Answer:
x = 20 in
L = 40 in
Step-by-step explanation:
Solution:-
- Denote the following:
The side of square cross section = x
The length of package = L
- Given that the combined length "L" of the package and girth "P" of the package must be less than and equal to 120 in
- The girth of the package denotes the Perimeter of cross section i.e square:
P = 4x
- The constraint for our problem in terms of combined length:
L + 4x ≤ 120
L = 120 - 4x .... Eq1
- The volume - "V" -of the rectangular package with a square cross section is given as:
V = L*x^2 ... Eq2
- Substitute Eq1 into Eq2 and form a single variable function of volume "V":
V(x) = 120*x^2 - 4x^3
- We are asked to maximize the Volume - " V(x) " - i.e we are to evaluate the critical value of "x" by setting the first derivative of the Volume function to zero:
d [ V(x) ] / dx = 240x - 12x^2
240x - 12x^2 = 0
x*(240 - 12x) = 0
x = 0, x = 20 in
- We will plug in each critical value of "x" back in function " V(x) ":
V (0) = 0
V(20) = 120(20)^2 - 4(20)^3
= 16,000 in^3
- The maximizing dimension of cross section is x = 20 in, the length of the parcel can be determined by the given constraint Eq1:
L = 120 - 4*20
L = 40 in
- The maximum volume of the rectangular package is with Length L = 40 in and cross section of Ax = ( 20 x 20 ):
Answer:
54 degrees.
Step-by-step explanation:
All triangles equal 180 degrees. So, 180 minus 104 minus 22 equals 54. Since you can add 54, 104, and 22 together to get 180, that means that is the correct answer.
Answer:
1st Graph: Function
2nd Graph: Function
3rd Graph: Not a function
4th Graph: Not a function
Step-by-step explanation:
We can determine if a graph is a function or not using the Vertical Line Test. Since we see that 1 and 2 pass but 3 and 4 pass, 1 and 2 are functions while 3 and 4 are not.
For this type of problem, go back to basic learning about shift to the right or left, up or down.
then check with desmos.com
Answer:4
Step-by-step explanation: please just trust me!
