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Levart [38]
2 years ago
13

Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

Mathematics
1 answer:
vekshin12 years ago
4 0

Answer:

b=4

Step-by-step explanation:

So, we have the function f(x)=1/x. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b}  =-1/8

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

\frac{.5b-1}{2b-b^2} =\frac{-1}{8}

Now, cross multiply.

4b-8=b^2-2b

b^2-6b+8=0

Solve for b. Factor using the numbers -4 and -2.

=(b-4)(b-2)=0

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

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5•9-10<br> ————<br> 5-(-2).
Alenkinab [10]

Answer:

35/7 or 5

Step-by-step explanation:

so you multiply 5 and 9 which is 45- 10 which is 35 but then its 5-(-2) which when doing this a variable minus a negative makes it a positive so then its 5+2 which is 7 then you have 35/7 or 5

4 0
3 years ago
I really need help and this answered ASAP. thank you and sorry.
Semenov [28]

9514 1404 393

Answer:

  $2.50

Step-by-step explanation:

The question asks for the total cost of a notebook and pen together. We don't need to find their individual costs in order to answer the question.

Sometimes we get bored solving systems of equations in the usual ways. For this question, let's try this.

The first equation has one more notebook than pens. The second equation has 4 more notebooks than pens. If we subtract 4 times the first equation from the second, we should have equal numbers of notebooks and pens.

  (8n +4p) -4(3n +2p) = (16.00) -4(6.50)

  -4n -4p = -10.00 . . . . . . . . . . . simplify

  n + p = -10.00/-4 = 2.50 . . . . divide by the coefficient of (n+p)

The total cost for one notebook and one pen is $2.50.

__

<em>Additional comment</em>

The first equation has 1 more notebook than 2 (n+p) combinations, telling us that a notebook costs $6.50 -2(2.50) = $1.50. Then the pen is $2.50 -1.50 = $1.00.

One could solve for the costs of a notebook (n) and a pen (p) individually, then add them together to answer the question. We judge that to be more work.

4 0
3 years ago
Read 2 more answers
On the 25th of every month, Tamesha pays her rent
Alchen [17]
Ok? What’s the question?
3 0
2 years ago
Given: AB with coordinates of AC-3, -1) and B(2, 1)
andrezito [222]

Answer:

up 2, right 3

Step-by-step explanation:

up 2, to the right 3.

8 0
2 years ago
Find the measure of center:<br> 1, 2, 3, 4, 5, 6, 7
Eva8 [605]

Answer:

Mean: 4

Median : 4

Mode: 1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

Measure of center is:

Mean: Average

Median: Middle number

Mode: Often number

Mean: Add all number then divide by the total number in data set.

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

28/7 = 4

Median: Middle number

1,2,3,4,5,6,7

Mode: most often number

1,2,3,4,5,6,7

<u><em>Kavinsky</em></u>

8 0
2 years ago
Read 2 more answers
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