Question

The graph of the function \( h \) represents how the values of \( s \) and \( h(s) \) are related and vary together. Let \( V=h(s) \). Recall that \( s \) represents the length of the side of the square that is cut from each corner of a 15 inch by 18 inch of paper and \( h(s) \) represents the box's volume. Use the three modes in applet to answer the following questions. Drag the purple \( X \) to vary the value of the length of the side of the square cutout. a. Estimate \( h(2) \). Preview b. Solve \( h(s)=200 \) for \( s \). (Enter a comma-seperated list, if needed.) \( s= \) Preview c. As \( s \) increases from 3 to 5 , the value of \( h(s) \) Select an answer \( \boldsymbol{V} \) from to d. Determine the range of \( h \) ? Use interval notation. Preview e. Use the graph of \( h \) to evaluate \( \frac{h(2.5)-h(1)}{2.5-1} \) Select an answer \( \boldsymbol{V} \) Preview Which of the following decribes what \( \frac{h(2.5)-h(1)}{2.5-1} \) represents in the context of this problem. Select all that apply. The average rate of change of the box's volume with respect to the box's side-length, \( s \), on the interval from \( s=1 \) to \( s=2.5 \) inches. The constant rate of change of the box's volume with respect to its side length on the interval from \( s=1 \) to \( s=2.5 \) that would result in the same change in volume as was achieved by \( h \) on that interval. The ratio of the change in the box's volume and the change in the value of \( s \) on the interval from \( s=1 \) to \( s=2.5 \). The change in the box's volume as the value of \( s \) increases from 1 to \( 2.5 \).

          The graph of the function \( h \) represents how the values of \( s \) and \( h(s) \) are related and vary together. Let \( V=h(s) \). Recall that \( s \) represents the length of the side of the square that is cut from each corner of a 15 inch by 18 inch of paper and \( h(s) \) represents the box's volume.

Use the three modes in applet to answer the following questions. Drag the purple \( X \) to vary the value of the length of the side of the square cutout.
a. Estimate \( h(2) \).
Preview
b. Solve \( h(s)=200 \) for \( s \). (Enter a comma-seperated list, if needed.) \( s= \)
Preview
c. As \( s \) increases from 3 to 5 , the value of \( h(s) \) Select an answer \( \boldsymbol{V} \) from to
d. Determine the range of \( h \) ? Use interval notation.
Preview
e. Use the graph of \( h \) to evaluate \( \frac{h(2.5)-h(1)}{2.5-1} \)
Select an answer \( \boldsymbol{V} \) Preview
Which of the following decribes what \( \frac{h(2.5)-h(1)}{2.5-1} \) represents in the context of this problem. Select all that apply.
The average rate of change of the box's volume with respect to the box's side-length, \( s \), on the interval from \( s=1 \) to \( s=2.5 \) inches.

The constant rate of change of the box's volume with respect to its side length on the interval from \( s=1 \) to \( s=2.5 \) that would result in the same change in volume as was achieved by \( h \) on that interval.
The ratio of the change in the box's volume and the change in the value of \( s \) on the interval from \( s=1 \) to \( s=2.5 \).
The change in the box's volume as the value of \( s \) increases from 1 to \( 2.5 \).

The graph of the function h represents how the values of s and h(s) are related and vary together. Let V=h(s). Recall that s represents the length of the side of the square that is cut from each corner of a 15 inch by 18 inch of paper and h(s) represents the box's volume.

Use the three modes in applet to answer the following questions. Drag the purple X to vary the value of the length of the side of the square cutout.
a. Estimate h(2).
Preview
b. Solve h(s)=200 for s. (Enter a comma-seperated list, if needed.) s=
Preview
c. As s increases from 3 to 5 , the value of h(s) Select an answer V from to
d. Determine the range of h ? Use interval notation.
Preview
e. Use the graph of h to evaluate (h(2.5)-h(1))/(2.5-1)
Select an answer V Preview
Which of the following decribes what (h(2.5)-h(1))/(2.5-1) represents in the context of this problem. Select all that apply.
The average rate of change of the box's volume with respect to the box's side-length, s, on the interval from s=1 to s=2.5 inches.

The constant rate of change of the box's volume with respect to its side length on the interval from s=1 to s=2.5 that would result in the same change in volume as was achieved by h on that interval.
The ratio of the change in the box's volume and the change in the value of s on the interval from s=1 to s=2.5.
The change in the box's volume as the value of s increases from 1 to 2.5.

Added by Emilia Q.

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