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3 years ago

A circular quilt is made from 113.04 square feet of fabric. How much trim is needed to go around it’s edge?

Mathematics

1 answer:

erik [133]3 years ago

6 0

Hey there!

We are looking for the circumference of the circle, which is the distance around it. We are given the area, which is the radius squared times pi.

First, we need to undo the area to find our radius.

113.04/3.14=36

We square root this to find the radius.

√36=6

Our radius is six. To find the circumference, we need to multiply the diameter by pi. The diameter is twice the radius.

6*2=12

12*3.14=37.68

Therefore, we will need 37.68 feet of trim to around the edge of the quilt.

I hope this helps!

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The equation of a circle of radius r and center $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The diameter is twice the radius, and is the maximum distance between two points inside a circle.

In this problem, the circular path is modeled by:

$x^2 + y^2 - 10x - 18y - 378 = 0$

We complete the squares to place it in the standard format, thus:

$x^2 - 10x + y^2 - 18y = 378$

$(x - 5)^2 + (y - 9)^2 = 378 + 25 + 81$

$(x - 5)^2 + (y - 9)^2 = 484$

Thus, the radius is:

$r^2 = 484 \rightarrow r = \sqrt{484} = 22$

Then, the diameter is:

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The maximum distance is the diameter of the circle, which is of 44 units.

A similar problem is given at brainly.com/question/24992361

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Andrews [41]

Step-by-step explanation:

Step 1: Write our Givens

${x}^{2} + 10x - 7 = 0$

Move the constant term ,(the term with no variable) to the right side.

Here we have a negative 7, so we add 7 to both sides

${x}^{2} + 10x = 7$

Next, we take the linear coeffeicent and divide it by 2 then square it.

$( \frac{10}{2} ) {}^{2} = 25$

Then we add that to both sides

${x}^{2} + 10x + 25 = 7 + 25$

${ {x}^{2} } + 10x + 25 = 32$

Next, we factor the left,

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we got 5 because 5 add to 10 and multiply to 25 as well.

so we get

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This is called a perfect square trinomial.

Next, we take the square root of both sides

$x + 5 = ± \sqrt{32}$

± menas that we have a positive and negative solution.

Subtract 5 form both side so we get

$x = - 5± \sqrt{32}$

The greater solution is when sqr root of 32 is positive so the answer to that is

$\sqrt{32} - 5 = 0.7$

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