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3 years ago

Using the approximation 3.14 for \pi what is the radius of a circle with circumference 44m

Mathematics

1 answer:

Feliz [49]3 years ago

8 0

Answer:

7 m

Step-by-step explanation:

Circumference of a circle uses the formula;

Circumference = 2 × pi × radius(r)

If the circumference = 44

then we use the formula above to calculate the value of the radius,

44 = 2 × pi × r...then divide both sides by (2 × pi(3.14))

Radius = 44 ÷ ( 3.14 × 2)

;Radius = 7.01

;Radius = 7m

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Math help @Alessandroarenas

frez [133]

Accordinly to the details, i think that A could work.

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3 years ago

A circle centered at (-2,3) and contains point (5,9) which represents the equation

SIZIF [17.4K]

The standard form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle, (x,y) is a point of the circle, and r is the length of the radius of the circle. When the equation of a circle is written, h,k, and r are numbers, while x and y are still variables. (x-2)^2 + (y-k)^2 = 16 is an example of a circle. The problem gives us two of the three things that a circle has, a point (5,9) and the center (-2,3). We need to find the radius in order to write the equation. We substitute -2 for h, 3 for k, 5 for x, and 9 for y to get (5 - (-2))^2 + (9 - 3)^2 = r^2 We simplify: 49 + 36 = r^2, r^2 = 85. We only need to know r^2 because the equation of a circle has r^2. We now have all the information to write the equation of a circle. (x + 2)^2 + (y - 3)^2 = 85.

8 0

3 years ago

Mr. Thomas spent $1,600 of his savings on a television set and 2/5 of the remainder on a refrigerator. He had 1/3 of his origina

Katena32 [7]

Answer:

The amount spent on the refrigerator is $ 800 .

Step-by-step explanation:

Given as :

The amount spent on television = $ 1600

Le The total amount in the account = $ A

so, The amount left in account after spent on television = $ A - $ 1600

The amount spent on refrigerator = $\frac{2}{5}$ × ( A - 1600 )

The amount left in his saving account = $\frac{1}{3}$ × A

Now, According to question

A - ( 1600 + $\frac{2}{5}$ × ( A - 1600 ) ) = $\frac{1}{3}$ × A

Or, A - $\frac{1}{3}$ × A = 1600 + $\frac{2}{5}$ × ( A - 1600 )

Or, $\frac{2}{3}$ × A = 1600 + $\frac{2}{5}$ × A - $\frac{2}{5}$ × 1600

or, $\frac{2}{3}$ × A - $\frac{2}{5}$ × A = 1600 - 640

Or, $\frac{10 - 6 }{15}$ × A = 960

or, $\frac{4}{15}$ × A = 960

∴ A = $\frac{960\times 15}{4}$

I.e A = 3600

So, The amount in the saving account is $3600

∵ , The amount spent on refrigerator = $\frac{2}{5}$ × ( 3600 - 1600 )

Or, The amount spent on refrigerator = $\frac{2}{5}$ × 2000

I.e The amount spent on refrigerator = $ 800

Hence The amount spent on the refrigerator is $ 800 . Answer

4 0

3 years ago

Does anyone have know if there’s a answer key for this if not pls help.

KATRIN_1 [288]

Answer:

I'm not sure, but I could kinda help

Step-by-step explanation:

to find the slope using a graph, using the formula :

$\frac{y2 - y1}{x2 - x1}$

I hope this helps

5 0

2 years ago

A normal window is constructed by adjoining a semicircle to the top of an ordinary rectangular window, (see figure ) The perimet

Dima020 [189]

Let's find the perimeter of the window.

The bottom side is $x$ . The left and right sides make $2y$ .
The perimeter of a circle is $2\pi r$ , so the perimeter of a semicircle must be $\pi r$ , The radius is $\frac{1}2x$ , so that gives $\frac{1}2\pi x$ for the curve. All of that is equal to 12.

$x+2y+\frac{1}2\pi x=12$

We only want to use one variable to create the area formula, so let's solve for $y$ .

$2y=12-x-\frac{1}2\pi x$

$y=6-\frac{1}2x-\frac{1}4\pi x$

Now that we have a value for $y$ in terms of $x$ , we can find the area in terms of $x$ .

The area of the rectangle is going to be $xy$ , which then becomes

$A_r=x(6-\frac{1}2x-\frac{1}4\pi x$

$A_r=6x-\frac{1}2x^2-\frac{1}4\pi x^2$

The area of the semicircle is going to be $\frac{1}2\pi r^2$ .

Since $r=\frac{1}2x$ , $A_{sc}=\frac{1}2\pi (\frac{1}2x)^2$ .

$A_{sc}=\frac{1}2\pi \frac{1}4x^2$

$A_{sc}=\frac{1}8\pi x^2$

Now let's add the areas of the rectangle and semicircle.

$A=A_r+A_{sc}$

$A=6x-\frac{1}2x^2-\frac{1}4\pi x^2+\frac{1}8\pi x^2$

$A=6x-\frac{1}2x^2-\frac{1}8\pi x^2$

If you wanted to factor out $\frac{1}8$ like you did, this would become

$\boxed{A(x)=\frac{1}8(48x=4x^2-\pi x^2)}$

Now what we want to do is find what $x$ is when $A$ is at its highest point, Once we have the value for $x$ we can also find the value for $y$ , of course.

Let's put our equation in the general form of a quadratic.

$A(x)=(-\frac{1}2-\frac{1}8\pi )x^2+6x$

Now we can use the vertex formula $x=\frac{-b}{2a}$ .
( $a$ and $b$ refer to $ax^2+bx+c$ .)

$x=\frac{-6}{2(-\frac{1}2-\frac{1}8\pi)}$

$x=\frac{-6}{-\frac{1}4\pi -1}$

$x=\frac{-24}{-\pi -4}$

$\boxed{x=\frac{24}{\pi +4}}$

Now let's plug that in for $y=6-\frac{1}2x-\frac{1}4\pi x$ .

Since our final answers are in decimal form and not exact form, we can make our lives a little easier here and just use $x\approx3.36059492$ .

$y\approx6-\frac{1}2(3.36059492)-\frac{1}4\pi(3.36059492)$

<span> $y\approx6-(1.68029746+2.63940507809)$

</span><span> $\boxed{y\approx1.68029746191}$

Let's take our answers for $x$ and $y$ and round to 2 decimal places.

$\boxed{x\approx 3.36\ ft}$

$\boxed{y\approx 1.68\ ft}$ </span>

3 0

3 years ago