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2 years ago

Richard has two circular sprinklers to water his rectangular backyard as shown.

Mathematics

1 answer:

makvit [3.9K]2 years ago

8 0

Answer:

109.88 ft² (nearest hundredth)

Step-by-step explanation:

Formulae

Area of a rectangle = width × length
Area of a circle = πr²

To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.

From inspection of the diagram

width of rectangle = 2r
length of rectangle = 4r
area = 512 ft²

Substituting the values into the area of a rectangle formula, and solving for r:

⇒ 512 = 2r × 4r

⇒ 512 = 8r²

⇒ r² = 64

⇒ r = ±8

As distance is positive, r = 8 ft

Area of one circle = π8² = 64π ft²

Therefore,

Area not watered = area of rectangle - 2 × area of circle

= 512 - 2(64π)

= 109.88 ft² (nearest hundredth)

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Answer:

Part 1) The graph in the attached figure

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Step-by-step explanation:

we know that

To graph a line we need to plot two points

If a point solve the linear equation, then the point is a solution of the linear equation

step 1

Find the first point that solve the equation

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The x-intercept is the value of x when the value of y is equal to zero

For y=0

$x - 4(0) =-18$

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The x-intercept is the point (-18,0)

step 2

Find the second point that solve the equation

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The y-intercept is the value of y when the value of x is equal to zero

For x=0

$0 - 4y =-18$

$-4y=-18$

$y=4.5$

The y-intercept is the point (0,4.5)

step 3

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Plot the intercepts and join the points to graph the line

using a graphing tool

see the attached figure

step 4

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Assume a value for x and then solve for y

I assume x=-2

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$-2 - 4y =-18$

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

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Mariulka [41]

Answer:

Question 1: y = 3/4x + 1/4.

Question 2: y = 6/5x + 7/5.

Step-by-step explanation:

Question 1: A line perpendicular to another line would have a slope that is the negative reciprocal of the other line. If the slope of the first line is -4/3, the slope of a line perpendicular to the first would have a slope of 3/4.

Since the line goes through (5, 4), we can just put the points into the equation, y = 3/4x + b.

4 = 3/4(5) + b

b + 15/4 = 4

b = 16/4 - 15/4

b = 1/4

So, the equation of the line is y = 3/4x + 1/4.

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As stated before, a line perpendicular to another will have a slope that is the negative reciprocal of the other. So, the slope of the other line is 6/5.

The line goes through (-2, -1), so we can put the points into the equation, y = 6/5x + b.

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Hope this helps!

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