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Bess [88]
3 years ago
5

A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of

the circle. What is the ratio of the area of the square to the area of the circle?

Mathematics
1 answer:
Ksivusya [100]3 years ago
7 0

r=AB=AC=BC, AD=r/2, ED=DF=CD=squareroot(3.r)/2

The area of square is : (EF)^2=(squareroot(3.r))^2=3r^3

The area of circle is : (pi.r^2)

The ratio will be: 3/pi

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Solve system of equations 2x + 2y + 5z = 7 6x + 8y + 5z = 9 2x + 3y + 5z = 6
svet-max [94.6K]

Answer:

the values of x, y and z are x= 2, y =-1 and z=1

Step-by-step explanation:

We need to solve the following system of equations.

We will use elimination method to solve these equations and find the values of x, y and z.

2x + 2y + 5z = 7     eq(1)

6x + 8y + 5z = 9     eq(2)

2x + 3y + 5z = 6     eq(3)

Subtracting eq(1) and eq(3)

2x + 2y + 5z = 7

2x + 3y + 5z = 6

-    -       -        -

_____________

0 -y + 0 = 1

-y = 1

=> y = -1

Subtracting eq(2) and eq(3)

6x + 8y + 5z = 9    

2x + 3y + 5z = 6    

-     -      -          -

______________

4x + 5y +0z = 3    

4x + 5y = 3      eq(4)

Putting value of y = -1 in equation 4

4x + 5y = 3

4x + 5(-1) = 3

4x -5 = 3

4x = 3+5

4x = 8

x= 8/4

x = 2

Putting value of x=2 and y=-1 in eq(1)

2x + 2y + 5z = 7

2(2) + 2(-1) + 5z = 7

4 -2 + 5z = 7

2 + 5z = 7

5z = 7 -2

5z = 5

z = 5/5

z = 1

So, the values of x, y and z are x= 2, y =-1 and z=1

5 0
3 years ago
If F(x)=x^3-2x^2, which expression is equivalent to f(I) -2+i,-2-i,2+i,2-i
Romashka-Z-Leto [24]

Hello from MrBillDoesMath!

Answer:

2 - i

Discussion:

Evaluate F(x) = x^3 - 2 x^2 when x = i.

i^2 = -1 for i^3 = i ( i^2) = i (-1) = -i

So F(i) =  (i)^3 - 2 (i)^2                      

          =   -i     - 2(-1)

          = -i      +  2

          =  2      -  i


which is the last answer shown


Thank you,

MrB

6 0
3 years ago
Solve x to the second power = 144
vfiekz [6]

x ^ 2 = 144

x = 12, x = -12

Check:

12 * 12 = 144

-12 * -12 = 144

6 0
3 years ago
Read 2 more answers
Graph the point (4, -1) on the coordinate plane below.<br>​
dimulka [17.4K]
See the blue dot in the attached image.



First, find the x value on the coordinate plane. The x value is the first number in the point coordinates, so in this case, it is 4. Move to the right 4. (If it was negative, you would move to the left.)

Then, find the y value, which is the second number of the coordinates. In this case, it is -1, so move down 1. (If it was positive, you’d move up.)

Now, mark this point. This is (4, -1).

4 0
3 years ago
Read 2 more answers
Trish takes a Frenchy want to $5500 at a simple interest rate of 6% per year. Which of the following is closest to the amount of
lesya [120]

Answer:

F

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6%/100 = 0.06 per year,

then, solving our equation

I = 5500 × 0.06 × 2.5 = 825

I = $ 825.00

The simple interest accumulated

on a principal of $ 5,500.00

at a rate of 6% per year

for 2.5 years is $ 825.00.

4 0
3 years ago
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