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SVETLANKA909090 [29]
3 years ago
12

A company is building a new park in the shape of a circle with a 25 ft diameter. Portions of the new park will be covered with g

rass. A diagram of the park is given below, with the shaded region representing the areas that will be covered in grass. Use 3.14 for. Note: image is not drawn to scale. The area of the regions covered by grass is approximately sq ft.

Mathematics
1 answer:
emmasim [6.3K]3 years ago
4 0

Answer: The area of the regions covered by grass is approximately 313.375 sq ft.

Step-by-step explanation:

Given: A company is building a new park in the shape of a circle with a 25 ft diameter.

Then radius = \dfrac{25}{2}=12.5\ ft

Required area = Area of circle - Area of rectangle + Area of triangle

Formula: Area of circle = \pi r^2

Area of rectangle = length x width

Area of triangle = 0.5 x base x height

Area of circle = (3.14)(12.5)^2=490.625\ \text{ft}^2

Area of rectangle = 20 ft x 10ft = 200 ft²

Area of triangle = 0.5 x 7 x 6.5 = 22.75 ft²

Required area = 490.625 -200+22.75 = 313.375 ft²

Hence, The area of the regions covered by grass is approximately 313.375 sq ft.

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2 years ago
Find a polynomial function of degree 3 with 2, i, -i as zeros.
sergiy2304 [10]

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p(x)= x^3-2x^2+x-2

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if \alpha , \ \beta \ \& \ \gamma are the zeros of the cubic polynomial , then ,

\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)

Here in place of the Greek letters , substitute 2,i and -i , we get ,

\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

\sf  \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}

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Simplify by opening the brackets ,

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Rearrange ,

\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}

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2 years ago
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Answer:

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Add equations for 1.

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2 years ago
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