Question
4. Find the tangent line approximation, L(x), of f(x)=x^2/3 at x = 8.
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)
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)
Answers
I 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
#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
Thank you so much! I'm getting number 7 as .9%, correct?
Nevermind, I figured them out! :) Thank you!
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