The statement best describes Cheryl's computer is option C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph.
<h3>How to find the function which was used to make graph?</h3>
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
If we know that the function crosses the x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Let's assume the graph of Cheryl's commute was like the one below.
We can see that she started at 0 mph.
One minute later, she was up to 65 mph, so she had accelerated (increased her speed).
At 6.5 min (5.5 min later) her speed was still 65 mph therefore, she was driving at a constant speed.
Over the next 2.5 min, her speed dropped to 45 mph, therefore she was decelerating.
Learn more about finding the graphed function here:
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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).
So you divide 0.8 by 6.25 and your answer is 7.8125 and then you add 5.5 minutes of your other number and you get the answer of 13.3125
Answer:
4) choice a 30%
5) choice b 62.5%
Step-by-step explanation:
4) 3/10 = 0.30 or 30%
5) 5/8 = 0.625 or 62.5%
