Differentiate Vx(x + 2) with respect to x.

Differentiate Vx(x + 2) With Respect To X.

Answers

Answer 1

Answer:

[tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]

General Formulas and Concepts:

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Product Rule: [tex]\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

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

Step 2: Rewrite

[tex]y=x^{\frac{1}{2} } (x+2)[/tex]

Step 3: Differentiate

Product Rule [Basic Power/Chain Rule]:                 [tex]y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)[/tex]Simplify:                                                                            [tex]y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}[/tex]Rewrite:                                                                                        [tex]y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}[/tex]Add:                                                                                                       [tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]

Related Questions

At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at most 2 prizes?
0.09

0.33

0.58

0.91

Answers

The probability of winning one prize in 3 attempts is P = 0.41.

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, the chance of winning a prize is 0.45, Kyle plays the game 3 times. we need to find the probability that she wins at most 2 prizes

Out of 3 attempts, the probability of winning one prize is:

P(1) = (0.45)x(0.55)²p

where p is the number of permutations, you can win on the first attempt, second attempt, or third attempt, so there are 3 permutations.

Then the probability is:

P(1) = (0.45)x(0.55)²x3 = 0.41

Hence, the probability of winning one prize in 3 attempts is P = 0.41,

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Answer: D 0.91

Step-by-step explanation:

Add 0.17 + 0.41 + 0.33 = 0.91

To get 0.17:

0.41 + 0.33 + 0.09 = 0.83

1 - 0.83 = 0.17

:)

A school had 45 classrooms. there are 27 in each classroom how many students are in all 45 classrooms?

Answers

Answer:

1215

Step-by-step explanation:

Answer:

1,215

Step-by-step explanation:

just multiply 27 &45

1.) A tower casts a shadow that is 60 feet long when the angle
of elevation of the sun is 65". How tall is the tower?

Answers

Answer:

128.67 ft

Step-by-step explanation:

Let the height of the tower be x feet.

[tex] \tan \: 65 \degree = \frac{x}{60} \\ \\ 2.1445069205 = \frac{x}{60} \\ \\ x = 2.1445069205 \times 60 \\ \\ x = 128.670415 \\ \\ x = 128.67 \: ft[/tex]

Solve for x: 3x − 2 > 5x + 10. (5 points)
1) x > 6

2) x −6

Answers

Answer:

[tex]x<-6[/tex]

Step-by-step explanation:

[tex]3x-2>5x+10[/tex]

Add 2 to both sides

[tex]3x-2+2>5x+10+2[/tex]

Simplify

[tex]3x>5x+12[/tex]

Subtract [tex]5x[/tex] from both sides

[tex]3x-5x>5x+12-5x[/tex]

Simplify

[tex]-2x>12[/tex]

Multiply both sides by [tex]-1[/tex] (reverse the inequality)

[tex](-2x)(-1)<12(-1)[/tex]

Simplify

[tex]2x<-12[/tex]

Divide both sides by [tex]2[/tex]

[tex]\frac{2x}{2} <\frac{-12}{2}[/tex]

Divide the numbers: [tex]\frac{2}{2} =1[/tex]

[tex]=x[/tex]

Divide the numbers: [tex]\frac{-12}{2}[/tex]

Apply fraction rule: [tex]\frac{-a}{b} =-\frac{a}{b}[/tex]

[tex]=\frac{12}{2}[/tex]

Divide the numbers: [tex]\frac{12}{2} =6[/tex]

[tex]=-6[/tex]

[tex]x<-6[/tex]

Answer:

x < -6

Step-by-step explanation:

I just took the test. When you are dividing by a negative variable, flip the sign.

Jordan is starting to save $150 to buy a new cell phone. In December, he saved $5. In January, he plans twice as much as he did in December, for a total savings of $15 ($5 + $10). If Jordan continues to save twice as much he saved from the previous month, in which month will his total savings will be enough to buy the phone.

Answers

9514 1404 393

Answer:

  April

Step-by-step explanation:

The sequence of amounts saved is a geometric sequence. The sum of those amounts is given by the formula ...

  Sn = a1·(r^n -1)/(r -1)

where a1 is the amount saved in month 1, r is the common ratio, and n is the number of months. We want to find n such that ...

  150 ≤ 5(2^n -1)/(2 -1)

  30 ≤ 2^n -1

  31 ≤ 2^n

We can solve this using logarithms, or we can make use of our knowledge of powers of 2: 2^5 = 32. That is, n = 5 will be the first month when Jordan's total savings exceeds $150.

The fifth month will be April. Jordan's total savings will be enough in April.

__

The attached shows a spreadsheet that computes Jordan's amount of savings each month, and his running total. Once the formulas are written, they can be copied down as far as required to see where the total savings is enough.

nth term (math) asap please.

Answers

Answer:

Just do minus two, and you will get 27-100=-73

Step-by-step explanation:

Until the scale was changed in 1995, sat scores were based on a scale set many years ago. For math scores, the mean under the old scale in the early 1990s was 470 and the standard deviation was 110. In 2016, the mean was 510 and the standard deviation was 103. Gina took the sat in 1994 and scored 500. Her cousin colleen took the sat in 2016 and scored 530. Who did better on the exam, and how can you tell?.

Answers

Gina—her standardized score is higher than Colleen’s. The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Gina

Gina took the SAT in 1994 and scored 500 on the Math test.

For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.

x = 500

μ = 470

σ = 110

Hence, the z score is given as:

z = 500 - 470/110

z = 0.27273

Gina's z or standardized score is 0.27273

For Colleen

Her cousin Colleen took the SAT in 2016 and scored 530 on the Math test.

In 2016 the mean was 510 and the standard deviation was 103.

x = 530

μ = 510

σ = 103

Hence, the z score is given as:

z = 530 - 510/103

z = 0.19417

Colleen's z or standardized score is 0.19147

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pls help. polynomials solving equations

Answers

Answer:

+9or -9 is the answer ☺️ you

Answer:

y will be equal to 0, 9, or 1

(y=0, 9, 1)

Help ASAP I’ll give brainliest

Answers

Answer:

B

Step-by-step explanation:

—Math

–x/4 < 7

–x < 28

x > –28

follow my account^^

Answer:

B. x > -28

Step-by-step explanation:

-x/4 < 7    =

Multiply both sides by 4

-x < 28

x > -28

Help me with this it’s for geometry

Answers

Answer:

x = 4

Step-by-step explanation:

The transversal line is perpendicular to both the parallel lines. So ,

[tex]21x+6=90\\=>21x=90-6=84\\=>x = \frac{84}{21} = 4[/tex]

x=4 I dont knowhhahahahahahahha

Find the gradient of the line segment between the points (-3,3) and (2,5).
Give your answer in its simplest form.

Answers

Answer:

2/5

Step-by-step explanation:

5-3/2-(-3)=2/5

Manuel created a factor tree and wrote the prime factorization of 60 shown below.
A factor tree of 60. 60 branches to 4 and 15. 15 branches to 3 and 5. The equation is 60 = 3 times 4 times 5.
What is Manuel’s error?
He did not include 15 in the prime factorization.
He did not find the prime factors of 4.
He should have started the factor tree with 2 times 30.
He should not have found the factors of 15.

Answers

Answer:

The second one or B- "He did not find the prime factors of 4."

Step-by-step explanation:

I got it right on Edge2020

Answer:

B

Step-by-step explanation:

Hey, Whats The answer please explain your answer marking brainliest:D.....................................

Answers

30% of 70 is

A. 21

Bugbjyvjgbjhbghcfgdchgv

Answer:

A) 21

Step-by-step explanation:

30% of 70 is 21

what is the value of the fourth term in a geometric sequence for which a1 = 3- amd r = 1/2

Answers

The value of the fourth term in a geometric sequence is 3/8.

How to calculate the sequence?

We are meant to find the value of the fourth term in a geometric sequence for which a1 = 3- and r = 1/2.

It should be noted that the formula will be:

ar^n-1

where n = 4

r = 1/2

a = 3

Therefore, ar^n-1 = ar^(4-1) = ar³

= ar³.

= 3(1/2)³

= 3 × 1/8

= 3/8

Thw 4th term is 3/8.

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50 POINTS AND BRAINLIEST

Answers

C because if you sub any number in it comes out to one or greater than one
C because if you sub any number in it comes
out to one or greater than one.

Please help me, inequalities...............................

Answers

Answer:

x is greater than or equal to 1

Step-by-step explanation:

how many lines of symmetry does the Eiffel Tower have?

Answers

Answer:

it has 2 lines of symmetry 1 going across it diagonally and 1 going straight through the middle.

Step-by-step explanation:

The answerwould be 2 !

Write in slope intercept form . y+4=−12(x−2)

Answers

Answer:

20

Step-by-step explanation:

y+4=−12(x−2)

Step 1: Add -4 to both sides.

y+4+−4=−12x+24+−4

y=−12x+20

Yeah the answer Should be 20

4(x - 6) + 2 = 6x -2
solve the equation

Answers

Answer:

x=−10

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x−6)+2=6x−2

Step 1: Simplify both sides of the equation.

4(x−6)+2=6x−2

(4)(x)+(4)(−6)+2=6x+−2(Distribute)

4x+−24+2=6x+−2

(4x)+(−24+2)=6x−2(Combine Like Terms)

4x+−22=6x−2

4x−22=6x−2

Step 2: Subtract 6x from both sides.

4x−22−6x=6x−2−6x

−2x−22=−2

Step 3: Add 22 to both sides.

−2x−22+22=−2+22

−2x=20

Step 4: Divide both sides by -2.

−2x

−2

=

20

−2

x=−10

Answer:x=-10

Step-by-step explanation:4x-24+2=6x-2 -22+4x=6x-2 , 2x=-20 , x=-10

Ill make you brainlist write in y=mx+b form

Answers

Answer:

y = [tex]\frac{2}{5}[/tex] x + 2

Step-by-step explanation:

Graph below.

Answer:

y = 2/5x + 2

Step-by-step explanation:

y = mx + b

First, we find out the slope. The slope is the change in y over the change in x.

The change in y is the second y-value subtracted from the first. The first y-value is 0 and the second is 2.

0 - 2 = -2

The change in x is the second x-value subtracted from the first. The first x-value is -5 and the second is 0.

-5 - 0 = -5

The slope is the change in y over the change in x.

-2/-5 = 2/5

y = 2/5x + b

b is the y-intercept, which is the value of y when x = 0.

When x = 0, y = 2 (0,2), so b = 2.

y = 2/5x + 2

Hope this helps!

Help please math people

Answers

Answer:

29

Step-by-step explanation:

[tex]f(x)=4x+9[/tex]

Substitute x = 5 in the equation.

[tex]f(5)=4(5)+9\\f(5)=20+9\\f(5)=29[/tex]

Therefore, the answer is 29. The third choice.

simplify 5n+11n=16n PLEASE

Answers

Answer:

16n=16n or n=1

Step-by-step explanation:

5n + 11n = 16n       add like terms

16n = 16n               divide both sides by 16

n = 1

Answer:

16n = 16nTrue

Explanation:

Add to simplify:

5n + 11n equals 16n

So, the final answer is:

16n = 16n True  (16n does equal 16n)

Hope this helps! :)

Solve for y: 20x + 4y = 28

Answers

Answer:

y = 7 - 5x

Step-by-step explanation:

20x + 4y = 28

4y = 28 - 20x

y = 28/4 - 20x/4

y = 7 - 5x

-TheUnknownScientist

what is a polygon with only 3 sides​

Answers

Answer:

triangle?duh ..........

could someone please help me with this?

Answers

Here’s the correct answer and how I got it :)
I’m alive but I’m dead. Sad :( rip x

Find the missing side of this triangle, round to the nearest tenth if needed PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

The value of x:

[tex]x\:\approx \:8[/tex] in

Step-by-step explanation:

Given

[tex]b=4.8[/tex] in

[tex]c=9.3[/tex] in

a = x

we have to determine 'x'.

As the given triangle is a right-angled triangle.

Pythagorean Theorem:

For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as

[tex]c=\sqrt{a^2+b^2}[/tex]

so

[tex]a=\sqrt{c^2-b^2}[/tex]

as

[tex]b=4.8[/tex] in[tex]c=9.3[/tex] ina = x

substituting the values

[tex]x=\sqrt{9.3^2-4.8^2}[/tex]

[tex]x\:\approx \:8[/tex] in

Thus, the value of x:

[tex]x\:\approx \:8[/tex] in

I’m not sure how to do this can anyone help!!!!!

Answers

9514 1404 393

Answer:

  22/44

Step-by-step explanation:

The probability of black is the ratio of black cards to all cards. If the Ace and 2 are removed from each suit, there will be 11 of the 13 cards remaining. 2 suits are black, for a total of 2×11 = 22 black cards. Of course there are 4 suits altogether, for a total of 4×11 = 44 total cards. Then you have ...

  P(black) = (black cards)/(total cards)

  P(black) = 22/44

_____

You are expected to be familiar with the fact that a deck of 52 playing cards consists of 4 suits: diamonds, clubs, hearts, spades. Each suit has 13 cards, identified as Ace, 2, 3, ..., 10, Jack, Queen, King. The clubs and spades are black; the diamonds and hearts are red.

The local newspaper has letters to the editor from 30 people. If this nunber represents 5% of all of the
newspaper's readers, how many readers does the newspaper have?

The newspaper has___readers.

Answers

Answer:

600 readers

Step-by-step explanation:

just do 100/5=20

and then 30x20=600 readers

The distribution of random variable r has mean 10 and standard deviation 4. The distribution of random variable s has mean 7 and standard deviation 3. If r and s are independent, what are the mean and standard deviation of the distribution of r−s ?.

Answers

The random variable r has a mean μ = 10 and σ = 4. For the variable s, the μ = 7 and σ = 3. The mean of r-s will be obtained by arithmetic subtraction of the μ for r and a. The standard deviation isn't independent since it's obtained by square root of the variance of a distribution. The standard deviation will be obtained by obtained through the square root of the squared sum of σ.

μ (r-s) = μ(r) -μ(s)

μ (r-s) = 10 -7 = 3

σ (r) -σ(s) = √(σ (r))²+ (σ (s))²

σ (r) -σ(s) = √(4²+ 3²)

σ (r) -σ(s) = √(16+ 9)

σ (r) -σ(s) = √25 = 5

thus, the mean is 3 and the standard deviation is 5.

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what is 11 = 12 - q ?

Answers

Answer:

1

Step-by-step explanation:

12 - 1 = 11

to solve for q all you had to do was 12-11=1 (switch 11 and one)

Hey there!

11 = 12 - q

-q + 12 = 11

SUBTRACT 12 to BOTH SIDES

-q + 12 - 12 = 11 - 12

SIMPLIFY IT!
-q = 11 - 12

-q = -1

-1q = -1

DIVIDE -1 to BOTH SIDES

-1q/-1 = -1/-1

SIMPLIFY IT!

q = -1/-1

q = 1


Therefore, your answer should be:

q = 1


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

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