U varies inversely which means p³ will come as a denominator of the constant k.
Therefore, The equation formed will be:
The shape is composed of three squares and two semicircles.Select all the expressions that correctly calculate the perimeter of
1 answer:
Answer:
100+20π
Step-by-step explanation:
Find the diagram attached.
Perimeter of a square =4L
L is the side length of a square
From the diagram;
L = 10
Perimeter of a square = 4(10) = 40
Perimeter of 3 squares = 3(40) = 120
2 semi circle = a circle
Perimeter of a circle= 2πr
radius of the Circle = length of a side of the square.
Area of the circle = 2π(10)= 20π
Perimeter of the shape = Perimeter of the two semicircle + area of the 4squares = 100+20π
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Start by writing the system down, I will use to represent
Substitute the fact that into the first equation to get,
Simplify into a quadratic form (),
Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,
which then must factor into
And the solutions will be .
Clearly for small coefficients like ours , this is very easy to figure out. To get 5 and 6 we simply say that
.
This fits the definition as and
.
So as mentioned, solutions will equal to but these are just x-values in the solution pairs of a form
.
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are and
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Hope this helps :)