In City A, the temperature rises F from 8 A. M. to 9 A. M. Then the temperature drops F from 9 A. M. to 10 A. M. In City B, the temperature drops F from 8 A. M. to 9 A. M. Then the temperature drops F from 9 A. M. to 10 A. M. Write an expression that represents the change in temperature from 8 A. M. to 10 A. M. for each city. Simplify and interpret each sum. Use pencil and paper. Which city has the greater change in temperature? Which expression represents the change in temperature for City A?

Here is the full question.

In city A, the temperature rises 9° F from A.M to 9 A.M. Then the temperature drops 8°F from 9 A.M. to 10 A.M. in city B, the temperature drops 1°F from  8 A.M. to 9 A.M. Then the temperature drops 3°F from 9 A.M. to 10 A.M.

Write an expression that represents the change In temperature from  8 A.M. to 10 A.M for each city. Simplify and interpret each sum. Use a pencil and paper. Which expression represents the change in temperature for city A?

In City A, the expression for the change in temperature is = 9 + (-8)

The amount the temperature changes for City A = 1°F

In City B, the expression for the change in temperature is -1 + (-3)

The amount the temperature changes for City B = -4°F

Thus, City A has a greater change in temperature.

Step-by-step explanation:

From the information above; Given that:

In City A, the rise in temperature from 8 A.M to 9 A.M is = 9°F

In City A, the drop in temperature from 9 A.M to 10 A.M = 8°F

Similarly;

In City B, the drop in temperature from 8 A.M to 9 A.M = 1°F

In City B, the drop in temperature from 9 A.M to 10 A.M = 3°F

∴

For City A

The temperature change from 8 A.M to 10 A.M are :

8 A.M to 9 A.M = +9°F

9 A.M to 10 A.M = -8°F

In conclusion, The sum for the change from 8 A.M to 10 A.M = 9 + (-8) = 1°F

For City B

The temperature change from 8 A.M to 10 A.M are:

8 A.M to 9 A.M = -1°F

9 A.M to 10 A.M = -3°F

In conclusion, The sum for the change from 8 A.M to 10 A.M = -1 + (-3) = -4°F

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step-by-step explanation:

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step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt