Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 22x + 3
Factor out the negative
f(x) = -( 16x^2 -22x -3)
= -(8x+1)(2x-3)
Find the x intercepts
Set y = 0
0 = -(8x+1)(2x-3)
Using the zero product property
8x+1 =0 2x-3 = 0
8x = -1 2x = 3
x = -1/8 x =3/2
The x intercepts are ( -1/8, 0) and ( 3/2, 0)
The end behavior
-16 x^2 is the dominate term
Let x →-∞
f(-∞) = -16 (-∞)^2 = -16 (∞) = -∞
As x goes to negative infinity y goes to - infinity
Let x →∞
f(∞) = -16 (∞)^2 = -16 (∞) = -∞
As x goes to infinity y goes to - infinity
We know this is a downward facing parabola a < 0 and this is a quadratic
We have the x intercepts
We can find the axis of symmetry from the zeros
(-1/8+ 3/2) /2 = (-1/8 + 12/8)/2 = (11/8)/2 = 11/6
The axis of symmetry is x = 11/16
Using the axis of symmetry and the equation, we can find the maximum point
y = -(8*11/16+1)(2*11/16-3) = 169/16
The vertex is at (11/16, 169/16(
Answer:
Step-by-step explanation:
Domain is the set of all x values.
Range is the set of all y - values.
{ ( - 2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Domain = { -2 , 1 , 3 }
{ ( -2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Range = { - 2 , 0 , 4 }
Hope I helped!
Best regards! :D
Answer:
Option B. 93.46 ft³
Step-by-step explanation:
In the given question tow solids are given.
Their heights are same and the cross sectional areas at every level parallel to the respective bases are same which means total volume of solids are also same.
We have to find the volume of the cone.
We know the formula of volume of a pyramid
Now area of the base = area of a right angle triangle =
Here height of the right angle triangle = 8 ft
and base of the triangle =
Now area of base =
Now volume of cone = volume of pyramid =
Therefore Option B. is the answer.