Answer:
Quadratic Equation:


From the standard form of a Quadratic Function, we get:

Discriminant:



From the discriminant, we conclude that the equation will have two real solutions.
State that:



By the way, solving the equation given:





Answer:
- 21
Step-by-step explanation:
The minimum value occurs at the vertex of the function
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Given
f(x) = x² - 6x - 12
add/ subtract ( half the coefficient of the x- term)² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 - 12
= (x - 3)² - 21
with vertex = (3, - 21 )
The minimum is the value of k, that is minimum value = - 21
You can't tell the dimensions from the area. There are an infinite number of correct answers. The length of the fence is 2 times (length of the pond + width) and the length and width can be anything, just as long as their product is 2956.5 .
<h3>Given:</h3><h3>Large cone:</h3>
<h3>Small cone:</h3>
<h3>Note that:</h3>
<h3>To find:</h3>
- The volume of the frustum of the given cone.
<h3>Solution:</h3>
- Frustum is a part of a cone formed by cutting off the top by a parallel plane.

Let's solve!
First, let's find the volume of the smaller cone.
Substitute the values according to the
formula.


Now, we can round off to the nearest hundredth.
The value in the thousandths place is smaller than 5 so we won't have to round up.

Next, let's find the volume of the bigger cone.
Substitute the values according to the formula.


Now, we can round off to the nearest hundredth.
The value in thousandths place is smaller than 5 so we won't have to round up.

Now, we can find the volume of the frustum.
We'll have to minus the volume of the smaller cone from the bigger cone.


<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>