Find the derivative of the function. (Simplify your answer completely.)
g(u) = 4u^2/(u^2+u)^7
g ' (u) =

Answers

Answer 1

The derivative of the function g(u) = \(4u^2/(u^2+u)^7\) is given by g'(u) = \((8u(u+1))/((u^2+u)^8)\).

To find the derivative of the function g(u), we can use the quotient rule. The quotient rule states that if we have a function of the form f(u)/h(u), where f(u) and h(u) are both functions of u, then the derivative of the function is given by \([h(u)f'(u) - f(u)h'(u)] / [h(u)]^2\).

Applying the quotient rule to g(u) = \(4u^2/(u^2+u)^7\), we need to find the derivatives of the numerator and the denominator. The derivative of \(4u^2\) with respect to u is 8u, and the derivative of (u^2+u)^7 with respect to u can be found using the chain rule.

Using the chain rule, we have d/dx \([(u^2+u)^7]\) = \(7(u^2+u)^6 * d/dx [u^2+u]\). Applying the derivative of u^2+u with respect to u gives us 2u+1. Substituting these derivatives into the quotient rule formula, we get g'(u) =\((8u(u+1))/((u^2+u)^8)\). This expression represents the simplified form of the derivative of the function g(u).

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Related Questions

what is 5.6 times 10 to the 7th power

Answers

it’s 56,000,000 just move the decimal place 7 places to the right

what is the density of the rock???!!!!!!!!!!

what is the density of the rock???!!!!!!!!!!

Answers

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

most are in range 3.0-3.7g/cm^3

3x - 4y = 10
X + 4y = -21

Answers

ANSWER:

X=-3x-11

Y=3x/4-5/2

Step-by-step explanation:

Which equations match the graph?

The graph of both x and y axis having range minus four to four by increment of one and every alternate tick marks are labeled. In the graph two lines g and f are intersecting at the point (0, 1). The other point on the line g is (-1, -1) and on the line f is (3, 2).

A. f(x) = 2x + 1 and g(x) = 13(6x) + 1
B. f(x) = 13x + 1 and g(x) = 23(2x) + 1
C. f(x) = 3x – 8 and g(x) = 23(3x) + 1
D. f(x) = 13x + 1 and g(x) = 13(6x) + 1

Answers

Answer:

D.

Step-by-step explanation:

Answer:

D

I know because I have that class and my teacher explained it.

The probability of the simultaneous occurrence of two events A and B is equal to the probability of A multiplied by the conditional probability of B giten that A has occurred (it is also equal to the probability of B multiplied by the conditional probability of A given that B has occurred).

Answers

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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no solution for 6x-3x+4-2x

Answers

Answer:

4+x

Step-by-step explanation:

you combine your like terms so you take 6x-3x and you end up with 3x than you take that 3x and subtract the 2x from it so you are left with just x so that would be 4+x

PLEASE HELP MEEE
Write a linear function that related y to x

PLEASE HELP MEEEWrite a linear function that related y to x

Answers

Answer:

\(y = \frac{x}{ - 4} \)

EMERGENCY!!!!! THIS IS AN EMERGENCY!!!!! ANSWER FAST PLEASE!!!!!!! Do not answer if you do not know what the answer is PLEASE!! YOU HAVE TO WRITE IT IN

YOUR OWN WORDS!!


What is an additive inverse? What does an additive inverse always equal? Explain!!

Answers

Answer:

The additive inverse of a number is what you add to a number to create the sum of zero. So in other words, the additive inverse of x is another number, y, as long as the sum of x + y equals zero. The additive inverse of x is equal and opposite in sign to it (so, y = -x or vice versa).

Step-by-step explanation:

Answer two questions about Equations A and B:

A. 5x=3x

B. 5=3

1) How can we get Equation B to Equation A?

Choose 1 answer:

(Choice A) Add/subtract the same quantity to/from only both sides

(Choice B) Add/subtract a quantity to/from only one side

(Choice C) Multiply/divide both sides by the same non-zero constant

(Choice C) Multiply/divide both sides by the same non-zero constant

(Choice D) Multiply/divide both sides by the same variable expression

2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?

Choose 1 answer:

(Choice A) Yes

(Choice B) No

Answers

Answer:

Question 1 is choice D.

Question 2 is no

Step-by-step explanation:

This is simple and logical

(1 point) a 17 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 16 feet above the ground?

Answers

When the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

This is a related rates problem involving a ladder leaning against a wall. Let's denote the distance of the foot of the ladder from the wall as x, and the height that the top of the ladder reaches as y. We are given that dy/dt = -2 ft/s (since the top is slipping down the wall) and we want to find dx/dt (the speed at which the foot of the ladder is moving away from the wall) when y = 16 ft.

Using the Pythagorean theorem, we have:

\(x^2 + y^2 = 17^2\)

Differentiating implicitly with respect to time, we get:

\(2x(dx/dt) + 2y(dy/dt) = 0\)

Substituting the given values, we get:

\(2x(dx/dt) + 2(16)(-2) = 0\)

Simplifying, we get:

\(2x(dx/dt) = 64\)

Dividing both sides by 2x, we get:

dx/dt = 64/(2x)

We know that y = 16, so we can use the Pythagorean theorem to solve for x:

\(x^2 + 16^2 = 17^2x^2 = 17^2 - 16^2x^2 = 33\)

Taking the square root, we get:

\(x = sqrt(33)\)

Substituting this into our expression for dx/dt, we get:

\(dx/dt = 64/(2*sqrt(33)) ≈ 3.86 ft/s\)

Therefore, when the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

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The measures of the angles of a triangle are shown in the figure below. Solve for x.
54°
(7x+1)°

Answers

The value of x according to the complete task content as given is; 5.

Sum of interior angles in a triangle.

It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).

Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;

90° + 54° + 7x + 1° = 180°

7x = 180° - 90° - 54° - 1°

Evaluate the right side of the equation;

7x = 35°

Divide both sides by; 7;

x = 35°/7

x = 5.

Ultimately, the value of x according to the task content is; 5.

Remark:

The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.

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What innovation was made possible in part because of the Carterfone decision in 1968? Select one a. COBOL b. radiospectrum allocation c. the public Internet d. SMS

Answers

The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.


This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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Afternselling 328 stickers, John had 857 stickers left. How many stickers did John have at first

Answers

Answer:

529

Step-by-step explanation:

Answer: 1185

Step-by-step explanation: add 328 and 857

Please answer these for brainlyest!!

Please answer these for brainlyest!!

Answers

1. (3z+1)+(1+5)
= 10z+6
2. 11(x-1)

a triangle has two sides of length 5 and 9. what compound inequality describes the possible lengths for the third side, x?

Answers

The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

What is meant by triangle?

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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(a) Consider the family of curves given by the polar equations r sin(n), where n is a positive integer. How is the number of loops related to n? Check all that apply. A. There are 4n loops when n is odd. B. There are 2n loops when n is even. C. There are n loops when n is odd. D. There is exactly 1 loop for each n. E. There are n loops when n is even. F. There are no loops. G. There are 4n loops when n is even H. There are 2n loops when n is odd.

Answers

The correct answers are option C for when n is odd and option E for when n is even.

The number of loops in the polar curves given by r sin(n), where n is a positive integer, is related to the parity of n. If n is odd, then the curve will have n loops, and if n is even, the curve will have 2n loops. Therefore, options C and E are correct.

To understand why this is the case, we can consider how the sine function behaves. The sine function oscillates between -1 and 1 as its argument increases from 0 to 2π. When n is odd, the argument of sin(nθ) increases from 0 to 2π as θ goes from 0 to π, resulting in n oscillations of the sine function in this interval. When n is even, the argument of sin(nθ) increases from 0 to 4π as θ goes from 0 to π, resulting in 2n oscillations of the sine function in this interval. This behavior translates into the number of loops in the polar curve, where each oscillation of the sine function corresponds to one loop.

Therefore, the number of loops in the polar curve r sin(n) depends on the parity of n, with n loops for odd values of n and 2n loops for even values of n.

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mrs. rosenblatt's class has an average grade of 87. later on she realizes she left out joe's score. his grade was a 65. the new mean will ,....

Answers

Mrs. Rosenblatt's class has an average grade of 87. After realizing she left out Joe's score of 65, the new mean will be lower than 87.

Explanation:

To find the new mean, we need to calculate the sum of all the grades in the class, including Joe's score of 65, and divide it by the total number of students in the class. Let's assume there are n students in the class.

The sum of all the grades in the class, including Joe's score, will be (87 * n) + 65, since the average grade before Joe's score was added was 87. Therefore, the new mean will be:

[(87 * n) + 65] / (n + 1)

Expanding this expression, we get:

(87n + 65) / (n + 1)

Simplifying this expression, we get:

(87n / (n + 1)) + (65 / (n + 1))

Since n is a positive integer, the value of (87n / (n + 1)) will be slightly less than 87. Therefore, the new mean will be slightly less than 87, reflecting the lower score added to the class average.

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In your math notebook: Give an approximation of the width of the river, support your answer with reasoning from the measurements given. Set up an equation and solve for the width of the Klamath River. Enter the width of the river.

TwT plz help​

In your math notebook: Give an approximation of the width of the river, support your answer with reasoning

Answers

Answer:

um i cant read it and why do you use cringet emojis like TwT

Step-by-step explanation:

Answer:

ehbsbshshwhajwj

Step-by-step explanation:

whhwbwbsbsbbsh

Can I get help please

Can I get help please

Answers

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

What is compound interest?

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .

Answers

If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.

This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.

The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.

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The complete question is:

Complete the interpretation for the p-value:

If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .

Three runners are training for a marathon. one day, they all run about ten miles, each at their own constant speed. which of the three runners has the fastest pace?

Answers

You did not post enough information.

Sound travels 340 m/s. The function d(t)=340t gives the distance d(t), in meters, that sound travels in t seconds. How far does sound travel in 56 s

Answers

The sound travelled a distance of 19040 meters in 56 seconds

How to determine the distance travelled in 56 seconds?

From the question, the distance function is given as

d(t) = 340t

Also, from the question;

The time is given as

Time = 56 seconds

Rewrite as

t = 56

Substitute t = 56 in the equation d(t) = 340t

So, we have

d(56) = 340 * 56

Evaluate

d(56) = 19040

Express the units

d(56) = 19040 meters

Hence, the distance travelled in 56 seconds is 19040 meters

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ASAP PLEASE
-WILL MARK BRIANIST

ASAP PLEASE-WILL MARK BRIANIST

Answers

Answer:

D

Step-by-step explanation:

A. 9x9 = 81

B. 2x2x2x2x2 = 32

C. 10x10 = 100

D. 5x5x5x5 = 625

Answer:

5⁴ has the greatest value

Step-by-step explanation:

9² = 9 x 9 = 81

2⁵ = 2 x 2 x 2 x 2 x 2 = 32

10² = 10 x 10 = 100

5⁴ = 5 x 5 x 5 x 5 = 624

Therefore, 5⁴ has the greatest value!

Hope this helps!

what was the mean number of miles the hiker walked for the 6 days?

Answers

Answer:

Incomplete question

...

rectangle has a length of 24 in. and a width of 14 in. it is dilated and the image has a width of 21 in. what is length of the image of the rectangle? (

Answers

Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

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The old film-style cameras created photos that were best printed at 3.5 inches by 5 inches. Today's new digital cameras create photos that are best printed at 4 inches by 6 inches. Neither size picture will scale perfectly to fit in an 11-inch by 14-inch frame. Which type of camera will you minimize the loss of the edges of your picture?​

Answers

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since the aspect ratio of 4:6 is closer to that of an 11-inch by 14-inch frame (which is approximately 1:1.5) than the aspect ratio of 3.5:5 (which is approximately 7:10).

By minimizing the difference in aspect ratio between the photo and the frame, you will minimize the loss of the edges of the picture when trying to fit it into the frame.

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize the loss of the edges of the picture when trying to fit it into an 11-inch by 14-inch frame.

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To visit your favorite ice cream shop, you must travel 490 mm west on Main Street and then 970 mm south on Division Street.

Find the total distance you traveled.

Answers

The total distanced travelled by me is 1086.74 mm approximately.

Use the Pythagorean theorem to calculate the total distance travelled.

The distance is the hypotenuse of a right triangle whose two legs are the lengths of Main Street and Division Street, respectively.

We know that West direction and South direction are in perpendicular direction with each other.

The Pythagorean theorem is used:

Total Distance² = 490² + 970²

Total Distance² = 240100 + 940900

Total Distance² = 1181000

Total Distance = √1181000

Total Distance = 1086.74 [Rounding off to nearest hundredth]

Hence the total distanced travelled by me is 1086.74 mm approximately.

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Find the measure of

Find the measure of

Answers

Answer:   146 degrees

=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12​

Answers

C. 48 is the answer for 3(2x^2-£)

Whats the best anime character (from any anime)

Answers

Answer:

Phil is superior

Step-by-step explanation:

From TPN by the way

Answer:

(insert almost every Danganronpa character here)

(i said almost bc of haji Teruteru and Hifumi)

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