The volume as a function of the location of that vertex is
... v(x, y, z) = x·y·z = x·y·(100-x²-y²)
This function is symmetrical in x and y, so will be a maximum when x=y. That is, you wish to maximize the function
... v(x) = x²(100 -2x²) = 2x²(50-x²)
This is a quadratic in x² that has zeros at x²=0 and x²=50. It will have a maximum halfway between those zeros, at x²=25. That maximum volume is
... v(5) = 2·25·(50-25) = 1250
The maximum volume of the box is 1250 cubic units.
Answer:
-8x - 22
Step-by-step explanation:
Step 1: Define
g(x) = -8x - 3
g(2) is x = 2
Step 2: Find g(2)
g(2) = -8(2) - 3
g(2) = -16 - 3
g(2) = -19
Step 3: Find g(x) + g(2)
-8x - 3 + -19
-8x - 3 - 19
-8x - 22
Answer:
See explanation
Step-by-step explanation:
So what you would need to do is take 300/10
300/10 which is 1/10 of 300, would be 30
You can also check your work by doing 30 x 10
This equals 300, so its correct.
Answer:
Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.
Step-by-step explanation:
With the information provided, you can say that the sum of the pounds of each type of candy is equal to 7, which can be expressed as:
x+y=7
Also, the statement indicates the 7 pound box costs $3.65 and you can say that the sum of the results of multiplying the price of each candy for the number of pounds is equal to $3.65, which is:
0.45x+0.65y=3.65
You have the following equations:
x+y=7 (1)
0.45x+0.65y=3.65 (2)
Now, you have to solve for x in (1):
x=7-y (3)
Then, you have to replace (3) in (2):
0.45(7-y)+0.65y=3.65
3.15-0.45y+0.65y=3.65
0.20y=0.50
y=0.50/0.20
y=2.5
Finally, you can replace the value of y in (3) to find x:
x=7-y
x=7-2.5
x=4.5
According to this, the answer is that Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.
An equation for those could be: x*y= t*y-10= 30 so x,y,t could be 6,5,8
