Compare linear functions using_____

From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

5 0

1 year ago

Geometry question, will give brainiest

Kipish [7]

C. 135
Corresponding parts of congruent figures are the same

7 0

2 years ago

Read 2 more answers

.. pls help me....!!!!! Determine whether the point (-2,4) satisfy y<3x+5,y=3x+5 or y >3x+5..

nasty-shy [4]

Answer:

$y > 3\cdot x + 5$

Step-by-step explanation:

Let $A(x,y) = (-2,4)$ and $y = 3\cdot x + 5$ . Now we evaluate the given function at $x = -2$ :

$y = 3\cdot x + 5$ (1)

$y = 3\cdot (-2)+5$

$y = -6 +5$

$y = -1$

Which means that $y$ is less than the y-component of A. Therefore, the right answer is $y > 3\cdot x + 5$ .

7 0

2 years ago

Find the number of possible outcomes in the sample space.

nikitadnepr [17]

I believe it’s A.

good luck!!

8 0

2 years ago

Math Question :

saw5 [17]

Let x = amount of mortgage (aka the amount by the bank)

25% of the monthly income of $3000 is 0.25*3000 = 750 dollars

So using this rule, the family can pay up to $750 per month on mortgage

1% of the amount loaned (x) is equal to this figure, so

0.01*x = 750
0.01*x/0.01 = 750/0.01
x = 75000

Therefore, the most expensive mortgage this family can afford is $75,000. Anything higher and they go over budget.

7 0

2 years ago

Compare linear functions using______ and graphs.