Find the derivative of the function. g(x) = ∫5 x 4 x u2 − 1u2 +1 dug'(x) = g

Answers

Answer 1

Answer:

[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]

Step-by-step explanation:

The question can be better structured and represented as :

[tex]g(x) = \int ^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ du[/tex]

now the derivative of the function of g(x) is g'(x) which is equal to:

[tex]g'(x) = \dfrac{(5x)^2-1}{(5x)^2 +1 }\dfrac{d}{dx}(5x) - \dfrac{(4x)^2-1}{(4x)^2 +1 }\dfrac{d}{dx}(4x)[/tex]

[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]


Related Questions

You are part of a construction company that is supposed to build houses. An architect has left you plans to build houses on each island. Bridges connect the islands. Island A and Island B have a total of 30 houses. Island A and Island C have a total of 40 houses. Island B and Island C have a total of 36 houses. A total of 53 houses is to be built on the three islands. Determine how many houses are to be built on each island. Show how to represent the problem in each of the following ways and solve them. (This is the verbal description, use sentences to explain) I. Concrete or pictoral representation II. Graph III. Algebraic Formula IV. Table

Answers

Answer:

Island A=17 house

Island B= 13 house

Island C=23 house

Step-by-step explanation:

Island AB=30 house

Island AC=40 house

Island BC=36 house

Island ABC=53 house

53 - 30= 23 house which is the total of house on island c

53-40=13 house which is the Total of house on island b

53-36=17 house which is the Total of house on island A

Mr. Stewart bought a new battery for his car. The battery cost $72. Since batteries are a taxable item, he had to pay a sales tax of 7.5%. What was the total cost of the battery in dollars and cents?

Mr. Stewart spent $77.40 on his new car battery.

Answers

Answer: $77.40

Step-by-step explanation:

First you take the 7.5% and turn it into a decimal and to do that you have to divide 7.5 by 100 which gives you .075. You then multiply 72 by .075 to know how much money you will pay with tax and you get $5.40. then you add $5.40 to $72 to get the total coast of the battery, which is $77.40.

The total cost of the battery was $77.40.

A class of 128 students from civil, mechanical and electrical engineering backgrounds is divided into 2 sections (sections A and B). Section A contains of 18 civil engineers and a total of 50 students. Section B contains 44 mechanical engineers. There are a total 40 civil engineers and 60 mechanical engineers in the class. What is the probability that a random electrical engineering student is from section A

Answers

Answer:

The probability is 0.5714

Step-by-step explanation:

This is a probability question. We are interested in calculating the probability that a random electrical engineering student is from section A.

Mathematically the probability will be;

Number of electrical engineering students in section A/ Total number of electrical engineering students in both sections

Total number of electrical engineering students = 128 - 60 -40 = 28

Now let’s calculate the number of electrical students from section A

Number of mechanical and electrical = 50-18 = 32

Now, there are a total of 60 mechanical engineers and 44 in B; So the number of mechanical engineers in A = 60-44 = 16

So the number of electrical engineers in A = 32-16 = 16

So the probability will be;

16/28 = 4/7 = 0.5714

Find the decimal that is equivalent to: 4/11

Answers

Answer:

0.3636 repeating

Step-by-step explanation:

When you divide them, it is 0.36363636 going on forever.

It’s 0.36 repeating

What is the product?

Answers

Answer:

20s³ + 50s² + 32s + 6

Step-by-step explanation:

( 4s + 2 ) ( 5s² + 10s + 3)

use the distribution property:

20s³ + 40s² + 12s + 10s² + 20s + 6

combine like terms:

20s³ + 50s² + 32s + 6

therefore

the expand value = 20s³ + 50s² + 32s + 6

If apples cost $1.18/lb, how many grams (g) of apples may be purchased for $20.00? Round to 3 Digits.

Answers

Answer:

Step-by-step explanation:

First calculate how many pounds of apples you can buy for 20 dollars.

20/1.18 = 16.949 pounds

Now convert that to grams

1 pound = 454 grams

16.949   = x

Cross multiply

1 x = 16.949 * 454

x = 7694.915 grams.

Round to 3 digits

9690 grams.

Choose the expression that completes the equation. 24 ÷ 6 + 20 =______

Answers

Hey there!

ANSWER: [tex]24[/tex]EXPLANATION:

[tex]\text {Choose the expression that completes the equation}\\24/6+20=?[/tex]

To complete the equation, we will need to use the order of operations(PEMDAS). Let's start with division since that's the highest in the order.

[tex]24/6=4[/tex]

Now let's addition since that's all that is left.

[tex]4+20=24\\24(ANSWER)[/tex]

So now let's complete the equation.

[tex]24/6+20=24(ANSWER)[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

calculate the pay for the following day of a weekly time card given a wage $13/hr
HELP PLEASE

Answers

Answer:

$130

Step-by-step explanation:

The person gets $13 and hour and works for 10 hours 15 minutes. You round down to 10 hours and 10x13=130.

Hope this helps.

The required wage or pay for the day of the weekly time card is $113.75.

Given that,
A table has been shown,
Describing the working hours,
pay per hour =  $13/hr.

Daily wage to be determined

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

What is simplification?

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Here are the total working hour,
= 4:00 + 4:45
= 8:45 hours or (8 + 3/4) hours

Wage per hour = $13/hour
                          = 13 *  35/4
                          = $113.75

thus, the required wage or pay for the day of the weekly time card is $113.75.

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Find two consecutive whole numbers that √56 lies between (PLEASE HELP NEED ASAP!!!)

Answers

Answer:

8 and 7

Step-by-step explanation:

because the square root of something is something used in math

can someone answer this please.

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{12\pi \: mm}}}}}[/tex]

Step-by-step explanation:

[tex] \star[/tex] Radius of a circle ( r ) = 6 mm

[tex] \star[/tex] Circumference of a circle ( C ) = ?

Finding the circumference of a circle having radius ( r ) of 6 mm

[tex] \boxed{ \sf{circumference \: of \: a \: circle = 2\pi \: r \: }}[/tex]

[tex] \hookrightarrow{ \sf{circumference = 2 \times \pi \: \times \: 6}}[/tex]

[tex] \hookrightarrow{ \sf{circumference = 12\pi \: \: mm}}[/tex]

Circumference of the given circle = 12π mm

Hope I helped!

Best regards ! :D

~TheAnimeGirl

what are strategies to find rational numbers

Answers

Rational number x and y is to dived their sum by 2

You are baking cookies for your family. You have 12 family members and you have baked 5 cookies so far. Write an equation to find the additional
number of x of cookies you need to bake. Then solve for x.

Answers

Answer:

7 cookies

hope this helped you

please mark as the brainliest (ㆁωㆁ)

Write each percent as a fraction
170%
120%
220%

Answers

Answer:

Step-by-step explanation:

1.17/10

2.6/5

3.11/5

answers:

170% as a fraction is [tex]\frac{17}{10}[/tex] or 1 [tex]\frac{7}{10}[/tex]

120% as a fraction is [tex]\frac{6}{5}[/tex] or 1 [tex]\frac{1}{5}[/tex]

220% as a fraction is [tex]\frac{11}{5}[/tex] or 2 [tex]\frac{1}{5}[/tex]

hope this helps! best of luck <3

Identify the function's local and absolute extreme values, if any, saying where they occur. f(x) = x^3 + 4x^2 - 3x - 4 A) local maximum at x = -1/3; local minimum at x = 3 B) local maximum at x = -1; local minimum at x = 1 C) local maximum at x = -3; local minimum at x 1/3 D) local maximum at x = -1; local minimum at x = 1

Answers

Answer: C) local maximum at x = -3; local minimum at x = 1/3

Step-by-step explanation:

Given the function:

f(x) = x^3 + 4x^2 - 3x - 4

Set f'(x) = 0

f'(x) = 3x² + 8x - 3

f'(x) = 0

3x² + 8x - 3 = 0

Using the quadratic function calculator :

x = - 3 or x = 1/3

Critical points = - 3 ; 1/3

To find the maximum and minimum points :

f''(x) = 6x + 8

Substitute the values of X in

At x = - 3

6(-3) + 8

-18 + 8 = - 10

At x = 1/3

6(1/3) + 8

2 + 8 = 10

Value of f''(x) at - 3 is negative, hence - 3 is the maximum point

Value of f''(x) at 1/3 is positive , hence 1/3 is the minimum point

I dont understand this​

Answers

Answer:

Nell's mom's

Step-by-step explanation:

That's a lot even if you devide, you can see the difference easier

mom= 30/2 = 15

dad = 65/5 = 13

The lesser milk the mother had made her chocolate more chocolatery, and you can see that she has a 0.2 more than the father

Answer:

The correct answer is Nell's mom.

Step-by-step explanation:

Nell's mom makes chocolate syrup with 30 ml for every chocolate syrup for every 2 ounces of milk.

Nell's dad adds 65 ml of chocolate syrup for every 5 ounces of milk.

To compare who makes a more chocolaty drink we need to have same amount of milk.

Least common multiple of 2 and 5 is given by 10.

Thus in 10 ounces of milk, Nell's mom adds 30 × 5 = 150 ml of chocolate syrup.

In 10 ounces of milk, Nell's dad adds 65 × 2 = 130 ml of chocolate syrup.

Thus on comparison we can say Nell's mom adds more chocolate syrup and hence makes a more chocolaty milk.

Determine whether the relation represents y as a function of x

2x+y^2=6

Answers

Answer:

rabi pati le crabby pati vi qui faste un fadi xx

Help ASAP please please

Answers

5/6

Write all numerators above common denominators

3x3/10x3+8x2/15x2

9/30+16/30

9+16/30

25/30

Simplify to get 5/6

Brainliest?

Answer:

5/6

Step-by-step explanation

A water bird is flying 11 feet above the surface of a pond.
It dives 15 feet down and then rises 3 feet to catch a fish.
What is the new position of the bird relative to the
surface of the water?

Answers

68.54 of the surface of the water

Sara received 73 votes, Ben received 23 fewer than Sara. How many students voted? How many votes did Ben receive?

Answers

There was a total of 123 student voters. Ben received 50 votes.

PLEASE HELP PRECALC WHAT IS THE SECOND ROW MULTIPLIED BY?

Answers

Answer:

the answer is .5 i think

The answer is D (0.5)

AHHHH please help answer and I’ll give you points

Answers

Answer: Yes She is correct

Step-by-step explanation:

William read 15 books in 6 months. What was his rate of reading in months per book? {pls i need help}

Answers

Answer:

His rate would be 2.5 books per month

Can somebody help me and show yo work please

Answers

Answer:

17

Step-by-step explanation:

A= 5 B= 3 C=4

Substitute each number to the right letter

4 + (5^2 + 3) -15

Square 5

4 + (25 + 3) -15

Do parentheses first

4 + 28 - 15

32 - 15

Answer = 17

The sum of three consecutive multiples of 4 is 444. Find these multiples.

Answers

First multiple of 4 is x = 144

Second multiple of 4 is x + 4 = 144 + 4 = 148

Third multiple of 4 is x + 8 = 144 + 8 = 152

Step-by-step explanation:

Let the first multiple of 4 be x and second multiple be (x + 4) and third multiple be (x + 8) ...[Since, the number are consecutive multiple of 4]

☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\\[/tex]

[tex]:\implies \sf x \: + \: x \: + \: 4 \: + \: x \: + \: 8 \: = \: 444 \\ \\ \\ [/tex]

[tex]:\implies \sf 3x \: + \: 12 \: = \: 444 \\ \\ \\ [/tex]

[tex]:\implies \sf 3x \: = \: 444 \: - \: 12 \\ \\ \\ [/tex]

[tex]:\implies \sf 3x \: = \: 432 \\ \\ \\ [/tex]

[tex]:\implies \sf x \: = \: \dfrac{432}{3} \\ \\ \\ [/tex]

[tex]:\implies\underline{ \boxed{\sf x \: = \: 144}} \\ [/tex]

_________________

Therefore,

[tex]\bullet\:\:\textsf{First multiple of 4 = x = \textbf{144}} \\ [/tex]

[tex]\bullet\:\:\textsf{Second multiple of 4 = x + 4 = 144 + 4 = \textbf{148}} \\ [/tex]

[tex]\bullet\:\:\textsf{Third multiple of 4 = x + 8 = 144 + 8 = \textbf{152}}[/tex]

Two balls are to be pulled from a vase that contains 7 red balls 9 green balls and 2 black balls. After the first ball Is drawn, it is not the replaced. What is the probability that two black balls are chosen from the vase?

Answers

Answer:

[tex]\frac{1}{153}[/tex]

Step-by-step explanation:

There are a total of 7 + 9 + 2 = 18 balls in the vase, therefore, when not replacing the first ball, there would be 18 · 17 = 306 ways to pull 2 balls. There are 2 ways to choose the first black ball and then 1 way to choose the second black ball so there are 2 · 1 = 2 ways to choose 2 black balls. Therefore, the probability is 2 / 306 = [tex]\frac{1}{153}[/tex].

0.4x+3=0.2(3x+1)−x someone plz help

Answers

Answer:

x =-3.5

Step-by-step explanation:

0.4x+3=0.2(3x+1)−x

Distribute

.4x +3 = .6x+.2 -x

Combine like tersm

.4x+3 = -.4x+.2

Add .4x to each side

.4x+3 +.4x = -.4x +.2 +.4x

.8x +3 =.2

Subtract 3 from each side

.8x+3-3 = .2-3

.8x = -2.8

Divide each side by .8

.8x/.8 = -2.8 /.8

x =-3.5

Answer:

x=-3.5

Step-by-step explanation:

Marsha was shopping for a new dishwasher and researched the different models she could afford. Using Marsha’s frequency distribution table, determine the median price for dishwashers. Price,p($) Frequency,f 250 2 275 4 280 1 290 2 310 6 315 2 320 1 325 7 330 1 335 1 340 1 350 2 ​

Answers

Answer

310

Step-by-step explanation:

add them all up and divide by 12

9. All state names have at least two syllables. True or false

Answers

Answer:

False

Step-by-step explanation:

Only six states have two syllables in their name.

No, only six states have at least two syllables.

Here,

We have to check the given statement '' All state names have at least two syllables'' is true or false.

What are states which have at least two syllables?

There are only 6 states have at least two syllables.

1. Georgia.

2. Kansas.

3. New York.

4. Texas.

5. Utah.

6. Vermont.

Now,

There are only 6 states have at least two syllables.

Hence,

The given statement '' All state names have at least two syllables'' is false.

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1. Name the property the equation illustrates.
–2.1 × 1 = –2.1

Multiplication Property of –1
Inverse Property of Multiplication
Identity Property of Addition
Identity Property of Multiplication

2. Name the property the equation illustrates.
8.2 + (–8.2) = 0

Inverse Property of Multiplication
Addition Property of 0
Identity Property of Addition
Inverse Property of Addition

Answers

Answer:

1) ident. prop. of mult.

2) add. prop. of add.

Step-by-step explanation:

have a good day!

use the graph of the function to find the domain and range of f

Answers

Answer:

Step-by-step explanation:

Domain:  since x begins to the right of x = -2 and ends at x =2, the domain is  (-2, 2]

Range:  The smallest y value shown is y = -5 and the largest is y = 4.  Thus, the range is [-5, 4].

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