Hello there!
There are two ways to find the minimum value of this function, but before I show you how, I am going to teach you a little bit about minimum value.
The minimum value on a parabola is the vertex or turning point. This means that the slope of the tangent line is horizontal, having a slope of 0.
The algebraic way to find the minimum or maximum value on a parabola is to use the formula -b/2a. Let's do it...
y=4x^2+4x-35
where a=4, b=4, and c=-35
-b/2a
-4/2(4)
-4/8
-1/2
Now let me show you the other way...
Take the derivative of
y=4x^2+4x-35
y'=8x+4
And set it equal to 0...
8x+4=0
8x=-4
x=-1/2
We got the same answer. Now that we know x=-1/2, plug this into the original equation to find y.
y=4x^2+4x-35
y=4(-1/2)^2+4(-1/2)-35
y=-1-2-35
y=-38
So the minimum point on this parabola is (-1/2,-38)
I really hope th
Answer:
600 Cheese and 900 Pepperoni
Step-by-step explanation:
Setup the equation with 2c(Cheese) + 2.5p(Pepperoni) = $3450(Total Made).
In addition to the equation c + p = 1500(Number of pizzas sold)
Using the second equation (c + p = 1500) solve for one of the variables.
Lets use :
- p = 1500 - c
- Plus this equation into the original equation, 2c + 2.5(1500 - c) = 3450
- Distribute 2.5, 2c + 3750 - 2.5c = 3450
- Combine like terms -0.5c + 3750 = 3450
- Solve for c: c = 600
- Plus 600 in for c into any equation ( lets use c + p = 1500)
- 600 + p = 1500
- P = 900
Answer:
The height of the cone h = 27(x^4)y
Step-by-step explanation:
Firstly, we calculate the volume of the cylinder.
Mathematically, the volume of the cylinder is pi * r^2 * h
using the radius x and height y
The volume V of the cylinder is ;
V = pi * x^2 * y
Now we know they have the same volume V, the formula for the volume of a cone is ;
1/3 * pi * r^2 * h
Substituting the values of r to be 1/3x and the height which is not given here left as h, we have the volume of the cone to be;
V = 1/3 * pi * (1/3x)^2 * h = pi * x^2 * y
The pi gives way as it cancels out on both sides and we have the following;
h/27x^2 = x^2y
Mathematically h = x^2 * y * 27x^2
h = 27(x^4)y
p.s: I personally feel the radius of the cone was to be given as x/3 and not 1/3x . It is in that way we can have the height of the cone purely in y terms and no x
Answer:
whats the question
Step-by-step explanation:
Answer:
x=-8
Step-by-step explanation:
Subtract 2 from both sides
Simplify
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
Subtract 2x from both sides
Simplify
