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2 years ago

A circle is cut from a square piece of cloth, as shown: How many square inches of cloth are cut from the square? (π = 3.14)

Mathematics

1 answer:

Vinil7 [7]2 years ago

8 0

Answer:

2122.64 in^2

Step-by-step explanation:

Use the formula for the area of a circle: A=πr^2

The radius will be half the width of the cloth so 52÷2=26

26^2=676

Multiply by π given as 3.14

676×3.14=2122.64 square inches.

The symbol (carat) ^ is used to indicate an exponent when the keyboard doesn't have superscript.

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2 years ago

Select the correct answer.

garri49 [273]

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Step-by-step explanation:

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2 years ago

What is the equation of the circle with center (-3,1) that passes through the point (-5, 3)?

Natali5045456 [20]

Answer:

Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by:

$(x-h)^2 + (y-k)^2 = r^2$

Given

Center = (h,k) = (-3,1)

=> h = -3

=> k = 1

The distance between the center of circle and the point through which the circle passes will be the radius.

The distance formula is given by:

$r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Given

$(x_1,y_1) = (-3,1)\\(x_2,y_2) = (-5,3)$

Putting the values in the formula

$r = \sqrt{(-5+3)^2+(3-1)^2}\\r = \sqrt{(-2)^2+(2)^2}\\r = \sqrt{4+4}\\r = \sqrt{8}$

Putting the values of h,k and r in general form of equation

$\{x-(-3)}^2\} +(y-1)^2 = (\sqrt{8})^2\\(x+3)^2+(y-1)^2 = 8$

Hence,

Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.

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2 years ago

What is the value of this expression? Select all that apply. (8.59 × 104) – (3.2 × 103)

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Answer:

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3 years ago

What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?

gizmo_the_mogwai [7]

Answer:

The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is $\mathbf{y=-\frac{5}{4}x+3}$

Step-by-step explanation:

We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.

The equation will be of form $y=mx+b$ where m is slope and b is y-intercept.

Finding slope of the line:

Since both the lines are parallel, and we know that parallel lines have same slope.

The slope of given line $5x+4y=16$ can be found by writing in slope-intercept form $y=mx+b$

$5x+4y=16\\4y=-5x+16\\y=-\frac{5}{4}x+16$

Comparing with $y=mx+b$ the slope m is: $m=-\frac{5}{4}$

So, the slope of required line is: $m=-\frac{5}{4}$

Now, finding y-intercept b

y-intercept can be found using slope $m=-\frac{5}{4}$ and point (8,-7)

$y=mx+b\\-7=-\frac{5}{4}(8)+b\\-7=-5(2)+b\\-7=-10+b\\b=-7+10\\b=3$

So, we get y-intercept: b=3

Now, the equation of required line having slope $m=-\frac{5}{4}$ and y-intercept b=3 is:

$y=mx+b\\y=-\frac{5}{4}x+3$

So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 $\mathbf{y=-\frac{5}{4}x+3}$

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2 years ago