On some tubes of caulking, the diameter of the circular nozzle opening can be adjusted to produce lines of varying thickness. The table shows the length (L) of caulking obtained from a tube when the nozzle opening has diameter (d) and cross-sectional area (A).
31) Does L vary inversely with d? Explain. d (in.) A (in.2) L (in.)
.125 0.012 1440
.25 0.049 360
.375 0.110 160
32) Does L vary inversely with A? Explain. .5 0.196 90
If L varies inversely with d the product must be constant.
.125*1440=.25*360=.375*160 These are not the same so L and d do not vary inversely
If L and A vary inversely their products must be the same
.012*1440=.049*360=.110*160 These products are 17.28, 17.64, and 17.6 they are not the same but they are close if the answers were rounded in the table they could be inversely related. If the numbers in the table are exact they are not inversely related
To determine whether L (length of caulking) varies inversely with d (diameter of the nozzle opening) or A (cross-sectional area), we can look at the values in the provided table.
Inversely proportional relationships can be identified by checking if the product of the variables remains constant. If L * d or L * A is constant for different values of d or A, respectively, then L is inversely related to that variable.
Let's first check if L varies inversely with d by calculating L * d for each row in the table:
For the first row: L * d = 1440 * 0.125 = 180
For the second row: L * d = 360 * 0.25 = 90
For the third row: L * d = 160 * 0.375 = 60
Since the product L * d is not constant for all the rows, we can conclude that L does not vary inversely with d.
Next, let's check if L varies inversely with A by calculating L * A for each row in the table:
For the first row: L * A = 1440 * 0.012 = 17.28
For the second row: L * A = 360 * 0.049 = 17.64
For the third row: L * A = 160 * 0.110 = 17.60
For the fourth row: L * A = 90 * 0.196 = 17.64
Since the product L * A is approximately constant (around 17.6) for all the rows, we can conclude that L varies inversely with A. This means that as the cross-sectional area of the nozzle opening increases, the length of caulking obtained decreases, and vice versa.
To summarize:
31) L does not vary inversely with d.
32) L varies inversely with A.