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My name is Ann [436]
2 years ago
9

[SCREENSHOT INCLUDED] Which of the following is the best estimate of f '(2) based on this table of values?

Mathematics
1 answer:
mel-nik [20]2 years ago
6 0

Using derivatives, it is found that the best estimate of f '(2) based on this table of values is of 10.

The rate of change <u>from x = 0 to x = 2</u> is given by:

r_1 = \frac{2 - (-16)}{2 - 0} = \frac{18}{2} = 9

From <u>x = 2 to x = 4</u>, it is given by:

r_2 = \frac{24 - 2}{4 - 2} = \frac{22}{2} = 11

The average of these rates is:

A = \frac{r_1 + r_2}{2} = \frac{9 + 11}{2} = 10

Hence, the best estimate of f '(2) based on this table of values is of 10.

To learn more about derivatives, brainly.com/question/18590720

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A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom
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a) 0.012ft³

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c)0.791 lb

d) 0.012ft³

e) 6 inches

Step-by-step explanation:

a) To determine the volume of the shell of the jar we must determine the volume of the hollow cylinder:

V=3.1416\cdot{h}\cdot{(R^2-r^2)

Where r is the inside radius and R the outer radius.

V=3.1416\cdot{6}\cdot{(3.1875^2-3^2)=21.87

convert to cubic ft:

=21.87\cdot{0.0005787}=0.01266

The volume of the glass shell is 0.012 ft³

b) The weight of the cylinder can be determined because we have the volume and the density. Weight is defined as the product of volume and density:

M=p\cdot{v}=165\cdot{0.01266}=2.09

The weight of the jar is 2.09 lb

c) The displacement of water is just the density of water mutliplied by the volume of the jar:#

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d) The volume of the water displaced is:

[tex]=0.791/62.5=0.01266

e) The jar will be fully submerged because the density of the jar is larger than water.

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