1) the main formula of circle equation is (x - a)² + (y – b)²= R², (a, b) is the center and R is the radius. So we replace easily (a, b) by (–2, 3), and R=5 for finding the answer, it is (x +2 )² + (y – 3)²= 5²= 25
2) if a circle (x - a)² + (y – b)²= R² , ((a, b) is the center) passes with A(u, v), so we can write the equation as (u- a)² + (v – b)²= R², so we have
(2 + 1)² + (-2 -2)² = R², R²=9+16=25, which implies R=5, and the diameter is given by D=2*R=10, so the answer is The diameter is 10.
3) firstly, D=AB, let's calculate the length of AB,
AB= sqrt[(5+1)^2+(4+4)^2]=sqrt[36+64]=sqrt[100], so D=AB=10, but we know that D=R*2, so R=10/2=5, the equation of the circle must be as follow (x - a)² + (y – b)²= R², after changing the value of R, the equation is
(x – 2)² + y² = 25
Answer:
x=36/11=3.2727...
Step-by-step explanation:
The solution can be found by solving for x.
First, combine like terms and simplify each side of the equation.
![-12x+26 = -(15)-x+2+3\\-12x+26 = -15-x+5\\-12x+26=-10-x](https://tex.z-dn.net/?f=-12x%2B26%20%3D%20-%2815%29-x%2B2%2B3%5C%5C-12x%2B26%20%3D%20-15-x%2B5%5C%5C-12x%2B26%3D-10-x)
Second, use inverse operations to move terms across the equal sign.
![-12x+26 = -10-x\\-12x+x+26=-10-x+x\\-11x+26=-10\\-11x+26-26=-10-26\\-11x=-36\\x=36/11=3.2727...](https://tex.z-dn.net/?f=-12x%2B26%20%3D%20-10-x%5C%5C-12x%2Bx%2B26%3D-10-x%2Bx%5C%5C-11x%2B26%3D-10%5C%5C-11x%2B26-26%3D-10-26%5C%5C-11x%3D-36%5C%5Cx%3D36%2F11%3D3.2727...)
Answer:
![{22cm}^{2}](https://tex.z-dn.net/?f=%20%7B22cm%7D%5E%7B2%7D%20)
to the nearest tenth
Step-by-step explanation:
find the area of the semi circle
![\frac{\pi \times 5}{2} = {7.85cm}^{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cpi%20%5Ctimes%205%7D%7B2%7D%20%20%3D%20%7B7.85cm%7D%5E%7B2%7D%20)
find area of the whole shape
![5 \times 6 = {30cm}^{2}](https://tex.z-dn.net/?f=5%20%5Ctimes%206%20%3D%20%7B30cm%7D%5E%7B2%7D%20)
then subtract both areas to get shaded area
![30 - 7.85 = 22.15](https://tex.z-dn.net/?f=30%20-%207.85%20%3D%2022.15)
F(t) = 2(0.4)^t
To solve f(-2) we should substitute t = -2 into the equation:
f(-2) = 2(0.4)^(-2)
= 2(6.25)
= 12.5
The difference between arcsin and csc is that the result of arc sine is an angle either degrees or radians. csc or cosecant is the inverse of sine in which the value is a number with no units (as it is a ratio). These two are often mistaken but these are different