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marta [7]
3 years ago
7

I will give you brainiest if you can answer the questions below.

Mathematics
1 answer:
Anon25 [30]3 years ago
8 0

Answer:

a. i. 3000 cm² ii. 220 cm  b.  6 feet

Step-by-step explanation:

A. i. The area of the sector AOB is A = ¹/₂r²θ where r = radius of circle = 50 cm and θ = angle subtended at the center of the circle by the sector in radians = 2.4 radians.

So, A = ¹/₂r²θ

= ¹/₂(50 cm)² × 2.4 rad

= ¹/₂ × 2500 cm² × 2.4 rad

= 1250 cm² × 2.4 rad

= 3000 cm²

ii. The perimeter of the sector is P = 2r + rθ = (2 + θ)r

substituting r and θ, we have

P = (2 + θ)r

= (2 + 2.4) × 50 cm

= 4.4 × 50 cm

= 220 cm

B. Since length of an arc L = rθ where r = radius = length of pendulum and θ = angle swept by pendulum =  ½ radian and length of the arc swept = 3 feet, the radius is

r = L/θ

= 3 feet ÷ ½ rad

= 3 × 2

= 6 feet

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Vika [28.1K]

The length and width of a new rectangle playing field are 214 yards and 52 yards respectively.

<h3>What is the area of the rectangle?</h3>

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

The length of a new rectangle playing field is 6 yards longer than quadruple the width.

Let's suppose the length is l and width is w of a rectangle:

From the problem:

l = 6 + 4w

Perimeter P = 2(l + w)

532 = 2(l + w)

Plug l = 6+4w in the above equation:

532 = 2(6 + 4w + w)

266 = 6 + 5w

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Thus, the length and width of a new rectangle playing field are 214 yards and 52 yards respectively.

Learn more about the area of rectangle here:

brainly.com/question/15019502

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Answer:

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Step-by-step explanation:

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Equation of a line with an slope of 1/2 that contains (-4, 7)
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Equation of a line with an slope of 1/2 that contains (-4, 7) is y=\frac{1}{2} x+9

<em><u>Solution:</u></em>

We have been given a point and slope of an equation and have been asked to write it in an equation. The two forms of writing a point and slope in equation are point slope form and standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

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