Answer:
12.86 sq ft
Step-by-step explanation:
Find area of square and subtract out area of semi-circle; the diameter of the semi-circle equals the side of the square, which is 4 so radius is 2
A(square) = 4 x 4 = 16
A(semi-circle) = πr²/2
= 4π/2 or 2π
Area of Shaded Region = 16-3.14 which is 12.86
We have to set up 2 different equations if we are to solve for 2 unknowns. The first equation is x = y + 4. One number (x) is (=) 4 more than another (y + 4). Since we have determined that x is larger (cuz it's 4 more than y), when we set up their difference, we are going to subtract y from x cuz x is bigger. The second equation then is
![x^{2} - y^{2} =64](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%3D64)
. In our first equation we said that x = y + 4, so let's sub that value in for x in the second equation:
![(y+4) ^{2} - y^{2} =64](https://tex.z-dn.net/?f=%28y%2B4%29%20%5E%7B2%7D%20-%20y%5E%7B2%7D%20%3D64)
. Expand that binomial to get
![y^{2} +8y+16- y^{2} =64](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%20%2B8y%2B16-%20y%5E%7B2%7D%20%3D64)
. Of course the y squared terms cancel each other out leaving us with 8y + 16 = 64. Solving for y we get that y = 6. Subbing 6 in for y in our first equation, x = 6 + 4 tells us that x = 10. Yay!
Answer/Step-by-step explanation:
27.
✔️Sin 23 = opp/hyp
Sin 23 = t/34
34*sin 23 = t
t = 13.3
✔️Cos 23 = adj/hyp
Cos 23 = s/34
s = 34*cos 23
s = 31.3
28.
✔️Sin 36 = opp/hyp
Sin 36 = s/5
s = 5*sin 36
s = 2.9
✔️Cos 36 = adj/hyp
Cos 36 = r/5
r = 5*cos 36
r = 4.0
29.
✔️Sin 70 = opp/hyp
Sin 70 = w/10
w = 10*sin 70
w = 9.4
✔️Cos 70 = adj/hyp
Cos 70 = v/10
v = 10*cos 70
v = 3.4
High school track is shaped as a rectangle with a half circle side. Jake Plans on running four laps. How many meters will Jake run? - 12490731.
In order for us to get the hypotenuse of a right triangle, let's follow the Pythagorean Equation:
h^2 = a^2 + b^2
Getting the hypotenuse:
<span>h = square root (a^2 + b^2)
</span>h = square root (10<span>^2 + 24^2)
</span>h = square root (100<span> + 576)
</span>h = square root (676)
h = 26
So the hypotenuse is equal to 26 cm.