Show that f '(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f − g is constant? If f '(x) = g'(x) for all x in an interval (a, b), then f − g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.

Answers

Answer 1

Answer:

Answer: 15 cm

Step-by-step explanation:

Answer 2

The derivative of a function at a point can be defined as its slope at that point. For f'(x) = g'(x) in the interval (a,b), it is proved that f - g is constant in (a,b).

What is a Derivative?

A derivative of a function is its rate change of increase or decrease in a given interval with respect to its variable. Derivative of a constant function is always zero.

Given that, f'(x) = g'(x) for all x.

Taking integral on both sides

f(x) + C₁ = g(x) + C₂

=> f(x) - g(x) = C₂ - C₁

=> f(x) - g(x) = C

Thus, f(x) - g(x) is constant is proved.

Similarly for interval an interval (a,b),

f(x) - g(x) = C

=> f(x)= g(x) + C

Hence, it is proved that in an interval (a,b), if  f'(x) = g'(x) then f(x)= g(x) + C.

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Related Questions

giving brainliest to whoever gets it right

Answers

Answer: i know the answer

Step-by-step explanation: plz plz pick me

Answer:

umm... i'm not sure. all i know is that they were rotated and reflected. sorry

Step-by-step explanation:

I hate school I’m supposed to be in 12th but I’m in 11th I’m doing my credit recovery classes it’s just exhausting for me

Answers

That sucks I wish you the best you can do it even if you feel like failing trying your best can still be rewarded in different ways and remember to do the assignments because getting no grade for it is worse than getting a low grade even if it’s not the best!

why dose my teacher make me have my cam on even tho im eating

Answers

Answer:

Probably so she knows you are not playing video games and you are paying attention to what she is saying.

Step-by-step explanation:

Brainliest Please!!

- Hermionia

Answer:

because she's lonely and she misses seeing you guys I guess. My teachers ~itch abt it but they dont make us.

Step-by-step explanation:

What is the constant in the expression?


15x² + 2x – 3

Answers

Answer: -3

Step-by-step explanation:

Answer:

the constant in this expression is 3

Step-by-step explanation:

the constant is a single number

nts
3.2 Domain and Range
Score: 30/190 3/19 answered
Question 8
Complete the description of the piecewise function graphed below.
{
f(x) = {
{
+
2
+
8
8
if -6 ≤ x ≤ -1
if -1 < x≤2
if 2 < x≤6

Answers

the missing functions in the piecewise function are f(x) = - x - 4 for - 6 ≤ x ≤ - 1, f(x) = 4 for 1 < x ≤ 2 and f(x) = - 1 / 2 x - 6 for 2 < x ≤6.

We are given the graph of a piecewise function.

We need to complete the function to represent the graph completely.

We know that, a piecewise function is a function that has different functions for a particular set of values for x.

Here, we can see that:

For the values of x in between - 6 and - 1 that is - 6 ≤ x ≤ - 1, we get the function as:

f(x) = - x - 4

For the values of x in between - 1 and 2 that is - 1 < x ≤ 2, we get the function as:

f(x) = 4

For the values of x in between 2 and 6 that is 2 < x ≤6, we get the function as:

f(x) = - 1 / 2 x - 6

Therefore, we get that, the missing functions in the piecewise function are f(x) = - x - 4 for - 6 ≤ x ≤ - 1, f(x) = 4 for 1 < x ≤ 2 and f(x) = - 1 / 2 x - 6 for 2 < x ≤6.

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Question 10 of 10
Jerry drew AJKL and AMNP so that ZK = ZN, LL LP, JK= 6, and
MN = 18. Are AJKL and AMNP similar? If so, identify the similarity postulate
or theorem that applies.
O A. Similar - AA
O B. Cannot be determined
C. Similar - SSS
OD. Similar - SAS

Answers

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠ K = ∠ N and ∠L = ∠P are there.

It is given that two triangles that are JKL and MNP are considered in which:

∠K = ∠N

∠L = ∠P

JK = 6

MN = 18.

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠ K = ∠ N and ∠L = ∠P are there.

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Your question was incomplete. Please refer the content below:

Jerry drew JKL and MNP so that K= N,L= P, JK=6, and MN=18. Are JKL and MNP similar? IF so, identify the similarity postulate or theorem that applies.

A. Similar - AA

B. Cannot be determined

C. Similar - SSS

D. Similar - SAS

A spinner with 6 equally sized slices has 3 yellow slices, 1 red slice, and 2 blue slices. The dial is spun and stops on a slice at random. What is the probability
that the dial stops on a yellow slice?
Write your answer as a fraction in simplest form.

Answers

Answer:

Step-by-step explanation:

3/6

Jonathan has a summer job earns $8.15 per hour .one week , he works 15 3/4 hours . He deposits $120 in a bank and decides to use the rest of the money to buy raffle tickets. Each raffle ticket costs $0.50 . How many raffle tickets can Garth buy ?

Need answers ASAP pliss

Answers

Answer:

16....................

Find the length of GH

Answers

Answer:

y=√(x1-x2)^2+(y1-y2)^2

y=√(-3-(-11))^2+(15-0)^2

y=√8^2+15^2

y=√64+225

y=√289

y=17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

x₁ = -3 and x₂ = -11

y₁ = 15 and y₂ = 0

√(-3 - -11)² + (15 - 0)²

√( 8² ) + ( 15² )

17

Need help with this ASAP​

Answers

Given:

[tex](3x-2)^9[/tex]

To find:

The coefficient of [tex]x^6[/tex] in the expansion of [tex](3x-2)^9[/tex].

Solution:

We know that, in the expansion of [tex](x+y)^n[/tex],

[tex]T_{r+1}=^nC_rx^{n-r}y^r[/tex]       ...(i)

[tex](3x-2)^9[/tex] has only one x and in [tex]x^6[/tex], the power of x is 6. It is possible if

[tex]n-r=6[/tex]

[tex]9-r=6[/tex]

[tex]9-6=r[/tex]

[tex]3=r[/tex]

Putting n=9, r=3, x=3x and y=-2 in (i), we get

[tex]T_{3+1}=^9C_3(3x)^{9-3}(-2)^3[/tex]

[tex]T_{4}=\dfrac{9!}{3!(9-3)!}\times (3x)^{6}(-8)[/tex]

[tex]T_{4}=\dfrac{9\times 8\times 7\times 6!}{3\times 2\times 1\times (9-3)!}\times (729x^{6})(-8)[/tex]

[tex]T_{4}=84\times (729)\times (-8)\times x^{6}[/tex]

[tex]T_{4}=-489888x^6[/tex]

Therefore, the coefficient of [tex]x^6[/tex] in the expansion of [tex](3x-2)^9[/tex] is -489888.

Which expression represents the perimeter of the rectangle shown below

Answers

Answer:

D

Add all of the sides together. 2x+1 plus 2x+1 equalls 4x +2

Then add that to (xsquared+3x-2 + xsquared+3x-2) which is 2xsquared +6x-4+4x+2 which equalls D

Its D

------------------

find the domain and range of {(x, y) : |x| + y ≥ 2}

Answers

Answer:

[tex]\textsf {Domain} : -\infty \: < x < \infty \\\textsf {In interval notation: } (-\infty, \infty)}[/tex]

[tex]\textsf {Range: } f\left(x\right)\le \:2 \\\textsf {In interval notation:} \:(-\infty \:,\:2][/tex]

Step-by-step explanation:

There are no undefined points for the function. So the domain is the set of all x values

The domain of x is (-∞, ∞) so x can be negative or positive. However, |x| is always positive

So if the inequality |x| + y ≥ 2 is to hold good then y has to be less than equal to 2, otherwise the left side drops below 2 and the inequality is not satisfied.

So the range is the set of all values in the interval (-∞, 2)

Check out the graph for a visual interpretation


Sam bought an $85.00 jacket for 40% off of the regular price. He also has to pay 5% for tax. How much did he pay for the jacket after the discount and tax?

Answers

55.25. You multiply 0.40 by 85 and you’ll get 34, subtract 85 by 34 and you’ll get 51. Then you multiply 0.05 by 85 and get 4.25. Add 4.25 by 51 and you’ll get 55.25.

The ratio of athletes to non-athletes at Taylor Middle School is 3 to 4. If there are 225 athletes in the school, how many non-athletes are there?

Answers

Answer:

0 because no one wants to be a nerd

Answer:

300 non athletes

Step-by-step explanation:

The spinner is spun 240 times. What is a reasonable prediction for the number of times the spinner will land on a 3.

Answers

Answer:120 times

Step-by-step explanation:4/8 = x/240. 4/8 x 240/1 4/1 x 30/1 = 120/1 = 120.

Reduce 8 to 1 and 240 to 30.

Answer:

120

Step-by-step explanation:

What the input calue for y=3x + 5

1.the input value is x
2.The input value is y

Which one ??

Answers

the input value is x because when you use the equation you need x to get y.

Need help with 5 and 6 will give branliest to the first to answer

Answers

Answer:

j

Step-by-step explanation:

Answer:

i think the first on is A.

Step-by-step explanation:

There is an installation fee to join the Pine River country club as well as monthly dues the total cost of her seven month membership will be $3200 and after one and a half years $3970 find both the intuition feet and the monthly dues

Answers

Answer:

Monthly charges = $70

Intuition charges = $2710

Step-by-step explanation:

There is intuition fee and per month fee for joining the Pine River country club.

Total cost for 7 months is $3200

Total cost for one and a half years is $3970

one and a half years means 18 months.

To find:

Intuition fee and monthly dues?

Solution:

Let the intuition fee = [tex]i[/tex]

Let the monthly dues = [tex]m[/tex]

Total cost for 7 months can be represented as

[tex]i+7m = 3200[/tex] ..... (1)

Total cost for 18 months can be represented as

[tex]i+18m = 3970 .... (2)[/tex]

Here, we have 2 equations and 2 variables whose values are to be found.

Let us use elimination method to solve the equations.

Subtracting equation (1) from (2):

[tex]11m = 770\\\Rightarrow m = 70[/tex]

Therefore, the monthly dues are $70.

Using equation (1), we can find the value of [tex]i[/tex].

[tex]i + 70\times 7 = 3200\\\Rightarrow i = 3200 - 490\\\Rightarrow i = \$2710[/tex]

Therefore, intuition charges are $2710.

Simplify the expression: 7(9x + 6y)

Answers

Answer:

63x + 42y

Step-by-step explanation:

P.S Can I have brainliest?

ANSWER ASAP
-2X=34
SHOW WORK

Answers

Answer:

-2x =34

Step-by-step explanation:

-2x = 34

or , -x = 34 ÷2

or , -x = 17

x = -17

Answer:

x = -17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

-2x = 34

Step 2: Solve for x

Divide -2 on both sides:                    x = -17

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                    -2(-17) = 34Multiply:                               34 = 34

Here we see that 34 does indeed equal 34.

∴ x = -17 is the solution of the equation.

Line n is parallel to Line P. Find the measure of each angle.
Please help

Answers

Answer:

m<1=140

m<2= 40

m<3= 140

m<4= 40

m<5=140

m<6= 40

m<7= 140

Answer:

Step-by-step explanation:

m∠1 = 180-40= 140° (suplementary angles)

m∠2= 40° (vertical angles are ≅)

m∠3= 140° ( is ≅ to ∠1)

m∠4 = m∠6 = 40° ( same side corresponding ∠s, and vertical angles)

m∠5 = m∠7 = 140° ( same side corresponding ∠s, and vertical angles)

Help my 5th Grade son with his I-Ready


The question is Multiply 1 by 5 and the equation is 152 x 61 but there's a box above the number 1 and a box under 6, what do we put and how do we solve it?

Answers

Answer:

well the answer will come out to 9272

Step-by-step explanation:

sort the words into a category based on welther they indicate a positive number or a negative number.
- loss
- gain
- below
- adding
- taking away
- above​

Answers

Answer:

Negative numbers: Loss, below, taken away

Positive numbers: Gain, Adding, Above

K
The selling price of a refrigerator, is $724.50. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?

Answers

If the markup is 5% of the dealer's cost then the dealer's cost of the refrigerator is $690.

Markup can be calculated using the formula.

Markup= (Selling price - Cost )/Cost

In the given question

The selling Price = $724.50

markup = 5% = 0.05

let the dealer's cost be "x".

Substituting the values in the dealer's formula we get

Markup= (Selling price - Cost )/Cost

0.05=(724.50-x)/x

0.05x=724.50-x

x+0.05x=724.50

Solving further we get

1.05x=724.50

x=724.50/1.05

x=690

Therefore , the dealer's cost of the refrigerator is $690.

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5) Write the equation of the line to the right.

Answers

Answer:

y = -3x - 4

Step-by-step explanation:

to get -3x, you calculate the slope, so you can pick a point and use rise over run, and to get -4, it starts -4 down on the x line

Ok, the explanation is horrible, but i promise the answer is correct

Answer:

y=-1/3x-4

Step-by-step explanation:

What is K=a-y;y solve for

Answers

y = K/a

Starting with K = a - y.

First, subtract the a on both sides to isolate the y.

-y = K/-a

Then, multiply both sides by negative one to get rid of the negative on the y.

y = K/a

Hope this helps!

Solve the area formula fora triangle, A= 1/2bh, for b. A. b=A/2h. B. b=2h/A. C.b=h/2A. D.b=2A/h

Answers

Answer:

D.  b=2A/h

Step-by-step explanation:

GivenA= 1/2bhSolving for b A= 1/2bh             ⇒ given2A = bh               ⇒ multiply by 22A/h = b              ⇒ divide by hb = 2A/h

Option D is correct

the dot plot shows the heights of the players on two basketball team​

Answers

I can’t see it is too burly I’m Srry

Answer:

H. Team B has a greater range in player heights than Team A has.

Step-by-step explanation:

I just took the quiz

Which expressions are equivalent to 6 + 12x?
Select each equivalent expression.

Answers

Answer:

2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)

Step-by-step explanation:

Given the expression 6 + 12x.

The following functions are equivalent;

Factoring out common number;

For 2;

2(3) + 2(6x)

2 (3 + 6x)

Factoring out 3;

3(2) + 3(4x)

3 (2 + 4x)

Factoring out 6;

6(1) + 6(2x)

6 (1 + 2x)

Hence the possible equivalent expressions are 2 (3 + 6x), 3 (2 + 4x) and 6 (1 + 2x)

Alan got 72 questions correct on the last math exam. He got 85 questions correct this time. By what percent did the number of questions correct increase? (Round to the nearest whole percent)

A. 84%
B. 16%
C. 118%
D. 18%

Answers

Answer:

D.

Step-by-step explanation:

the difference between 85 and 72 is 13. 13 is 18% of 72.

I think the answer is D not sure
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