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January 27, 2015

January 27, 2015

Posted by **Samantha** on Thursday, December 19, 2013 at 9:25pm.

L(x) = 4/3x-20/3

L(x) = 2/3x+8

L(x) = 4(x-8)

L(x) = 1/3x + 4/3

*L(x) = 4/3x - 8/3

5. A balloon is rising at a constant speed of 5 ft/sec. A boy is cycling along a straight road at a constant speed of 15 ft/sec. When he passes under the balloon, it is 5 feet above him. Approximately how fast is the distance between the boy and the balloon increasing 3 seconds after he has passed underneath it?

12 ft/sec

16 ft/sec

20 ft/sec

*25 ft/sec

30 ft/sec

6. A factory is manufacturing a rectangular storage container with an open top. The volume of the container is 10 ft^3, and the length of the base is twice the width. The material for the base costs $10 per square foot, and the material for the sides costs $6 per square foot. Find the cheapest cost to make the container, given the conditions.

$27.85

$46.19

*$87.24

$147.85

$163.54

7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.

0.6%

0.9%

*1.2%

1.5%

1.8%

8. An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft^3/min, find the rate of change of the depth of the water when the water is 10 feet deep.

0.007 ft/min

0.449 ft/min

0.018 ft/min

*0.051 ft/min

0.065 ft/min

9. For the function f(x)=Inx/x^2, find the approximate location of the critical point in the interval (0, 5).

(0.5, −2.773)

(1, 0)

(1.649, 0.184)

*(2, 0.173)

(0.778, −1.813)

- Calc help - check rest of answers, please? -
**Reiny**, Thursday, December 19, 2013 at 10:42pmI did #4 and #5 for you in your previous post

#6

let the width of the base be x

let the length of the base be 2x

let the height be y

given: Volume = 10

2x^2y = 10

y = 5/x^2

which was the last choice.

cost = 10(2x^2) + 6( 2 ends + front + back)

= 20x^2 + 6(2xy + 2xy + 2xy)

= 20x^2 + 36xy

= 20x^2 + 36x(5/x^2) = 20x^2 + 180/x

d(cost)/dx = 40x - 180/x^2

= 0 for a min cost

40x = 180/x^2

x^3 = 180/40 = 9/2

x = (9/2)^(1/3)

subbing that into cost = ...

I get $163.54

- Calc help - check rest of answers, please? -
**Samantha**, Thursday, December 19, 2013 at 10:57pmThank you so much! I'm getting number 7 as .9%, correct?

- Calc help - check rest of answers, please? -
**Samantha**, Thursday, December 19, 2013 at 11:25pmNevermind, I figured them out! :) Thank you!

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