Answer:
The 2nd Graph is a function.
Step-by-step explanation:
You can tell it's a function because if you flatten the individual line segments along the x-axes, they all connect to form one long line.
HOWEVER, if some of the dots at the end of each line segment were empty circles instead, then it would not be considered a function. You can think of these as holes, not allowing the line to connect in those or that area.
Did that help? ;-;
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:
A. Area in square inches = 1760 square inches
B. Area in square feet = 12.2 square feet
C. 1 square inch = 
feet
Step-by-step explanation:
Given,
Length of the rectangle (l) = 55 inches
Breath of the rectangle (b) = 32 inches
A. Area of the rectangle = length × breath
⇒ 55 × 32
⇒ 1760 square inches
Area in square inches = 1760 square inches
B. 1 foot = 12 inches
1 inch = 
feet
1 square inch = feet
∴ 1760 square inches = 
feet
⇒ 12.2222 square feet
Area in square feet = 12.2 square feet
C. 1 square inch = feet
Answer:
$4.43
Step-by-step explanation:
10 bagels cost $3.69. 1 bagel costs $3.69/10=$0.369
12 bagels cost $0.369×12=$4.43
Answer:
Step-by-step explanation:
6,0 would be your coordinates
2,4
6,12
meaning that the numbers are multiplied by three. you can see the points without having to plot it on a graph
