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3 years ago

A square fits exactly inside a circle with each of its vertices being on the circumference of the circle.

Mathematics

2 answers:

swat323 years ago

8 0

Answer:

The side of the square is 5.971 cm

Step-by-step explanation:

If the square fits the circle exactly, then its diagonal is equal to the diameter of the circle. Since the side of the square has a length of $x$ cm, then it's diagonal have the length of $x\sqrt2$ cm. Using the circle's area we can find the diagonal of the square, as shown below:

$area = \pi*r^2\\56 = pi*r^2\\r^2 = \frac{56}{\pi}\\r = \sqrt{\frac{56}{\pi}}\\r = 4.222$

Since the diameter of the circle is the same as the diagonal of the square, then:

$x\sqrt{2} = 2*r \\x = \frac{2*r}{\sqrt{2}}\\x = \frac{2*4.222}{\sqrt{2}}\\x = 5.971$

The side of the square is 5.971 cm

miskamm [114]3 years ago

8 0

Answer:

5.97

Step-by-step explanation:

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A rectangle has a length of (x + 4) centimeters and a width of 12x centimeters. If the perimeter is 26 centimeters, what is the

mars1129 [50]

Width of rectangle is 8.4 cm

Step-by-step explanation:

Length of rectangle = x+4

Width of rectangle = 12x

Perimeter = 26 cm

We need to find width of rectangle.

The formula used is:

$Perimeter=2(length+width)$

Putting values and finding x first:

$Perimeter=2(length+width)$

$26=2(x+4+12x)$

$26=2(13x+4)$

$26=26x+8$

$26-8=26x$

$26x=18$

$x=\frac{18}{26}$

$x=0.7$

So, value of x is 0.7

Now width= 12x = 12(0.7)

=8.4 cm

So, width of rectangle is 8.4 cm.

Keywords: Perimeter of Rectangle

Learn more about perimeter of rectangle at:

#learnwithBrainly

5 0

3 years ago

Help me pls i don't understand the problem so can u give me the answers and also explain

WARRIOR [948]

Step-by-step explanation:

$\frac{2}{3} +\frac{4}{5} =\frac{10+12}{15}=\frac{22}{15} .$

2) the same value of the denominator of the fractions.

3) 4²*2²=16*4=64 or 4²*2²=(4*2)²=8²=64.

Megan's answer is correct.

4) if the given length is 2,25=9/4 (feet), then the length of each piece is 9/4 :3=3/4=0.75 (feet) or 3/4*12=9 (inches).

5) a. 4-6= -2; b. -4+6=2; c. -4-6= -10, so the required order is c<a<b.

6) A. -8+3= -5; B. -8*3= -24, so the greater value is (-5) - answer A.

7) if to calculate every option, then A. 2.3*6.5=14.95; B. 21.45-6.5=14.95; C. 8.32+6.63=14.95, - all of them are equal.

6 0

2 years ago

A rectangular poster is to contain 722 square inches of print. the margins at the top and bottom of the poster are to be 2 inche

Delvig [45]

Let
x ----------> the height of the whole poster
y ----------> the width of the whole poster

We need to minimize the area A=x*y

we know that
(x-4)*(y-2)=722
(y-2)=722/(x-4)
(y)=[722/(x-4)]+2

so
A(x)=x*y--------->A(x)=x*{[722/(x-4)]+2}
Need to minimize this function over x > 4

find the derivative------> A1 (x)
A1(x)=2*[8x²-8x-1428]/[(x-4)²]

for A1(x)=0
8x²-8x-1428=0
using a graph tool
gives x=13.87 in

(y)=[722/(x-4)]+2

y=[2x+714]/[x-4]-----> y=[2*13.87+714]/[13.87-4]-----> y=75.15 in

the answer is
the dimensions of the poster will be
the height of the whole poster is 13.87 in
the width of the whole poster is 75.15 in

6 0

3 years ago

The area of a rectangle is 35 ft2 , and the length of the rectangle is 8 ft less than three times the width. find the dimensions

atroni [7]

The width is five feet and the length is seven feet.

8 0

3 years ago

The function d(s) = 0.0056s squared + 0.14s models the stopping distance

victus00 [196]

Answer:

The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

Step-by-step explanation:

Let be $d(s) = 0.0056\cdot s^{2} + 0.14\cdot s$ , where $d$ is the stopping distance measured in metres and $s$ is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.

The procedure to find the speed related to the given stopping distance is described below:

1) Construct the graph of $d(s)$ .

2) Add the function $d = 7\,m$ .

3) The point of intersection between both curves contains the speed related to given stopping distance.

In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

4 0

3 years ago