course Mth 158

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Question: * 2.5.8 / 2.7.8 (was 2.6.6). y inv with sqrt(x), y = 4 when x = 9.

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Your solution:

Substitre: 4 = k / sqrt(9) so k= 4(3) = 12 so put in original to give

y = 12 / sqrt(x)

Confidence rating:

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Given Solution:

* * The inverse proportionality to the square root gives us y = k / sqrt(x).

y = 4 when x = 9 gives us

4 = k / sqrt(9) or

4 = k / 3 so that

k = 4 * 3 = 12.

The equation is therefore

y = 12 / sqrt(x). **

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Question: * 2.5.12 / 2.7.12 (was 2.6.10). z directly with sum of cube of x and square of y; z=1 and x=2 and y=3.

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Your solution:

z = k (x^3 + y^2) so substitute to get k= 1/17 put back in the original to get

z = (x^3 + y^2) / 17

Confidence rating:

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Given Solution:

* * The proportionality is

z = k (x^3 + y^2).

If x = 2, y = 3 and z = 1 we have

1 = k ( 2^3 + 3^2) or

17 k = 1 so that

k = 1/17.

The proportionality is therefore

z = (x^3 + y^2) / 17. **

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Question: * 2.5.20 / 2.7.20 (was 2.6.20). Period varies directly with sqrt(length), const 2 pi / sqrt(32)

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Your solution:

T = k sqrt(L)

k = 2 pi / sqrt(32)

T = 2 pi / sqrt(32) * sqrt(L)

Confidence rating:

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Given Solution:

* * The equation is

T = k sqrt(L), with k = 2 pi / sqrt(32). So we have

T = 2 pi / sqrt(32) * sqrt(L). **

**** What equation relates period and length? ****

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Self-critique (if necessary):

I think this equation relate period and length:

Period = 2 pi(length/a)^b

Self-critique Rating:

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Question: * 2.5.42 / 2.7.42 (was 2.7.34 (was 2.6.30). Resistance dir with lgth inversely with sq of diam. 432 ft, 4 mm diam has res 1.24 ohms. **** What is the length of a wire with resistance 1.44 ohms and diameter 3 mm? Give the details of your solution.

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Your solution:

R = k * L / D^2 substitute

1.24 = k * 432 / 4^2 simplify and get k = .046 so we put in original R = .046 * L / D^2

L = R * D^2 / (.046) and then L = 1.44 * 3^2 / .046 = 280 so wire is 280 ft.

Confidence rating:

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Given Solution:

* * We have

R = k * L / D^2. Substituting we obtain

1.24 = k * 432 / 4^2 so that

k = 1.24 * 4^2 / 432 = .046 approx.

Thus

R = .046 * L / D^2.

Now if R = 1.44 and d = 3 we find L as follows:

First solve the equation for L to get

L = R * D^2 / (.046). Then substitute to get

L = 1.44 * 3^2 / .046 = 280 approx.

The wire should be about 280 ft long. **

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