Let f(x)=root2x. If the rate of change of f at x=c is four times its rate of change at x=1 then c=?

Answers

Answer 1

Answer:

[tex]c=\frac{1}{16}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{2x}[/tex]

[tex]f'(x)=\frac{\sqrt{2x}}{2x}[/tex]

[tex]f'(1)=\frac{\sqrt{2}}{2}[/tex]

[tex]f'(c)=\frac{\sqrt{2c}}{2c}[/tex]

[tex]f'(c)=4f'(1)[/tex]

[tex]\frac{\sqrt{2c}}{2c}=4(\frac{\sqrt{2}}{2})[/tex]

[tex]\frac{\sqrt{2c}}{2c}=2\sqrt{2}[/tex]

[tex]\sqrt{2c}=4c\sqrt{2}[/tex]

[tex]2c=32c^2[/tex]

[tex]2=32c[/tex]

[tex]\frac{1}{16}=c[/tex]


Related Questions

how to rewrite 3/4 with the denominator 12

Answers

9/12
Multiply 4 by 3 and multiply 3 by 3 and you get 9/12

let f(x)=x-3 and g(x)= 3x^2. perform the function operation and then find the domain of the result. (f-g)(x)

Answers

Answer:

(f-g)(x) = f(x) - g(x)

         = x-3 - (3[tex]x^{2}[/tex])

          = x- 3 - 3[tex]x^{2}[/tex]

domain is all real number

Step-by-step explanation:

Find the ratio of the following is175and210​

Answers

Answer:

5:6

Step-by-step explanation:

175/210

Divide both sides by 5

175/5 : 210/5

35 : 42

Divide both sides by 7

35/7 : 42/7

5 : 6

The ratio of 175 and 210 in its simplest form is; 5:6

What Is a ratio

A ratio is the simplest form to which the quotient of two numbers can be represented.

The ratio of 175 and 210 can be evaluated by considering their HCF, highest common factor.

Their HCF is 35;

Hence, the ratio of 175 and 210 is ; 5:6

Read more on ratios;

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(b) Part B
How many solutions does the following the system of equations have?

Answers

Answer:

Its C.

Step-by-step explanation

:Took the test

You roll three six-sided dice. What is the probability that exactly two of the dice are odd? Write your answer as a fraction in simplest form.
The probability is

Answers

Answer:

1/4

Step-by-step explanation:

There are 36 boys for every 54 girls

Answers

Answer:

2 : 3 is ur ratio

Step-by-step explanation:

Answer:

2 : 3 is ur ratio

Step-by-step explanation:

Classify the following triangle as acute, obtuse, or right.

Answers

D. None of these.

Equilateral is the only triangle that has all the sides that are equal to each other. Hope this helped you :)

Option D . None of these is the correct answer.

help pls !! i am confused

1. 2. 3. 4.

Answers

<NOR and <ORS<QRO and < ROP

Given the points (4, 5) and (-2, 8), find the slope of the line that passes through the points.

Group of answer choices

9/6

-2/1

-1/2

1/2

Answers

Answer: c

Step-by-step explanation:

Formula of slope of line :

m=y2-y1/x2-x1

m=8-5/-2-4

=-3/6

m=-1/2

Can you help me please

Answers

I think it’s 32? i dont know good luck

Yaniq has these two spinners
Answer it all right NO wrong​

Answers

Answer:

b should be 2/11

c should be 2/11 as well

Step-by-step explanation:

Used The Graph info

total spins 11

both are 2over9

Step-by-step explanation:

9 results 2 only

find the some of -3x^2-x-10 and 10x^2+x-10

Answers

Add likewise terms together (add the coefficients of x^2 together, same with just x, etc)

10x^2 – 3x^2 = 7x^2

1x – 1x = 0

– 10 – 10 = –20

So the answer is 7x^2 – 20.

Answer:

( X - 2 )(3x + 5)  For 3x^2-x-10

Step-by-step explanation:

Which set of ordered pairs represents a function?
a
O {(7,4), (3,8), (-4, –4), (0,4)}
O {(-8,0), (-5,6), (-8, 1), (-6,5)}
{(-5, 1), (3, -7), (2, -4), (2,7)}
O {(4,2), (4, -9), (-9, -6), (7,1)}

Answers

The first set
(7,4), (3,8), etc

3. In a survey of 200 people about a bus company, 77 said they were satisfied with the bus
company's performance. What percent of the people were satisfied with the bus company's
performance?

O 23%

38.5%

061.5%

077%

Answers

The percentage of the people that were satisfied with the bus company's  performance is: B. 38.5%

Given the following data:

Population = 200 peopleSatisfied people = 77 people

To determine the percentage of the people that were satisfied with the bus company's  performance:

In this exercise, you're required to find the number of the people that were satisfied with the bus company's  performance as a percentage of the total population in this survey.

Thus, we would use this formula:

[tex]Percentage = \frac{Satisfied\;people}{Population} \times 100[/tex]

Substituting the given parameters into the formula, we have;

[tex]Percentage = \frac{77}{200} \times 100\\\\Percentage = \frac{77}{2}[/tex]

Percentage = 38.5%

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A system of equations is shown: 2x = â’y 6 â’4x 3y = 8 What is the solution to this system of equations? (â’1, â’4) (1, 4) (4, 1) (â’4, â’1).

Answers

The correct option is B. (1,4).

Given equations,

[tex]2x=-y+6....(1)\\-4x+3y=8....(2)[/tex]

We have to find the solution of the given system of equations.

Equation 2 can be written as,

[tex]-2\times(2x)+3y=8\\[/tex]

Now by substitution method, putting the value of [tex]2x[/tex] from Equation (1) in above equation, we get

[tex]-2\times(-y+6)+3y=8\\2y-12+3y=8\\5y-12=8\\5y=20\\y=4[/tex]

Now putting the value of y in equation 1 we get,

[tex]2x=-4+6\\2x=2\\x=1[/tex]

Hence the solution of the given system of equation will be (1,4).

For more details follow the link:

https://brainly.com/question/12824145

PLEASE HELP ME ASAP!!!!!!!!! GOD BLESS YOU IF YOU HELP ME THIS WILL RAISE MY GRADE

Answers

The answer is option 1.

The line has y-intercept of –3, meaning the line passes through the y axis at –3, to which only option 1 has the line passing through –3.

You can also see that the gradient of that line in option 1 is 1/2, using the rise/run method and can see that the line is positive as it moves in the / direction.

X, y, z are each a different digit
a. Max(2x+3y+7z)=?

Answers

Answer:

  101

Step-by-step explanation:

To get the largest weighted sum, you want to give the largest weight to the largest possible digit.

  Max( ) = 7·9 +3·8 +2·7 = 63 +24 +14 = 101 . . . . (x, y, z) = (7, 8, 9)

The maximum sum is 101.

What is the solution set for x^2 - 2x - 15 = 0

A. {-5, -3}

B. {5, -3}

C. {3, 5}

D. {-3, 5}​​

Answers

Answer:

B

Step-by-step explanation:

I have done this before

Find the value of x in the triangle shown below.

Answers

Answer:

u did a lot of this budy a lot of these

Step-by-step explanation:

find the number of tiles in the 57th figure. justify your answer using an algebraic expression

Answers

3,365 tiles! the equation is always (x+1)^2 (squared) + 1 = Y. because y is the number of tiles and the x is whatever figure you’re on. but the figures start like #1 is a 2x2 instead of a 1x1 so 57th figure would not be 57x57 but 58x58. and then add 1 because there’s always that top left corner tile! if you appreciate my answer giving it brainliest is always appreciated!!

EASY QUESTION! GET EASY POINTS!

if i paid $3.50 a month, how much would i pay a year?

EASY BRAINLIEST!
yw:)

Answers

Answer:You will pay $42 yearly. Step-by-step explanation:1 Year = 12 months=> 1 month = $3.50=> 12 months = $3.50 x 12=> 12 months = $42Conclusion:

Therefore, you will pay $42 after a year.

Hoped this helped.

[tex]-BrainaicUser1357-[/tex]

Answer:

42

Step-by-step explanation:

3.5*12=42

Answer the following question:
7/2h - 3 (5h - 7/2)

Answers

Answer:

For easy way

convert to decimals first

3.5h - 3 (5h - 3.5)

Open brackets

3.5h - 15h + 10.5

Answer = 10.5 - 11.5h

PLS HELP I WILL GIVE BRAINLYEST
Use the number line to find the distance between −10 and −4.
Enter the answer into the box

Answers

Answer:The distance between -9 and -4 is 6 units.Step-by-step explanation:

When we use the number line, we need to count forward from -10.

-9,-8,-7,-6,-5,-4Conclusion:

Therefore, the distance between -9 and -4 is 6 units.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

Julia wants to make a vegetable garden in her backyard for 6 different vegetables. She makes 6 sections in the
garden. The dimensions of the garden are 3 sections long by 2 sections wide. Each section is in the shape of a
square. The area of the vegetable garden is 73.5 square feet. What is the length of the vegetable garden?

Answers

Answer:

36.75 square feet

Step-by-step explanation:

First, we can divide 73.5 into 6 to calculate area for each section. We get the answer of 12.25. Next, it says that the garden is 3x2 sections, so we multiply 12.25 by 3 to get a total of 36.75

The Julia wants to make a vegetable garden in her backyard length of the vegetable garden is 10.5 feet.

The garden is divided into 6 sections.

The dimensions of the garden are 3 sections long by 2 sections wide.

Each section is in the shape of a square.

The area of the vegetable garden is 73.5 square feet.

Let's denote the side length of each square section as "s". Since there are 6 sections, the area of the vegetable garden can be calculated as:

Total Area = Number of Sections × Area of One Section

73.5 = 6 × s²

Now, solve for the side length "s":

s² = 73.5 / 6

s² = 12.25

Taking the square root of both sides:

s = √12.25

s = 3.5 feet

Since each section is a square and has a side length of 3.5 feet, the dimensions of the garden are 3 sections long by 2 sections wide, which translates to:

Length = 3.5 feet/section ×3 sections = 10.5 feet

To know more about length  here

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#SPJ3

Find the common factor in the given algebraic expressions: x(a-b), y (b-a)
Explain please.


Answers

Answer:

the common factor in the given algebraic expressions: x(a-b), y (b-a)

Step-by-step explanation:

(x-y)(a-b)

PLEASE HELPPPP

4(x−2 1/4)=−3.7

Answers


First let’s convert the mixed numbers to improper fractions 2 1/4 =9/4
Then u get 4(X-9/4) =-3.7
Now your gonna divide both sides by four
4(X-9/4) over 4 = -3.7 over 4
4/4 =1 …X=-9/4
-3.7/4 = -0.925
Now you’re going to add 9/4 to each side
X-9/4+9/4=-0.925 +9/4
-9/4 + 9/4 =0 (X)
Now you have just -0.925 and nine fourths
I converted 9/4 —> 2.25
Then u still have -0.925
So add 2.25+-0.925 u get ur X which is 1.325 (this is ur answer)

Can someone help me with these 2 problems I’ve been stuck on them for a very long time :’) tysm!!

Answers

Answer:

Christmas How many pouds this proportion to solve

Convert 112 degrees Fahrenheit to degrees Celsius

Answers

Equation

C = (F - 32) ÷ 1.8

Solution

C = (112 - 32) ÷ 1.8

=44.4  (44.4444444444)

Answer may vary depending on how your teacher wants you to do it and whether they want a exact answer.

Help!
NO LINKS!!!

Choose the correct set of y-values for the function y = -2x when x = -2, 0, 2.
A. (-2, -4), (0, 0), (2, 4)
B. (-2, 4), (0, 0), (2, -4)
C. (-2, -4), (0, 0), (2, -4)
D. (-2, 4), (0, -2), (2, 4)

Answers

Answer:

hi this should be your answer (-2,4),(0,0),(2,-4)

Step-by-step explanation:

hope this helps!

The diagram shows a rectangle 15cm long and 13cm wide.It has been split into four smaller rectangles. write the area of each small rectangle on the diagram.

Answers

Answer:The Answer is in the explanationStep-by-step explanation:

length of the rectangle = 15 cmBreadth of the rectangle = 13 cmArea of the rectangle = length × breadthArea of the rectangle = length × breadth = 15cm × 13cm =

[tex]195 cm^{2}[/tex]

Area of each splited rectangles =

[tex] \frac{195cm{}^{2} }{4} [/tex]

=

[tex]48.75 {cm}^{2} [/tex]

!! PLEASE MARK ME THE BRAINLIEST!!

AND I'M REALLY VERY SORRY IF MY ANSWER IS WRONG
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