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pochemuha
3 years ago
6

A rose garden is formed by joining a rectangle and a semicircle. The rectangle is 33ft long and 21ft wide. If the gardener wants

to build a fence around the garden, how many feet of fence are required. Use 3.14 for pi, and don't round your answer.
Mathematics
1 answer:
jeyben [28]3 years ago
3 0

Answer:

The perimeter of the garden is 126.81 feet.                                      

Step-by-step explanation:

We are given the following in the question:

Dimensions of rectangle:

Length, l = 33 feet

Width, w = 21 feet

Dimension of semicircle:

Diameter of circle, d = 33 feet

r = \dfrac{d}{2} = \dfrac{33}{2} = 16.5

Perimeter of garden =

P =\text{(Length + 2(Width)) + Perimeter of semi circle}\\P =l + 2(w) + \pi(r)\\P = 33 + 2(21) + 3.14(16.5)\\P = 126.81

Thus, the perimeter of the garden is 126.81 feet.

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Step-by-step explanation:

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Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos run
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Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

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Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

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\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}

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