query10

#$&*

course MTH 173

8/7/11

010. `query 10

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Question: `q query problem 1.6.7 5th ed; 1.6.12 4th; 1.6.9 (was 1.10.16)cubic polynomial

representing graph. What cubic polynomial did you use to represent the graph?

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Your solution:

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y = n(x-1)(x-5)(x+2)

2 = n(-1)(-5)(2)

2 = 10n

n = .2

y = .2(x-1)(x-5)(x+2)

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confidence rating #$&*:3

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Given Solution:

*&*& The given function has zeros at x = -2, 1, 5, so y = k (x+2)(x-1)(x-5).

At x = 0 the function has value 2, so 2 = k (0+2)(0-1)(0-5), or 2 = 10 k.

Thus k = .2 and the function is

y = .2 ( x+2)(x-1)(x-5). **

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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Question: `q Query problem 1.6.14 5th ed; 1.6.15 4th ed; 1.6.15 (formerly 1.4.19) s = .01 w^.25

h^.75what is the surface area of a 65 kg person 160 cm tall?

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Your solution:

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s = .01(65)^.25(160)^.75

s = 1.28m^2

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confidence rating #$&*:3

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Given Solution:

** Substituting we get

s = .01 *65^.25 *160^.75 = 1.277meters^2 **

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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Question: `q What is the weight of a person 180 cm tall whose surface area is 1.5 m^2?

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Your solution:

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1.5m^2 = .01(w)^.25(180)^.75

3.05237 = w^.25

(3.05237)^4 = (w^.25)^4

86.8 kg =~ w

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confidence rating #$&*:3

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Given Solution:

** Substituting the values we get

1.5 = .01 w^.25*180^.75 . Dividing both sides by 180:

1.5/180^.75

.01w^.25. Dividing both sides by .01:

3.05237 = w^.25 Taking the fourth power of both sides:

w = 3.052^4 = 86.806 **

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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Question: `q For 70 kg persons what is h as a function of s?

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Your solution:

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s = .01 (70)^.25 (h^.75)

(100s/(70^.25))^(4/3) = (h^.75)^(4/3)

112.62(s^(4/3)) =~ h

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confidence rating #$&*:3

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Given Solution:

** Substituting 70 for the weight we get

s = .01 *70^.25 h^.75

s = .02893 h^.75

s/.02893 = h^.75

34.60 s = h^.75

Taking the 1/.75 = 4/3 power of both sides:

(34.60 s)^(4/3) = h

h = 111 s^(4/3), approximately **

To solve

34.60 s = h^.75

for h you need to take the 1/.75 power of both sides, which gives you

(34.60 s)^(1/.75) = (h^.75)^(1/.75). The right-hand side becomes h^(.75 * (1/.75) ) = h^1 =

h, so we have

h = (34.60 s)^(1 / .75). Since 1 / .75 reduces to 4/3, we have

h = (34.70 s)^(4/3).

1 / .75 = 4/3 for the same reason $1.00 / $.75 = 4/3 (ratio of four quarters to three quarters,

where by 'quarter' I mean the coin we most commonly put into vending machines).

More formally 1 / .75 means 1.00 / .75 = 100 / 75. Dividing numerator and denominator by 25

reduces this to 4/3.

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Self-critique (if necessary):OK

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Self-critique Rating:OK

&#Very good responses. Let me know if you have questions. &#