Find the equation of the tangent line to y=sinx at x=2pie

Answers

Answer 1

Answer:

y = x - 2π

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

x₁ - x coordinate y₁ - y coordinate m - slope

Pre-Calculus

Unit Circle

Calculus

The definition of a derivative is the slope of the tangent line.

Derivatives of Trig Functions

sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)

Step-by-step explanation:

Step 1: Define

y = sinx

x = 2π

Step 2: Find Derivative

Take derivative:                   y' = cosx

This is the function of the tangent line for y.

Step 3: Find slope

Substitute in x into y':                    y'(2π) = cos2πEvaluate:                                        y'(2π) = 1

This tells us that the slope of the tangent line is 1 at x = 2π.

Step 4: Write equation

Find a point.

Substitute x into y:                     y(2π) = sin2πEvaluate:                                    y(2π) = 0Write coordinate:                      (2π, 0)

Write tangent function.

Substitute:                    y - 0 = 1(x - 2π)Simplify:                        y = x - 2π

This is the equation of the tangent line at x = 2π.


Related Questions

If a car travels 23 miles in 20 min what is the. car speed in miles per hour?​

Answers

Answer:

69 miles per hour

Step-by-step explanation:

car travels 23 miles in 20 min

So 20 min=20/60hour

=1/3. hour

Speed of the car=23÷1/3

=69 miles/hour

So the final answer is 69miles/hour

Use the order of operations to simplify 4 + 15 = 5
A 24 4/5
B 19 2/5
C 7 2/5
D 8​

Answers

Answer:

C

Step-by-step explanation:

pleas yall help me ill give a lot of points and brainiest

Answers

It’s the first one I believe.

Answer:

Third choice.

Step-by-step explanation:

The left side is "8 less than 4 times a number"

The right side is "2 times the difference of 2 times the number decreased by 3"

Answer: Third choice.

Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?

Answers

Answer:

0.0083

Step-by-step explanation:

From the given information;

The total number of individual in the team = 3

The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]

= (6×5×4×3!)/3!

= 6×5×4

= 120 ways

The probability of forming such a team with 6 people = 1/120

= 0.0083

Which of the following equations represent linear functions?

y=x2−3x

4x+y=5

y=|2x+1|

y=−5

Answers

4x+y=5 or b is the correct answer:) Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Mr. Santiago has a flight from New York to Paris that covers a distance of 3,640 miles in 7 hours. If the plane travels at the same speed per hour, how many miles will it have traveled after 4 hours?

2. Josh watches 720 shows in one year. If he watches the same number of shows each month, how many shows does he watch in 5 months?

Answers

Answer:He traveled 2080 miles after 4 hours. He covered 3640 miles in 7 hours with a constant speed, so we can calculate the speed: 3640/7=520 miles/hour. After 4 hours, he traveled 520*4=2080 miles.

Step-by-step explanation:

Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.) (8.99)3 using differentials

Answers

Answer:

726.572699

Step-by-step explanation:

According to differentials

(x+Δx)³ = x³ + 3x²Δx + 3x(Δx)² + (Δx)³ (Using binomial expansion)

Using this formula to solve (8.99)³, this can also be written as;

(8.99)³ =  (9-0.01)³ where

x = 9

Δx = -0.01

Substitute this vales into the differential expression above

(9+(-0.01))³ = 9³ + 3(9)²(-0.01) + 3(9)(-0.01)² + (-0.01)³

(9+(-0.01))³ = 729 + (243)(-0.01) + 27(0.0001) + (-0.000001)

(9+(-0.01))³ = 729-2.43+0.0027-0.000001

(9+(-0.01))³ = 729-2.43+0.0027-0.000001

(9+(-0.01))³  = 726.572699

Hence 8.99³ = 726.572699 (Using differential)

Using calculator;

8.99³ = 726.572699

Auto sales in a country increased from 16.5 million in 2014 to 17.5 million in 2015. Find the percent increase in auto sales from 2014 to 2015. Round to the nearest tenth of a percent._______%

Answers

Answer:

6.1%

Step-by-step explanation:

Amount increase=17.5-16.5

=1million

% increase= amount increase/original×100% amount

= 1/16.5×100%

= 6.1%

The percentage increase in auto sales is 6.1 %

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The auto sales of the country in 2014 = 16.5 million

The auto sales of the country in 2015 = 17.5 million

The increase in auto sales in 2015 from 2014 =
Auto sales of the country in 2015 - Auto sales of the country in 2014

The increase in auto sales in 2015 from 2014 = 17.5 million - 16.5 million

                                                                           = 1 million

Now , the percentage increase in auto sales =
( Increase in auto sales / Auto sales of the country in 2014 ) x 100

The percentage increase in auto sales = ( 1 / 16.5 ) x 100

                                                                 = 6.06 %

Therefore , the percentage increase is 6.1 %

Hence , the percentage increase in auto sales if 6.1 %

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If a freight train travels at a speed of 20 miles per hour for 6 hours, how far will it travel? A 120 miles B 80 miles C 26 miles D 12 miles​

Answers

Answer: The answer is A

Step-by-step explanation: Because 6*20= 120

What is a3 of the sequence 13, 18, 23, 28, 33, 38...

Answers

Answer:

23

Step-by-step explanation:

cuz it starts with 13 as a1

Two points on the graph of the linear function f are (0,3) and (3,9). Write a function g whose graph is a reflection in the x-axis of the graph of f ​

Answers

Two points on the graph of the linear function f are (0,3) and (3,9). Write a function g whose graph is a reflection in the x-axis of the graph of f

ian's car can go 99 miles on 3 gallons of gas During a drive last​ weekend,Ian used 7 gallons of gas.How far did he drive?Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas He used. He drove____ miles.

Answers

Answer:

The answer would be 231 miles.

Step-by-step explanation:

This is because you have to make this into the most common ratio, which would be 1/33. To get to 7 gallons, you must multiply 33 by 7, because you multiplied 1 by 7.

He drove 231 miles I think

Can you Explain how to do this plz

Answers

it is -18 because -18 divided by 6 is -3. then -5+-3 is -8

Which of the following values are solutions to the inequality 5 < 7+ 5x?

Answers

Answer:

x can equal to anything that is 1 and higher

Step-by-step explanation:

The equation is already correct, you just want to get x as a number that would increase the value.

the ratio 60 miles per hour is an example of a ______because it has two measurements having different units of measure
Answers:

1.Annex
2.Rate
3.Unit rate
4.Least common multiple

Answers

Answer:

3. Unit Rate

Step-by-step explanation:

The answer is Unit Rate because it is describing two units of measurements compared to one another.

Is the sum of any 2 consecutive prime numbers also prime?

Answers

Answer:

Yes! (it’s making me write 20 letters so yes is ur answer ok cool)

Yes beachside I really don’t know you it juts is

-3a - 4(a - 6) = 24 - 7a

Solve the equation

Thanks

Answers

-3a-4(a-6)=24-7a

-3a-4a+24=24-7a

-7a+24=24-7a

-7a+24=-7a+24

-7a+24-24=-7a+24-24

Simplify

Subtract the numbers

Subtract the numbers

−7a=-7a

Add 7a to both sides of the equation

-7a+7a =-7a+7a

Simplify

Combine like terms

Combine like terms

0=0

answer is 0=0

An article on polygraph testing of FBI agents indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is 0.25. Let x be the number of trustworthy FBI agents tested until someone fails the test. (Round your answers to four decimal places.)(a) Describe the probability distribution of x.
normalgeometric binomial(b) What is the probability that the first false-positive will occur when the third person is tested?(c) What is the probability that fewer than four are tested before the first false-positive occurs?(d) What is the probability that more than three agents are tested before the first false-positive occurs?

Answers

Answer:

???

Step-by-step explanation:

Imena earned $261 last week. If she worked 18 hours and earned the same amount each hour, how much was she paid per hour?

Answers

The answer to your question is $14.50 a hour

The amount paid to Imena per hour will be $14.5

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Imena earned $261 last week. She worked 18 hours and earned the same amount each hour.

Imena's earnings for an hour will be calculated as:-

Earning per hour = 261 / 18

Earning per hour = $14.5

Therefore, the amount paid to Imena per hour will be $14.5

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wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within + 5 lb. of population mean weight?

Answers

This question was not written properly

Complete Question

Wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight?

Answer:

0.68269

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question:

Standard deviation = 50 lb.

Sample size = 100

The weight is within ± 5Ib

For +5 lb

Z =+ 5/50/ √100

Z = +5/50/10

Z = +5/5

Z = 1

Using the Z table to find the probability of the Z score.

P(Z = 1) = 0.84134

For - 5 lb

Z = - 5/50/ √100

Z = - 5/50/10

Z = - 5/5

Z = -1

Using the Z table to find the probability of the Z score.

P(Z = -1 ) = 0.15866

Hence,

P (-Z<x<Z)

P(Z = +1 ) - P(Z = -1)

0.84134 - 0.15866

= 0.68269

The probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight is 0.68269

What is the u equal to -4=u/2-8

Answers

Answer:12. V is not needed, and just substitute the letters with the numbers the correspond to.

Step-by-step explanation:

evaluate the expression for x = 3 y= 1/3 and z= 5. 12 x - 3y / 4 x - Z​

Answers

Answer:

5

Step-by-step explanation:

12 x - 3y / 4 x - Z

=12×3-3×1/3÷4×3-5

=36-1/12-5

=35/7

=5

So the final answer is 5.

57x2.3 what is the anser pls help

Answers

Answer:

285.00

Step-by-step explanation:

Because you change 57 to a decimal (57.0) then you multiply.

57.0×2.3=285.00

today is my birthday wish me a happy birthday

Whoever answers correctly gets brainlist.

Answers

Answer:

1.- 4/5 + 5/12= 1  and 13/60

2.- 5/6 + 6/12= 1 and 1/3

3.- 1/3 + 2/6= 2/3

4.- 7/8 + 8/10=  1 and 27/40

The store bought the bike at a wholesale price. The bike store marked up the wholesale cost of the bike by 60%. What was the wholesale cost of the bike if the store sold the bike to Andre for $160?

Answers

Answer: The wholesale cost of the bike = $100

Step-by-step explanation:

Let x = wholesale cost of the bike

As per given,

Selling price = cost price + (Mark up percent) x ( cost price)  (i)

Selling price of bike = $160

Mark up percent = 60% =0.60

Substitute values in (i) , we get

[tex]160= x+0.6x\\\\\Rightarrow\ 160=1.6x\\\\\Rightarrow\ x=\dfrac{160}{1.6}\\\\\Rightarrow\ x= 100[/tex]

Hence, the wholesale cost of the bike = $100

Which equation is the inverse of y = 9x2 – 4?

Answers

Answer:

C

Step-by-step explanation:

For edge

Answer:

correct C on e2021

Step-by-step explanation:

A car travels 180 miles in 4 hours. What is
the car’s speed in feet per minute?

Answers

Answer:

3,960 feet per minute, brainliest pls

Step-by-step explanation:

Answer:

3960 feet per minute

Step-by-step explanation:

1 mile = 5280 feet

Therefore,

180 miles = 180*5280

180 miles = 950400 feet

1 hour = 60 minutes

So, 4 hours = 240 minutes

Speed if the car

= 950400/240

= 3960 feet per minute

Video game system and several games are sold for $664. The cost of the games is 3 times as much is a cost in system. Find the cost of the system the cost of the games.

Answers

Answer:

games=$483

system=$161

Step-by-step explanation:

Answer: the cost of the system is $166 and the cost of the games is $498.

Step-by-step explanation:

Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? a. 68 inches b. 23 inches c. 34 inches d. 48 inches

Answers

Answer:

d. 48 inches

Step-by-step explanation:

We assume the mirror is a rectangle

We solve for the length of a diagonal using Pythagoras Theorem

a² + b² = c²

c = √a² + b²

Where c = diagonal

a = 30 inches

b = 38 inches

c = √30² + 38²

c = √2344

c = 48.414873748 inches

Approximately = 48 inches

Charli bought 2 3/4 pounds of pears for 0.76 per pound and 2 3/4 pounds of grapes for 1.40 per pound. how much money in dollars and cents did charli pay for the pears and grapes?

Answers

Answer:

[tex]Total = \$5.94[/tex] ---- in dollars

[tex]Total = 594\ cents[/tex] ---- in cents

5 dollars 94 cents

Step-by-step explanation:

Given

Pears

[tex]Weight = 2\frac{3}{4}\ lb[/tex]

[tex]Amount = \$0.76[/tex] per pound

Grapes

[tex]Weight = 2\frac{3}{4}\ lb[/tex]

[tex]Amount = \$1.40[/tex] per pound

Required

Determine the amount paid for the fruit in dollar and cents

First, we need to calculate the amount paid for each fruit.

This is calculated by multiplying the amount per pound by the number of pounds bought.

For Pears:

[tex]Total_{Pears} = 2\frac{3}{4} * \$0.76[/tex]

Convert fraction to decimal

[tex]Total_{Pears} = 2.75 * \$0.76[/tex]

[tex]Total_{Pears} = \$2.09[/tex]

For Grapes

[tex]Total_{Grapes} = 2\frac{3}{4} * \$1.40[/tex]

Convert fraction to decimal

[tex]Total_{Grapes} = 2.75 * \$1.40[/tex]

[tex]Total_{Grapes} = \$3.85[/tex]

Next, we add both amounts together to get the total amount spent in dollars.

[tex]Total = Total_{Pears} + Total_{Grapes}[/tex]

[tex]Total = \$2.09 + \$3.85[/tex]

[tex]Total = \$5.94[/tex]

Multiply by 100 to convert this amount to cents

[tex]Total = 5.94 * 100\ cents[/tex]

[tex]Total = 594\ cents[/tex]

And it can be represented as dollars and cents as:

5 dollars 94 cents

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