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



The graph that represents possible functions is shown in the diagram below. Point C shows the point on y-axis where f(x) and g(x) crosses. The result should be interpreted by the level of steepness of each slope
g(x) has a steeper gradient than f(x) and this indicates steeper fee rise for producing the T-shirt. So if Marissa is to choose the better value for her money to produce T-shirt, she should choose the function f(x) providing there are no other factors to consider other than prices.
Answer:
<u>For</u><u> </u><u>A</u>

• The equation above has a common bracket "(x + 1)". So, let's first factorise out that bracket:

• now in the second bracket, the common factor is x and 2.

• Final answer;

<u>For</u><u> </u><u>B</u>

• In the equation, the common bracket is (x + 2).
So let's first factorise it out:

• In the second major bracket, the common bracket is (x - 1). so factorise it out:

• Final answer:

Answer:
Since there is 4 quarts in a gallon and 60 minutes in a hour.
60 x 60 = 3600
Multiply: 815 × 4 = 3260 quarts per hour
So 3260/3600 = 326/360 = 0.905 quarts per second
Step-by-step explanation:
Answer:
2244 cm
Step-by-step explanation:
The first first thing we must do is find the LCM of the following numbers
(51; 68) = 204.
This means that the first time they coincide is at 204.
Now, since his steps always coincide after 204
In Nick's case
Nick's 204 ÷ 51 = 4th step
and in the case of the father
204 ÷ 68 of his father = 3rd step.
Which means that in the 204 cm distance, there will be a total of 6 foot steps, except in the first 204 cm when your "initial" step is counted.
Replacing these values we have that the total distance will be:
67-1 (initial step) / (6 * 204) = 2244 cm