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klasskru [66]
3 years ago
15

Type the correct answer in the box. Assume that π = 3.14, and round your answer to the nearest integer.

Mathematics
2 answers:
Vinil7 [7]3 years ago
4 0

Answer: 648 yards.

Step-by-step explanation:

Given: Central angle = 280°

Radius = 35 yards

The length of arc with central angle x and radius r is given by :-

l=\dfrac{x}{360^{\circ}}\times2\pi r\\\\\Rightarrow\ l=\dfrac{280}{360}\times2\pi(35)\\\\\Rightarrow\ l=171.042266\approx171\text{ yards}

Total distance = 171 +45 = 216 yards

Now, if David runs around the field three times, he covers a distance = 3\times216 =648\text{ yards.}

KengaRu [80]3 years ago
3 0
Length of an arc of a circle:
L = n° / 360° · 2 r · π = 280°/360° · 2 · 35 · 3.14 
L = 170.9 yards 
170.9 + 45 = 215.9 
3 · 215. 9 = 647.7 ≈ 648 
... he covers the distance of 648 yards.
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A rancher has 200 feet of fencing to enclose two adjacent corrals
Arturiano [62]

Answer:

a) Each corral should be 33⅓ ft long and 25 ft wide

b) The total enclosed area is 1666⅔ ft²

Step-by-step explanation:

I assume that the corrals have identical dimensions and are to be fenced as in the diagram below

Let x = one dimension of a corral

and y = the other dimension

 

(a) Dimensions to maximize the area

The total length of fencing used is:

4x + 3y = 200

4x = 200 – 3y

x = 50 - ¾y

The area of one corral is A = xy, so the area of the two corrals is

A = 2xy

Substitute the value of x

A = 2(50 - ¾y)y

A = 100 y – (³/₂)y²

This is the equation for a downward-pointing parabola:

A = (-³/₂)y² + 100y

a = -³/₂; b = 100; c = 0

The vertex (maximum) occurs at  

y = -b/(2a)  = 100 ÷ (2׳/₂) = 100 ÷ 3 = 33⅓ ft  

4x + 3y = 100

Substitute the value of y

4x + 3(33⅓) = 200

4x + 100 = 200

4x = 100  

x = 25 ft

Each corral should measure 33⅓ ft long and 25 ft wide.

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6 0
3 years ago
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function h(t)= -16
tangare [24]

Answer:

(d)

Step-by-step explanation:

Given

h(t) = -16t^2 + 96t

Required

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These represent the start and end of the ball that is launched.

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3 years ago
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Fynjy0 [20]
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3 years ago
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blagie [28]
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