Mathematics, 29.10.2019 06:31 lilianna25
The area and circumference of a circle of radius r are given by a(r) = πr2 and c(r) = 2πr. suppose we increase
the radius of a sphere by 0.001 units from r to r + 0.001.
a. use the binomial theorem to write an expression for the increase in area volume a(r + 0.001) − a(r) as a
sum of three terms.
b. write an expression for the average rate of change of the area as the radius increases from r to r + 0.001.
c. simplify the expression in part (b) to compute the average rate of change of the area of a circle as the radius
increases from r to r + 0.001.
d. what does the expression from part (c) resemble?
e. why does it make sense that the average rate of change should approximate the area of a circle? think about
the geometric figure formed by a(r + 0.001) − a(r). what does this represent?
f. how could we approximate the area of the shell using circumference? and the average rate of change for the
area?
g. find the difference between the average rate of change of the area and c(r) when r = 1.
Answers: 2
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The label on the car's antifreeze container claims to protect the car between ? 40°c and 125°c. to convert celsius temperature to fahrenheit temperature, the formula is c = 5 over 9 (f ? 32). write and solve the inequality to determine the fahrenheit temperature range at which this antifreeze protects the car. ? 40 > 5 over 9 (f ? 32) > 125; ? 40 > f > 257 ? 40 < 5 over 9 (f ? 32) < 125; ? 40 < f < 257 ? 40 < 5 over 9 (f ? 32); ? 40 < f 5 over 9 (f ? 32) < 125; f < 257
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Identify which functions are linear or non-linear. a. f(x) = x2 + 1 b. f(x) = 2x + 5 c. f(x) = x 2 + 3 d. f(x) = 3 x + 7 e. f(x) = 4x + 10 2 - 5
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Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “c.” using the 68-95-99.7 rule, what percentage of students failed to earn a grade of at least “c”?
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Mathematics, 21.06.2019 22:30
How can you find the mean absolute deviation (mad) for this set of data?
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The area and circumference of a circle of radius r are given by a(r) = πr2 and c(r) = 2πr. suppose w...
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