Answer:
The radius of the circle is 
The length of the square is 
Step-by-step explanation:
we know that
The circumference of a circle is equal to 
The perimeter of the square is equal to 
so
Simplify
-----> equation A
The area of a circle is equal to 
The area of a square is 
The total area is equal to
-----> equation B
substitute equation A in equation B
![At=\pi r^{2}+[(12-\pi r)/2]^{2}](https://tex.z-dn.net/?f=At%3D%5Cpi%20r%5E%7B2%7D%2B%5B%2812-%5Cpi%20r%29%2F2%5D%5E%7B2%7D)
This is a vertical parabola open upward
The vertex is the minimum
The x-coordinate of the vertex is the radius of the circle that produce a minimum area
The y-coordinate of the vertex is the minimum area
Solve by graphing
The vertex is the point (1.68, 20.164)
see the attached figure
therefore
The radius of the circle is
Find the value of x
assume
Answer:
Each share lost $20 in value over 4 days time
Step-by-step explanation:
$5 loss for 4 days
5 x 4 = 20
$20 loss in 4 days.
By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
4x + 2y = 7 (equation 1)
y = 5x (equation 2)
Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.
4x + 2y = 7 (equation 1)
4x + 2(5x) = 7
4x + 10x = 7
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
4x + 10x = 7
14x = 7
x = 1/2
Substitute the value of x in the second equation and solve for y.
y = 5x
y = 5(1/2)
y = 5/2
Hence, the solution of the given system of equations is (1/2 , 5/2).
To learn more about solving systems of equations: brainly.com/question/25869125
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Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.
<h3>What does Chebyshev’s Theorem state?</h3>
When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:
- At least 75% of the measures are within 2 standard deviations of the mean.
- At least 89% of the measures are within 3 standard deviations of the mean.
- An in general terms, the percentage of measures within k standard deviations of the mean is given by
.
In this problem, considering a standard deviation of 40, we have that:
440 - 2 x 40 = 360.
440 + 2 x 30 = 520.
Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.
More can be learned about Chebyshev's Theorem at brainly.com/question/25303620
