Answer:
32
Step-by-step explanation:
32 × 1 = 32
8 × 4 = 32
Therefore, the LCM is 32
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3
. Find the
dimensions of the box that requires the least amount of cardboard.
Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize
A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make
the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute
this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing
something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax
or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t
hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From
these, we obtain x
2y = 8 = xy2
. This forces x = y = 2, which forces z = 1. Calculating second
derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum
for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices
of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small
so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither
closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage
something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each
of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus,
moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
Answer:
$6.50 per bag of popcorn
Step-by-step explanation:
let a bag of popcorn be represented by p and a candy bar be b
28p + 40b= $282
17p + 20b= $160.50
this is an example of stimatanelous equations
so you have to double the second equation to give 34p + 40b =$321
subtract the equations to give one
6p =$39
divide $39 by 6 to give the value of one bag of popcorn = $6.50
Answer:
5 people
Step-by-step explanation:
For each people Ms Hernandez bring to the zoo, she will pay $15.50, so if she go alone, 1×15.50, if she go with one person, 2×15.50, with three 3×15.50, and keep growing this way. The price each person pay is constant and equal to 15.50, and what will determine the final price is the number of people. Also remember that she always will have to pay $ 10 on parking, so you can write an equation with this:
15.50x +10 = y, as x being the number of people and y being the final price.
She have $100, so this is the max she can spend. Two know the number of people she can bring to the zoo, put 100 in place of y and find the value of x:
15.50x + 10 = 100
15.50x = 100 - 10
15.50x = 90
x = 90/15.50
x = 5.8
But there's no way to bring 0.8 person, so the max she can bring are 5 people, including her
