i need help...2 real quick questions for ya...?

Question

okay, does anyone know the answers to the following word problems? :::


"On average, and elephant lives from 30-40 years. Write an absolute value inequality that represents the typical ages of an elephant."



"Most fish can adjust to a change in the water temp. of up to 15 degrees F. if the change is not sudden. suppose a lake trout is living comfortably in water that is 58 degrees F. Write an absolute value inequality the represents the range of temp`s at which the lake trout can survive."

if someone can help me out...i`d appreiciate it soo much!!! i`m so lost. thanks!!! =)

Answer 1

In general, find the midpoint (take the average of the high and low values). Then find out how far to the top and bottom of the range.

So for 30-40, the mid-point is (30+40)/2 = 35. And the distance to the low value or high value is 5 (+/- 5 years)

For the age of an elephant:
| x-35 | <= 5

Similarly for the fish, the mid-point is already given as 58 degrees and the range is +/- 15 degrees.

For the temperature of the fish:
| x-58 | <= 15

If you graph these you'll see that the first case covers all ages from 30 to 40, but ages (values of x) below or above are not included. Same thing with the temperature ranges. 43 through 73 are included, but extreme temperatures (lower or higher) are not.

Answer 2

Let y be the average lifespan of an elephant in years.

30 <= y <= 40

Let t be the temp. of the fish water in degrees Fahrenheit

(58-15) <= t <= (58+15)
43 <= t <= 73

The <= means "less than or equal to"

Answer 3

On the elephant problem, they should have told you to either include the highest or least number. If it's the lowest it would be

|30=>x>40| You got to include the absolute symbols (||). If they give you an interval, you just put x in the middle and specify that it should be higher than the lowest and lesser than the highest. Depending on what they specify determines where the greater than/less than or equal to sign goes (<=, >=).

Same goes for the second problem.

Answer 4

Subract the number in the middle of the range, and the absolute value will be within half of the range. So,

|x-35|<5

and

|x-58|<15

Answer 5

1. |x + 35| < 5, which is equivalent to
-5 < x + 35 < 5, or 30 < x < 40.

2. |x + 58| < 15.