Calculus 3.10 Linearization (a) y=x^2sin2x (b) y=ln sqrt(1+t^2) find the differential of each.

Answers

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

(a) y=x^2sin2x

Using the Product Rule:

dy/dx = x^2*2cos2x + 2xsin2x

dy/dx = 2x(xcos2x + sin2x).

(b) y=ln sqrt(1+t^2)

     y = ln (1 + t^2)^1/2

Using the chain rule:

dy/dx =  1 / (1 + t^2)^1/2 * 1/2(1 + t^2)^-1/2 * 2t

=  2t/(1 + t^2)^1/2 * 1/ (2(1 + t^2)^1/2

=   2t / 2(1 + t^2)

= t / ( 1 + t^2).


Related Questions

Which equation represents a linear function?

2xy +y=9

y= 124 – 5

3y + x2 + x = 0

4x + 2 (y - 1) = 0

Answers

4x + 2 (y-1) = 0 is a linear function. Since, It doesn’t have any exponents.

consider the following formula used to estimate the height ,h, of a seedling after w weeks since planting:

Answers

Answer:

B

Step-by-step explanation:

solve for W

subtract 8/5 from both sides

then multiply by 5

hope this was helpful

mark bought 10 movie tickets for $120. how much will it to buy one ticket

Answers

12 tickets --

120/10= 12

Answer:

$12

Step-by-step explanation:

well 12 * 10 = 120 so 12 is 1 ticket

1/4 x 2/5 express your awnser in simplest form.

Answers

Answer:

1/4*2/5=(1*2)/(4*5)

= 2/ 20

= 1/10

So 1/4* 2/5=1/10

Answer:

1/10

Step-by-step explanation:

1)Draw the fractions.

2) Since you are basically dividing, divide 2

into 4 and your answer should be 2, cross

out 2 and put I because 2 into 2 goes one time,

and cross out 4 and put 2 because 2 into 4 goes 2 times

3) Multiply from across and you will get your answer

The revenue, in thousands of dollars, of a new flavor of liquor is given below as function of the number of gallons (in hundreds), x, sold:


[tex]r(x) = 50x - {x}^{2} [/tex]
What is the maximum revenue? Use units​

Answers

Answer:

  $625,000

Step-by-step explanation:

The maximum revenue will be found where the derivative of the revenue function is zero.

  r'(x) = 50 -2x = 0

  50 = 2x

  x = 25

When 2500 gallons are sold, the revenue is ...

  r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands

The maximum revenue is $625,000.

What's 5x5+6x3-1

Me brain is no working, please help

Answers

Answer:

42

Step-by-step explanation:

5*5+6*3-1

25+6*3-1

25+18-1

43-1

=42

I hope this helped, please give me Brainliest if it did. :)

Elizabeth ran 6 miles in 51 minutes. Assuming she always runs at that pace, how many miles can she run in 30 minutes? Round to the nearest tenth

Answers

Answer: 3.5 Miles

Step-by-step explanation: It would take her 8.5 min to run one mile because 51/6 is 8.5. Then I divided 30 by 8.5 to get 3.52, which is rounded to 3.5 miles in 30 min

Hope this helps :)

Find the union of A = {2,3,4} and B = {3,4,5)

Answers

Answer:

A U B = {2,3,4, 5}

Step-by-step explanation:

Union means join together

A U B = {2,3,4, 5}

Joseph earned $53 the first week he worked at Jim’s Candy Store and $62 the next week. How much did Joseph earn his first two weeks?
Explore:
Plan:
Solve:
Examine:

Answers

Answer:

$115

Step-by-step explanation:

Because the add does that like answer

I wait that you understand

1. What is the difference between a line and a line segment?
A. A line is a figure formed by two opposite rays with a shared endpoint, a line segment is a part of
a line that extends forever in one direction.
B. A line is a specific location that is represented by a dot, a line segment is a specific location
represented by two dots.
C. Aline is a portion of a line consisting of two points and all the points between them, and a line
segment is a figure formed by two opposite rays.
D. Aline is a figure formed by two opposite rays and a shared endpoint, and a line segment is a
portion of a line consisting of two points and all the points between them.

Answers

Answer: Choice DA line is a figure formed by two opposite rays with a shared endpointA line segment is a portion of a line consisting of two points and all points between them.

Explanation:

Basically a line goes on forever in both directions. A ray only goes off forever in one direction. If we glue together two rays that point in complete opposite directions (eg 1 points north, the other points south) then we form a line.

A line segment is a piece of a line. It doesn't go on forever in either direction. It has 2 endpoints and has a set fixed length. If you know the coordinates of each endpoint, you can use the distance formula to find that length.

A clothing manufacturer would like to determine whether celebrity endorsements and length of commercial influence a customer's decision to buy its products. In order to estimate this potential influence, the manufacturer premieres its latest series of commercials privately to potential buyers. There are two types of commercials: commercials without celebrities, and commercials with celebrities. There are two lengths of commercials: 30 seconds and 60 seconds. Each potential buyer is randomly assigned a type and length of commercial to view. What are the factors of interest to the manufacturer

Answers

Answer:

The correct response will be "whether or not the viewer will buy the product".

Step-by-step explanation:

To consider its clients, the manufacturer requires conducting this research, but the only element of interest would be to figure out whether or not the consumer purchases the product after seeing the ad. The response variable or perhaps the predictor variables determine "not if the audience can buy the advertisement" as well as "whether another advertisement becomes 30 or 60 seconds" including "not when the commercial involves a brand personality" have become the explanatory variables or even just the relationship between the independent variable.

9. Which of the following could be the areas of
the three squares below?

A. 12 ft?, 16 ft2 and 28 ft2
B. 8 f1?, 16 ft2 and 24 ft2
C. Both A and B
D. Neither A nor B

Answers

Answer:

The Answer can be A. 12ft2 ,16ft2 and 28 ft2

as well as B. 8ft2,16ft2 and 24ft2

a(2)+b(2)=c(2) a(2)+b(2)=c(2)

12+16=28 8 +16=24

Your answer is C.Both A and B

Hope you have a great day!

If you can do all three questions I’ll mark you brainlest!! Thanks <3

Answers

Answer:

1. Rate needed 9/6; Unit rate is 1.5/1; 1.5 cans of white paint are needed for each can of blue.

2. rate needed = 12/6; unit rate = 2/1;  Need 2 cups of water for every scoop of fruit mix.

3. 70 minutes

Step-by-step explanation:

1.  Set up a ratio

3white/2blue = xwhite/6blue

3/2 = x/6

cross multiply 2x = 18; x = 9

rate needed = 9/6

Unit rate is 1.5/1 (divide 3 by 2 or 9 by 6 to get unit rate_

2. 3/1.5 = x/6

1.5x = 18; x = 12

rate needed = 12/6

unit rate = 2/1

3. Set up a ratio.

3.5/.25 ( 1/4=.25)

3.5/.25 = x/5

.25x = 3.5(5)

.25x = 17.5

x = 70 minutes

Answer:

1) Rate: 3/2

  Unit Rate: 1.5/1

  Interpretation: Every 1 can of blue paint used requires 1.5 cans of white    

                           paint

 Solution: 9

Simplify:

22 - 3 × 6 + 52
A.
38
B.
139
C.
29
D.
65

Answers

Answer:

22 - 3 × 6 + 52 = 56

Step-by-step explanation:

Multiply

3×6 = 18

22-18+52

Add and subtract

22-18 = 4

4+52 = 46

Answer:

56

Step-by-step explanation:

To solve we must use the order of operations which is PEMDAS.

P-Parenthesis

E-Exponents

M-Multiplication

D-Division

A-Addition

and S-Subtraction

First we multiply -3 and 6 which gives us -18. So our equation is now 22-18+52.

Next we do addition. -18+52 is 34, plus 22 gives us 56.

Hope this helps :)

The thickness of photoresist applied towafers in a semiconductor manufacturing at a particular location onthe wafer is uniformly distributed between 0.2050 and 0.2150micrometers.(a) Determine the cumulative distributionfunction of photoresist thickness.(b) Determine the proportion of wafers that exceeds0.2125 micrometers in photoresist thickness.(c) What thickness is exceeded by 10% of thewafers?(d) Determine the mean and variance of photoresistthickness.

Answers

Answer:

a

  [tex]f(x)= 100 [x - 0.2050][/tex]

b

 [tex]P(X > 0.2125) =  0.25 [/tex]

c

  [tex]a = 0.2140[/tex]

d

Mean [tex]\mu  = 0.21[/tex]

Variance  [tex]\sigma ^2  =  0.0000083 [/tex]

Step-by-step explanation:

From the question we are told that

   The thickness of photoresist follows a uniform distribution

So

     [tex]X\   \~{}\ U \{  0.2050 , 0.2150 \}[/tex]

Generally the probability density function  is mathematically represented as

[tex]F(x) =  \left \{  \frac{1}{ 0.2150 - 02050} , 0.2150< x < 0.2150[/tex]

=>  [tex]F(x) =  \left \{   100 , 0.2150< x < 0.2150[/tex]

Generally the cumulative distribution function is

   [tex]f(x) =  \int\limits^{x}_{- \infty} {F(x)} \, dx[/tex]

Here [tex]- \infty[/tex] means the lower limit which in this case is  02050

So

    [tex]f(x) =  \int\limits^{x}_{0.2050} {100} \, dx[/tex]

    [tex]f(x) =  100 \int\limits^{x}_{0.2050} {1} \, dx[/tex]

=>   [tex] f(x)=100 [ x ] | \left \ x} \atop {0.2050}} \right.[/tex]

=>   [tex]f(x)= 100 [x - 0.2050][/tex]

Generally the proportion of wafers that exceeds 0.2125 is mathematically represented as

     [tex]P(X > 0.2125) =  1 - F(0.2125)[/tex]

=>  [tex]P(X > 0.2125) =  1- 100[0.2125 - 0.2050][/tex]

=>   [tex]P(X > 0.2125) =  0.25 [/tex]

Generally the thickness which is exceeded by 10% of the wafers is mathematically represented as

       [tex]P(X  > a ) =  0.10[/tex]

=>    [tex]1 - F(a) = 0.10[/tex]

=>     [tex]1 -100 (a - 0.2050) = 0.10[/tex]

=>     [tex]100(a -0.2050) =  0.90[/tex]

=>   [tex]a - 0.2050 =  0.009[/tex]

=>   [tex]a = 0.2140[/tex]

Generally the mean is mathematically represented as  

     [tex]\mu  =  \frac{ 0.2050 -0.2150 }{2}[/tex]

=>   [tex]\mu  = 0.21[/tex]

Generally the variance  is mathematically represented as

    [tex]\sigma ^2  =  \frac{1}{12} [0.2150 - 0.2050]^2[/tex]

=>  [tex]\sigma ^2  =  0.0000083 [/tex]

Which of the following is parallel to the equation of the following equation 3 x + 2 y = 10 and goes through the point (4, 10)?

Answers

Answer:

y=(-3/2)x+16

Step-by-step explanation:

the roots of a polynomial equation are 0, 5, and -2. what is the equation written in a factored form and in standard form?

Answers

Answer:

Check the pic

Pl ease help what is with give brainlist answer!

-5/6+6/18

1.-1/2

2.12/49

3.-1 and 1/6

4.12 ​

Answers

Answer:

option 1 is true. -1/2=-0.5

Answer:

-1/2

Step-by-step explanation:

-5/6 + 6/18

Simplify the second fraction by dividing the top and bottom by 3 ( then we will have like denominators)

-5/6 + 2/6

Combine the numerators since the denominators are the same

-3/6

Divide the top and bottom by 3

-1/2

Represent the following expressions as a power of the number a (a≠0):
((a^2)^−2)^5÷(a^15)​

Answers

Answer:

=0

Step-by-step explanation:


Dennis is saving up for a new video game console that costs $250. He already has $100. if he makes $10 per hour
nowing lawns, how many hours does he need to work in order to buy the console?

What is the equation and answer

Answers

Answer:

15 hours

Step-by-step explanation:

Step 1. $250-$100=$150

Step 2. $150÷$10=15 hours

To check answer:

$10x15(hours)=$150

$150+$100=$250

Answer:

15 hours

Explanation:

So start by taking 100 away from 250, to get 150. now divide 150 by 10. 15

1/5(12b+5) for b = 5/6​

Answers

Answer:

3

Step-by-step explanation:

eq.

1/5(12×5/6+5)

=1/5×(10+5)

=1/5×15

=3

Answer:

3

Step-by-step explanation:

can you help me for this m.c.m is of 10, 3 and 90.

Gracias (Thaks youuuuuuuuuuuuuuuuu)

Answers

Answer:

AR 27-10 supplements the MCM and is the ... available. The installation Trial Defense Service office will provide a military lawyer. If the. 3-1 ... away or assaulting you, enlist others to help.

Suppose you were to create a scatter plot of the data for speed and distance traveled. Would you expect to see a
positive, negative, or no relationship betwen the two variables. Explain your answer.
a. negative relationship, as the speed decreases, the distance increases.
b. positive relationship, as the speed decreases, the distance increases.
c. positive relationship, as the speed increases, the distance increases
d. no relationship.

Answers

Answer: its c. positive relationship; as the speed decreases, the distance increases.

Step-by-step explanation:

complete the square to make a perfect square trinomial. Write the result as a binomial square. a^2-20a​

Answers

Answer:

(a-10)^2 = 10^2

Step-by-step explanation:

a^2-20a=0

a^2-20a+100=100

(a-10)^2=100

Order 2/3,2/9,5/6,11/18 from least to greatest

Answers

11/18, 2/9, 5/6, 2/3

Answer: 2/9, 11/18, 2/3, 5/6

Step-by-step explanation:

2/3 = 0.6666...

2/9 = 0.2222...

5/6 = 0.8333...

11/18 = 0.61111...

Two flower seeds are randomly selected from a package that contains 8 seeds for red flowers and 9 seeds for white flowers. (Give your answer correct to three decimal places.)
(a) What is the probability that both seeds will result in red flowers?

Incorrect: Your answer is incorrect.


(b) What is the probability that one of each color is selected?


(c) What is the probability that both seeds are for white flowers?

Answers

Using the hypergeometric distribution, it is found that the probabilities are given as follows:

a) 0.2059 = 20.59%.

b) 0.5294 = 52.94%.

c) 0.2647 = 26.47%.

What is the hypergeometric distribution formula?

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

In this problem, the parameters are as follows: N = 17, k = 8, n = 2.

Item a:

This probbility is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,17,2,2) = \frac{C_{8,2}C_{9,0}}{C_{17,2}} = 0.2059[/tex]

Item b:

This probbility is P(X = 1), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,17,2,2) = \frac{C_{8,1}C_{9,1}}{C_{17,2}} = 0.5294[/tex]

Item c:

This probbility is P(X = 0), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,17,2,2) = \frac{C_{8,0}C_{9,2}}{C_{17,2}} = 0.2647[/tex]

More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394

A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 2cm. The chocolate used in the bon-bons has a density of 1.31 g/cm^3. If the chocolate
used costs $0.06 per gram, how much would the chocolate for 140 bon-bons cost, to
the nearest cent?

Answers

We will get the mass of each chocolate sphere, and the cost of 140 of these is $368.56

How much would it cost?

A sphere of radius R has a volume:

V = (4/3)*3.14*R^3

The mass of a sphere of chocolate will be given by the volume times the density, then one ball of chocolate has a mass:

M = (4/3)*3.14*(2cm)^3*(1.31 g/cm^3) = 43.88 g

And we know that the cost is of $0.06 per gram, the cost for 140 of these spheres is:

cost = 140*(44.88 g)*$0.06 = $368.56

If you want to learn more about density, you can read:

https://brainly.com/question/1354972

rewrite in simplest radical form 1 . show each step of your process.

-3/6

Answers

Answer:

what is this russian math?

Step-by-step explanation:

100$ Per Assignment
Anyone interested to do my assignments? I can pay 100$ per assignments. URGENT NEED

Answers

Answer:

which class

Step-by-step explanation:

which class are you in and which subject do u want

Kate wants to buy a new bicycle from a sporting goods stores the bicycle she wants normally sells for $440 the store has a sale? where all bicycle cost 3/4 of the regular price what is the sale price of the bicycle …

Answers

Given parameters:

Normal selling price off the bicycle = $440

Discount fraction  = [tex]\frac{3}{4}[/tex]

Unknown:

Sale price of the bicycle = ?

Solution:

The discounted sale price of the bicycle;

                      = normal selling price x discount fraction

Input the parameters and solve;

           Discounted sale price of the bicycle  =[tex]\frac{3}{4}[/tex] x 440

                                                                        = 3 x 110

                                                                        = $330

The discounted sale price of the bicycle is $330

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