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2 years ago

Find the average rate of change of f(x)=-x^2+2x+2 from x=2 to x=6. Simplify your answer as much as possible.

Mathematics

1 answer:

Eduardwww [97]2 years ago

8 0

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ 2, 6 ] , then

f(b) = f(6) = - 6² + 2(6) + 2 = - 36 + 12 + 2 = - 22

f(a) = f(2) = - 2² + 2(2) + 2 = - 4 + 4 + 2 = 2 , then

average rate of change = $\frac{-22-2}{6-2}$ = $\frac{-24}{4}$ = - 6

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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

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Answer:

984

Step-by-step explanation:

Solve for the base: 14 x 10

Solve for the sides: 2(1/2(10 x 24))

Solve for the backside: 10 x 24

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The solution for the system equations 8x-6y=-32 and -8x+5y=36

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Answer:

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Step-by-step explanation:

Add the two equations. Then we get

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2 years ago

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3 years ago

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A professor has recorded exam grades for 10 students in his class, but one of the grades is no longer readable. If the mean sco

Nostrana [21]

Answer:

unreadable score = 35

Step-by-step explanation:

We are trying to find the score of one exam that is no longer readable, let's give that score the name "x". we can also give the addition of the rest of 9 readable s scores the letter "R".

There are two things we know, and for which we are going to create equations containing the unknowns "x", and "R":

1) The mean score of ALL exams (including the unreadable one) is 80

so the equation to represent this statement is:

mean of ALL exams = 80

By writing the mean of ALL scores (as the total of all scores added including "x") we can re-write the equation as:

$\frac{R+x}{10} =80$

since the mean is the addition of all values divided the total number of exams.

in a similar way we can write what the mean of just the readable exams is:

$\frac{R}{9} = 85\\$ (notice that this time we don't include the grade x in the addition, and we divide by 9 instead of 10 because only 9 exams are being considered for this mean.

Based on the equation above, we can find what "R" is by multiplying both sides by 9:

$\frac{R}{9} = 85\\R=85*9= 765$

Therefore we can now use this value of R in the very first equation we created, and solve for "x":

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3 years ago

Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are ne

anyanavicka [17]

Answer:

3.1 gallons

Step-by-step explanation:

To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that

miles of gas / gallons = miles of gas / gallons

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If we write the gallons needed to go to Bob's mother's house as g, we can say

23 miles / 1 gallon = 72 miles/g

multiply both sides by 1 gallon to remove a denominator

23 miles = 72 miles * 1 gallon /g

multiply both sides by g to remove the other denominator

23 miles * g = 72 miles * 1 gallon

divide both sides by 23 miles to isolate the g

g = 72 miles * 1 gallon/23 miles

= 72 / 23 gallons

≈ 3.1 gallons

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2 years ago