Answer:
117.5 ft²
Step-by-step explanation:
To find the area of the shaded area, we can find the area of the square, then subtract the areas of the two semicircles.
First, we will find the area of the given square, by using the formula
, multiplying the length and width. The dimensions of this square are 14×14.
14 · 14 = 196
The area of the square is 196 ft².
We can now find the area of the two congruent half-circles. Since they are identical, we can simply find the area of one circle if it was whole. To find the area of a circle, we'll use the formula
. With some simple deduction, we can see that the diameter of the circle is 10 ft, so the radius would be 5 ft long. Plug our values into the formula.
A =
5²
We will use 3.14 for
.
A = 78.5
The area of both the semicircles is 78.5 ft².
Now, we can subtract.
196 - 78.5 = 117.5
The area of the figure is 117.5 ft².
Good luck ^^
Answer:
A.6.2i-4.2 j
Step-by-step explanation:
We are given that



We have to find the projection of w on to u.
The project of vector a on b
=


Using the formula
The projection of w on to u

The projection of w on to u=6.2i-4.2j
Hence, option A is true.
Answer:
Part 1) The expression for the perimeter is
or 
Part 2) The perimeter when z = 15 ft. is 
Step-by-step explanation:
Part 1)
we have

Find the roots of the quadratic equation
Equate the equation to zero

Complete the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient


Complete the square. Remember to balance the equation by adding the same constants to each side


Rewrite as perfect squares

-----> root with multiplicity 2
so
The area is equal to
![A=625(z-0.12)(z-0.12)=[25(z-0.12)][25(z-0.12)]=(25z-3)^{2}](https://tex.z-dn.net/?f=A%3D625%28z-0.12%29%28z-0.12%29%3D%5B25%28z-0.12%29%5D%5B25%28z-0.12%29%5D%3D%2825z-3%29%5E%7B2%7D)
The length side of the square is 
therefore
The perimeter is equal to



Part 2) Find the perimeter when z = 15 ft.
we have

substitute the value of z
