Answer:

The domain for x is all real numbers greater than zero and less than 5 com
Step-by-step explanation:
<em><u>The question is</u></em>
What is the volume of the open top box as a function of the side length x in cm of the square cutouts?
see the attached figure to better understand the problem
Let
x -----> the side length in cm of the square cutouts
we know that
The volume of the open top box is

we have



substitute

Find the domain for x
we know that

so
The domain is the interval (0,5)
The domain is all real numbers greater than zero and less than 5 cm
therefore
The volume of the open top box as a function of the side length x in cm of the square cutouts is

Caution: you need to use the same units of measurement throughout. If the spring stretches by 21 cm when a 135 newton object is attached, then you must ask for the mass (in newtons) of a fish that would stretch the spring by 62.1 cm.
We will need to assume that the spring is not stretched at all if and when no object is attached to the spring.
Write the ratio
21.0 cm 135 newtons
------------- = --------------------
62.1 cm x
Solve this for x. This x value represents the mass of a fish that would stretch the spring by 62.1 cm. You can cancel "cm" in the equation above:
21.0 135 newtons
------ = --------------------
62.1 x
Then 21.0x = (62.1)(135 newtons). Divide both sides of this equation by 21.0 to solve it for x.
At x = 0, y-coordinate is at -4 so that means f(0) = -4
Now for f(x) = 4, we need to find any x-coordinates such that y-coordinates is 4.
There are two possible answer: x = -8 and x = 8
So x = -8, 8
Hope this helps.
Answer:

Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to

we have
---> the radius is half the diameter

substitute

step 2
Find the volume of the cone
The volume of the cone is equal to

we have
we have
---> the radius is the same that the radius of the cylinder

substitute

step 3
Find the volume of the plastic object
we know that
The volume of the plastic object is equal to the volume of the cylinder minus the volume of the cone
so

assume


I think the answer is 1 1/8