2x+3y=60 solve for x...
x=(60-3y)/2
p=xy^3, using x from above:
p=y^3(60-3y)/2
p=(60y^3-3y^4)/2
dp/dy=(180y^2-12y^3)/2
dp/dy=90y^2-6y^2
dp/dy=0 when:
90y^2-6y^3=0
6y^2(15-y)=0, we know y>0 so
y=15, since x=(60-3y)/2
x=7.5
(We solved it this way because otherwise you get quartic equations and cubic derivatives, yuck :P)
If you cut a triangle out of a piece of paper, and move that triangle around (sliding, rotating, reflecting) then that triangle will retain its original shape and size. The three movement types mentioned are rigid motions. They do not change the size or shape of the triangle. If two triangles are congruent, then a sequence of one or more rigid motions can be applied to have them line up together.
Answer:
see below
Step-by-step explanation:
Usually, we're concerned about the relationship of y to x. Here, the question is asking you to consider the relationship of x to y.
The easiest way to find the answer to this one is to check the given explanations to see which is true. You can pretty much ignore the first row of the table and just look at the second row where x=5 and y=15.
- it is NOT TRUE that x is 3 times y (5 is not 3 times 15)
- it is TRUE that x is 1/3 of y (5 is 1/3 of 15)
- it is NOT TRUE that x is 5 times y (5 is not 5 times 15)
- it is NOT TRUE that x is 1/5 of y (5 is not 1/5 of 15)
_____
If you know your multiplication tables, you know that 15 = 3×5, so ...
5 = 15/3
5 = (1/3) × 15
The relationship of these numbers should not be a mystery.
Answer: 1208.96
Step-by-step explanation:
The volume of the cylinder is 
The volume of the prism is 
So, the total volume is 