Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. the cardboard is 10 cm by 10 cm. the volume v(x) in cubic cm of the open top box is a function of the side length x in cm of the square cutouts

The volume of a shape is the amount of space in it;

The volume as a function of side length (x) is:

From the question, we have the dimension of the cardboard to be;

When side length (x) is removed from the cardboard, the dimension of the box becomes:

So, the volume of the box is:

Substitute known values

Expand

Expand

Rewrite as:

Express as a function

Hence, the required function is:

Read more about volume functions at:

link

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

The question is

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

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.