What does parallel mean? Can you give an example of things that are parallel?
2 answers:
You might be interested in
Answer:
11.781 cubic inches (round accordingly)
Step-by-step explanation:
The formula for the volume of a cone is:
where r is the radius and h is the height.
For our ice cream cone:
d = 3 inches
r = 1.5 inches (the radius is half of the diameter)
h= 5 inches
So all we have to do is plug in our values and solve for the volume:
So our final answer is around 11.8 cubic inches.
Answer:
a. V = (20-x)
b . 1185.185
Step-by-step explanation:
Given that:
- The height: 20 - x (in )
- Let x be the length of a side of the base of the box (x>0)
a. Write a polynomial function in factored form modeling the volume V of the box.
As we know that, this is a rectangular box has a square base so the Volume of it is:
V = h *
<=> V = (20-x)
b. What is the maximum possible volume of the box?
To maximum the volume of it, we need to use first derivative of the volume.
<=> dV / Dx = -3 + 40x
Let dV / Dx = 0, we have:
-3 + 40x = 0
<=> x = 40/3
=>the height h = 20/3
So the maximum possible volume of the box is:
V = 20/3 * 40/3 *40/3
= 1185.185
We're given the implicit equation
x² + 2x + y² - 4y = 12
where "implicit" means that one of the variables is considered a function of the other. In this case, the variable y = y(x) depends on the value of the variable x - in other words, the possible values of y are implied by the value of x. We then say that this equation defines y as an implicit function of x.
We're also given the implicit derivative,
dy/dx = (-2x - 2)/(2y - 4)
which tells us the rate of change y as a function of both x and y. The value of dy/dx corresponds to the slope of the tangent line to the curve defined by the implicit equation above at some point (x, y).
The tangent line is horizontal when its slope is zero. This happens when
(-2x - 2)/(2y - 4) = 0
If y ≠ 2, then we can eliminate the denominator and we're left with
-2x - 2 = 0
Solve for x :
-2x = 2
x = -1
This tells us that the points on the curve with x-coordinate -1 have a tangent line to the curve that is horizontal.
The tangent line is vertical when its slope is undefined/infinite, or equivalently when the denominator of dy/dx is zero:
2y - 4 = 0
Solve for y :
2y = 4
y = 2
So any point on the curve with y-coordinate 2 will have a tangent line there that is vertical.
By completing the square in the implicit equation, we can easily identify where these points are located.
x² + 2x + y² - 4y = 12
x² + 2x + 1 + y² - 4y + 4 = 17
(x + 1)² + (y - 2)² = 17
This equation defines a circle centered at (-1, 2) with radius √17. When x = -1, we have
(y - 2)² = 17 ⇒ y = 2 ± √17
and when y = 2, we have
(x + 1)² = 17 ⇒ x = -1 ± √17
See the attached plot to see the circle and the tangents at these points.
