SOLUTION: I understand a and c of this problem but I cannot figure out b and d because of the month to days thing. The question is;
Newborn blue whales are approximately 24 feet long and
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Question 219561: I understand a and c of this problem but I cannot figure out b and d because of the month to days thing. The question is;
Newborn blue whales are approximately 24 feet long and weigh 3 tons. Young whales are nursed for 7 months, and by the time of weaning they often are 53 feet long and weigh 23 tons. Let L and W denote the length (in feet) and the weight (in tons), respectively, of a whale that is t months of age.
a.) If L and t are linearly related, express L in terms of t.
L=mt+b
53=m(7)+24
29/7=m
L=(29/7)m+24
b.) What is the daily increase in the length of a young whale? (Use 1 month= 30 days)
???
L=(29/7)?+24
c.) IF W and t are linearly related, express W in terms of t.
W=mt+c
23=m(7)+3
20/7=m
W=(20/7)m+3
d.) What is the daily increase in the weight of a young whale?
W=(20/7)?+3
Found 2 solutions by jsmallt9, solver91311:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
a.) If L and t are linearly related, express L in terms of t.
L=mt+b
53=m(7)+24
29/7=m
So far so good.
L=(29/7)m+24
Actually this should be
L=(29/7)t+24
b.) What is the daily increase in the length of a young whale? (Use 1 month= 30 days)
In part (a) you figured out the slope of the linear relationship between length and age. The slope represents how much the length changes per unit increase in the age. Since the time, t, is measured in months the slope is how many feet the length increase for each month. So the whale increases in length 29/7 feet per month. To find out what this is per day (and since we're told to use 1 month = 30 days), just divide by 30. The daily increase in length = feet per day.
c.) IF W and t are linearly related, express W in terms of t.
W=mt+c
23=m(7)+3
20/7=m
W=(20/7)m+3
Again, this should be
W=(20/7)t+3
d.) What is the daily increase in the weight of a young whale?
With the same logic as part (b), the daily increase would be tons per day.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have an error in parts A and D. I think perhaps you confused the symbol m meaning slope in a linear equation and the fact that time t is measured in months.
The correct answer to part A is:
And the correct answer to part D is:
As to part B:
The length at zero months is:
\,+\,24\ =\ 24)
The length at one month is:
\,+\,24\ =\ \frac{29}{7}\,+\,24)
And the difference is:
feet
meaning that the whale increases its length that much each month, or each 30 days. Therefore, the whale will increase its length one-thirtieth of that amount each day, namely:
feet.
You can do your own arithmetic.
Do part D the same way, namely take the slope number m from the weight equation and divide it by 30.
John
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