M is directionly proptional to r squared when r=2, m=14

A)work out the value of m when r is 12

b) work out the value or r when m is 224

9514 1404 393

  A) 504

  B) 8

Step-by-step explanation:

The statement of proportionality can be written as the equation ...

  m = kr²

Then we can find k from ...

  k = m/r² = 14/2² = 7/2

That is, ...

  m = (7/2)r²

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Using this relation, we can find m for r=12:

  m = (7/2)·12² = 7·72

  m = 504 . . . for r = 12

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And, we can use the same equation to solve for r when m=224.

  224 = 7/2·r²

  r² = 64

  r = √64

  r = 8 . . . for m = 224

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

it should be a.

hope it