F(x) = 4x^2 + 12
g(x) = x - 1
(f o g)(x) = f(g(x)) = 4(x - 1)^2 + 12 = 4(x^2 - 2x + 1) + 12 = 4x^2 - 8x + 4 + 12 = 4x^2 - 8x + 16
(f o g)(3) = 4(3)^2 - 8(3) + 16 = 4(9) - 24 + 16 = 36 - 8 = 28
The cross section of the satellite dish is an illustration of a quadratic function
The quadratic function that models the cross-section is y = 1/6(x^2 - 9)
<h3>How to determie the equation of the cross-section?</h3>
The given parameters are:
Width = 6 feet
Depth = 1.5 feet
Express the width the sum of two equal numbers
Width = 3 + 3
The above means that, the equation of the cross section passes through the x-axis at:
x = -3 and 3
So, we have:
y = a(x - 3) * (x + 3)
Express as the difference of two squares
y = a(x^2 - 9)
The depth is 1.5.
This is represented as: (x,y) =(0,-1.5)
So, we have:
-1.5 = a(0^2 - 9)
Evaluate the exponent
-1.5 = -9a
Divide both sides by -9
a = 1/6
Substitute 1/6 for a in y = a(x^2 - 9)
y = 1/6(x^2 - 9)
Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)
Read more about quadratic functions at:
brainly.com/question/1497716
Answer:
Step-by-step explanation:
To find the center and the radius, we need to put the equation in the (x-a)^2+(y-b)^2=r^2 [a is the x-coordinate, b is the y-coordinate, and r is the radius].
(x+6)^2+(y+7)^2 - 36 - 49 + 69 = 0
(x+6)^2+(y+7)^2 - 16 = 0
(x+6)^2+(y+7)^2 = 16
(x+6)^2+(y+7)^2 = 4^2
The center is (-6,-7) and the radius is 4.
Hope this helps!
Y-intercept: (0,-3)
x-intercept: (0,5)
Answer:
C =85
Step-by-step explanation:
n=180-133+180-142=47+38=85
