1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Solve for y<br><br> 13 = 6 + y
Leni [432]

Answer:

Step-by-step explanation:

6 + y = 13

y = 7

4 0
3 years ago
Read 2 more answers
PLEASEE HELPPP! <br> what is the measure of
Debora [2.8K]

Answer:

x=12

Step-by-step explanation:

Im not sure which measure you're talking about, but I'll show you what I did here:

A triangle = 180 degrees.

4x + 8x + 4x =16x

-8 - 1 - 3 = -12

180 = 16x - 12        -Add 12 to both sides

192 = 16x               -divide by 16 to get x by itself

12 = x

Angle A = 88 degrees (8 times 12 then subtract 8)

Angle B = 47 degrees (4 times 12 then subtract 1)

Angle C = 45 degrees (4 times 12 then subtract 3)

5 0
2 years ago
The point (3,-7) lies on a circle and the center of the circle is at (-2,-7). What is the equation of this circle
melomori [17]

Step-by-step explanation:

the answer is in the above image

4 0
3 years ago
Help please!!! Fast!! <br> The answer choices are:<br> 30 ft<br> 40 ft <br> 50 ft <br> 70 ft
valkas [14]
50 the answer is most likely 50
6 0
2 years ago
URGET PLEASE HELP QUICKLY
alexdok [17]

Answer: -0.5.

Step-by-step explanation:

The constant of variation k for the direct variation is given by:-

k= \dfrac{f(x_2)}{x_2}=\dfrac{f(x_1)}{x_1}

The given table:

x  f( x )

0   0

2   -1

4    -2

7   -3.5

Then,

k=\dfrac{-1}{2}=\dfrac{-2}{4}=\dfrac{7}{-3.5}=-0.5

Hence, the constant of variation k for the direct variation is -0.5.

4 0
3 years ago
Other questions:
  • How much of the 8% solution should we use to make 100g of a 3% solution?
    10·1 answer
  • An artist wants to frame a square with an area of 400 square inches. She wants to know the length of the wood trim that is neede
    15·1 answer
  • What color is the most predominate on the US flag
    6·2 answers
  • les had $26.00 when he went to the box city market to buy some fresh fruits and vegetables .when he left he had $11.70. how much
    7·2 answers
  • The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best inte
    10·1 answer
  • Which is greater 36km or 36000m
    9·2 answers
  • Which answer is the equation of the line represented in function notation?
    7·1 answer
  • The least common multiple of two numbers is 60, and one of the numbers is 7 less than the other number . What are the numbers ?
    13·1 answer
  • amal drew the function below. Which explains whether or not his function is linear? On a coordinate plane, a line with negative
    7·1 answer
  • Find a formula for the arithmetic sequence consisting of the positive multiples of 4
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!