Step-by-step explanation:
the formula of coordinates (x, y) that reflected across the x-axis : (x, y) => (x, -y)
so,
A(3, -2) => A'(3, 2)
B(5, 5) => B'(5, -5)
C(-4, 2) => C'(-4, -2)
Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):
- 9/4 - 2.25 - 2 4/1
- 8/3 - 2.67 - 2 2/3
- 23/6 - 3.83 - 3 5/6
- 11/2 - 5.5 - 5 1/2
- 17/5 - 3.4 - 3 2/5
- 15/8 - 1.875 - 1 7/8
- 33/10 - 3.3 - 3 3/10
- 29/12 - 2.416 - 2 5/12
I hope that this info helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)
Attach a photo so we can see the problem
The area of the triangle is
A = (xy)/2
Also,
sqrt(x^2 + y^2) = 19
We solve this for y.
x^2 + y^2 = 361
y^2 = 361 - x^2
y = sqrt(361 - x^2)
Now we substitute this expression for y in the area equation.
A = (1/2)(x)(sqrt(361 - x^2))
A = (1/2)(x)(361 - x^2)^(1/2)
We take the derivative of A with respect to x.
dA/dx = (1/2)[(x) * d/dx(361 - x^2)^(1/2) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(x) * (1/2)(361 - x^2)^(-1/2)(-2x) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(361 - x^2)^(-1/2)(-x^2) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(-x^2)/(361 - x^2)^(1/2) + (361 - x^2)/(361 - x^2)^(1/2)]
dA/dx = (1/2)[(-x^2 - x^2 + 361)/(361 - x^2)^(1/2)]
dA/dx = (-2x^2 + 361)/[2(361 - x^2)^(1/2)]
Now we set the derivative equal to zero.
(-2x^2 + 361)/[2(361 - x^2)^(1/2)] = 0
-2x^2 + 361 = 0
-2x^2 = -361
2x^2 = 361
x^2 = 361/2
x = 19/sqrt(2)
x^2 + y^2 = 361
(19/sqrt(2))^2 + y^2 = 361
361/2 + y^2 = 361
y^2 = 361/2
y = 19/sqrt(2)
We have maximum area at x = 19/sqrt(2) and y = 19/sqrt(2), or when x = y.
