 cm by 9 cm

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How to solve this question
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Answer:

45/51

Step-by-step explanation:

SOH CAH TOA

Sin x = Opposite/hyp

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4 0
3 years ago
A population of squirrels on an island has a carrying capacity of 350 individuals. If the maximum rate of increase is 1.0 per in
TiliK225 [7]

Answer:

The population growth rate is <u>59</u> squirrels per year.

Step-by-step explanation:

Given:

A population of squirrels on an island has a carrying capacity of 350 individuals. If the maximum rate of increase is 1.0 per individual per year and the population size is 275.

Now, to find the population growth rate.

Carrying capacity (K) = 350.

Maximum rate (r_{max}) = 1.0 per individual per year.

Population size (N) = 275.

Now, to get the population growth rate we put formula:

\frac{dN}{dT}= r_{max}\frac{K-N}{K}N

\frac{dN}{dT}=1.0\times \frac{350-275}{350}\times 275\\\\\frac{dN}{dT}=1.0\times \frac{75}{350}\times 275\\\\\frac{dN}{dT}=1.0\times 0.214\times 275\\\\\frac{dN}{dT}=58.85.

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Therefore, the population growth rate is 59 squirrels per year.

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