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
Answer:
Students ticket = $4
Child ticket = $1
Adult ticket = $5
Step-by-step explanation:
Let the price of the student ticket be $x and the price of a child ticket be $y. An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).
1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then
2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then
Now, solve the system of two equations:
Solve the last equation
Students ticket = $4
Child ticket = $1
Adult ticket = $5
Expanded form is when you just write it out.
so 9 cubed becomes:
9×9×9
and 20 squared becomes:
20×20
the exponent tells you how many times to multiply that number by itself. so, whenever it asks for expanded form, you just write the number how ever many times the exponent tells you to and multiply them all.
Answer:
#3. 
Explanation:
Pythagorean theorem: leg² + leg² = hypotenuse²
