Chapter 4.1, Problem 42PPS

a)

To determine

To use the equation $V=12(24-h)$ to find the related ordered pairs $(h,V)$ in tabular form and accordingly graph them in XY plane to get the nature of volume V as the height h increases.

Answer to Problem 42PPS

The required table showing all ordered pairs of form $(h,V)$ be :

h (in inches)	$V=12(24-h)$	$(h,V)$
4	Y1 $V=12\left(24-4\right)=12\times 20=240$	3 $\left(4,240\right)$
9	$V=12\left(24-9\right)=12\times 15=180$	$\left(9,180\right)$
14	$V=12\left(24-14\right)=12\times 10=120$	$\left(14,120\right)$
19	$V=12\left(24-19\right)=12\times 5=60$	$\left(19,60\right)$

Explanation of Solution

Given information: The volume V of seed in a bird feeder is given by the equation

  $V=12(24-h)$ , where h is the height .

Concept used: First let few positive increasing values of h , and then by plugging them in given equation, it is calculated the corresponding value of variable V , to get the required ordered pair $(h,V)$ in tabular form and then in graphical form by plotting them in XY plane.

Calculation: Table representing relation between h and V in ordered pair form $(h,V)$ is:

h (in inches)	$V=12(24-h)$	$(h,V)$
4	$V=12\left(24-4\right)=12\times 20=240$	$\left(4,240\right)$
9	$V=12\left(24-9\right)=12\times 15=180$	$\left(9,180\right)$
14	$V=12\left(24-14\right)=12\times 10=120$	$\left(14,120\right)$
19	$V=12\left(24-19\right)=12\times 5=60$	$\left(19,60\right)$

Conclusion: By above calculation in tabular form and from graph, it is cleared that as the height increases, the volume of seed, decreases.

b)

To determine

To use the equation $V=12(24-h)$ to graph the ordered pairs $(h,V)$ in XY plane to get the nature of volume V as the height h increases.

Answer to Problem 42PPS

Calculated ordered pairs in XY plane are shown as:

  

Explanation of Solution

Given information: The volume V of seed in a bird feeder is given by the equation $V=12(24-h)$ , where h is the height .

Concept used: First let few positive increasing values of h , and then by plugging them in given equation, it is calculated the corresponding value of variable V , to get the required ordered pair (h,V) in tabular form and then in graphical form by plotting them in XY plane.

Calculation: On graphing calculated coordinates in XY plane, it looks as:

  

Conclusion: By above calculation in tabular form and from graph, it is cleared that as the height increases, the volume of seed, decreases.

c)

To determine

To use the equation $V=12(24-h)$ to find the related ordered pairs $(h,V)$ in tabular form and accordingly graph them in XY plane to get the nature of volume V as the height h increases.

Answer to Problem 42PPS

By above graph, it is cleared that as the height increase, the volume of seed in a bird feeder decreases.

Explanation of Solution

Given information: The volume V of seed in a bird feeder is given by the equation

  $V=12(24-h)$ , where h is the height .

Concept used: Here, first let few positive increasing values of h , and then by plugging them in given equation, it is calculated the corresponding value of variable V , to get the required ordered pair (h,V) in tabular form and then in graphical form by plotting them in XY plane.

Calculation: Graph shows that as h coordinates increase, the values of V decrease. That concludes that as the height increases, the volume of seed, decreases.

Conclusion: By above calculation in tabular form and from graph, it is cleared that as the height increases, the volume of seed, decreases.