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Levart [38]
3 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:
vekshin13 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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49x^2=-21x-2 quadratic functions
lara [203]

Answer: 49x^2=-21x-2 quadratic functions -1/7and -2/7    



Step-by-step explanation:

Quadratic function:

In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.

Move terms to the left side

49x^{2}  =-21x-2

49x^{2}  -(-21x-2) =0

 Distribute

49x^{2}  -(-21x-2) =0

49x^{2}+21x+2=0

Use the quadratic formula



 x=(-b±√b^{2}  -4ac  ) / 2a

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

 49x^{2}+21x+2=0

let, a=49

b=21

c=2

 Replace with values in this equation

X=(-b±√b^{2}  -4ac  ) / 2a

Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Evaluate the square root

Multiply the numbers

x=(-21±7) /98

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.Separate

x=(-21+7) /98

x=(-21-7) /98

Solve

Rearrange and isolate the variable to find each solution

x=-1/7

x=-2/7



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Learn more about area here https://brainly.in/question/5597925

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3 0
1 year ago
What divided by 6 equals 7
vivado [14]

Answer:

42

Step-by-step explanation:

You can prove this by taking 42 and dividing it by 6, and you will see that the answer is 7. Tip: For future reference, when you are presented with a problem like "What divided by 6 equals 7?", all you have to do is multiply the two known numbers together.

6 0
3 years ago
Read 2 more answers
What is the slope, x intercept, y intercept for this question: 1/3x+ 1/2y= 9
Sergeeva-Olga [200]
Hope this helps you 3y=54-2
6 0
3 years ago
Identify is this is percent increase or percent decrease, then calculate percentage
vlabodo [156]

<em>Last year the chess club had 30 members. This year the club has 24 members. </em>

Last year, the chess club had 30 members. This year, the club has 24 members. Since this year had less than last year ( 30 > 24), the percent will be decreasing.

To find the percent decrease, you have to use the following formula.

\frac{Difference}{Original} \times 100

Difference refers to the difference between the two numbers, 24 and 30. The difference between 24 and 30 is 6. Original refers to the original number, which is last year's amount of members in the chess group. Therefore, original = 30.

Substitute the numbers into the formula.

\frac{Difference}{Original} =\frac{6}{30} =0.2

To convert the decimal to a fraction, multiply the decimal by 100.

0.2 \times 100 = 20 \%

The answer is the number of chess members decreased by 20%.

____

Since I started off by identifying whether it was decreasing or increasing, I did the work a bit differently. When finding the difference, you would usually subtract 30 from 24, which results in -6. Above I used 6, but if you used -6, you would end up with a result of -20%, which means it decreased by 20%. They bot end up with the same result, but you don't always have to first identify whether it's decreasing or increasing.

____

3 0
3 years ago
Answer to be marked as brainlist
zimovet [89]

Answer:

The SF is 3

Step-by-step explanation:

The sides are 3x the length of the sides of ∆ABC

4 0
2 years ago
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