2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2at

Hint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.

Answers

Answer 1

I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives

sec²(x) dx/dt = a exp(at)

Recall that

sec²(x) = 1 + tan²(x)

Then we have

(1 + tan²(x)) dx/dt = a exp(at)

(1 + exp(2at)) dx/dt = a exp(at)

dx/dt = a exp(at) / (1 + exp(2at))

If exp(y) = 1 + exp(2at), then differentiating with respect to t yields

exp(y) dy/dt = 2a exp(2at)

(1 + exp(2at)) dy/dt = 2a exp(2at)

dy/dt = 2a exp(2at) / (1 + exp(2at))

By the chain rule,

dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)

Then the first derivative is

dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))

dy/dx = (2a exp(2at)) / (a exp(at))

dy/dx = 2 exp(at)

Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write

dy/dx = f(t)

By the chain rule, the derivative is

d²y/dx² = df/dx

d²y/dx² = df/dt • dt/dx

d²y/dx² = (df/dt) / (dx/dt)

d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))

d²y/dx² = 2 (1 + exp(2at))

Related Questions

12. -2 times the difference of x and 4 is 14. What is the number

Answers

- 2x + 4 = 14

- 2x = 14 - 4

- 2x = 10

x = 10 / - 2

x = - 5

#FromIndonesia

PLEASE HELP!!! I ONLY HAVE A FEW MINUTES!!

Answers

Answer:

y=0.25x-6

Step-by-step explanation:

Please help me with this i am ver confused

Answers

1) the second option
2) the third option

hope this helped!

Answer:

1) 2/x³ the secound option

2)1/x²⁴ the secound option

I think

Select the correct answer. Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27

Answers

Answer:

(-5,-7)

Step-by-step explanation:

Set functions equal to each other.

2x+3= -4x-27

2x+4x = -3-27

6x=-30

x= -5

f(-5) = 2(-5) +3

f(-5) =-10+3 y= - 7

g(-5) = -4(-5) -27

g(-5) =20-27 y= -7

x=-5 y=-7

(-5,-7)

Answer:

(-5,-7)

Step-by-step explanation:

Your classmate is telling you how they plan to become financially secure.
Which of the following factors can help him do so?
A saving money
B investing money
C both saving and investing money
D neither saving nor investing money

Answers

Answer:

savind and investing money

the perimeter of a regular Pentagon is 100m how long is each side

Answers

Answer:

20 cm is the answer.

Step-by-step explanation:

the parameter of any shape is the sum of all sides and since the pentagon has 5 sides we just have to divide the parameter by 5

100÷5=20

A 7-pound bag of lollipops costs $12.18. What is the unit price?

Answers

Answer:

The unit price is 1.74$

Step-by-step explanation:

12.18 / 7

is 1.74

Answer=$1.74 since you do $12.18/7

Help me with writing a check please

Answers

Answer: pay to the order of: Price Chopper.... $145.19.... next line: One hundred forty-five and 19/100.... bottom left line: whatever the money is for.... next line: signature. 5. fifty-four and 68/100 dollars 6. One hundred seventeen and 92/100 dollars 7. twenty dollars

Step-by-step explanation:

Perform the indicated operations/solutions.
1. 12-7+45÷15x11=
2. 16x2+12-18÷9-4=

Answers

1. 12-7+45÷15x11=50.6
2. 16x2+12-18÷9-4=38

PLEASE HELP!!!!! I WILL REWARD

Answers

Answer:

the fourth bubble or d

Step-by-step explanation:

x has to equal to or less than 6

ANSWER:....x ≤ 6......

PLEASE HELP ME RN PLEASE

Answers

Answer:

[tex] \frac{n^{2} - 1 }{2} [/tex]

[tex] \sqrt{29} [/tex]

Step-by-step explanation:

Area of triangle=1/2×b×h

[tex] \frac{1}{2} \times (n - 1)(n + 1)[/tex]

[tex] \frac{( {n}^{2} + n - n - 1) }{2 } [/tex]

[tex] \frac{ {n}^{2} - 1 }{2} [/tex]

2. Area of triangle=14

[tex] \frac{ {n}^{2} - 1 }{2} = 14[/tex]

[tex] {n}^{2} - 1 = 28[/tex]

[tex] {n}^{2} = 29[/tex]

[tex]n = \sqrt{29} [/tex]

please rate well and mark BRAINLIEST.

thanks

Simplify \frac{10a^3}{55a^2} when a=3.

Answers

Answer:

(27000)(27225)

Step-by-step explanation:

Answer:

6/11

Step-by-step explanation:

A restaurant is serving a special dinner combo meal that includes a drink, a main dish, and a dessert. Cus
4 drinks, 5 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create Choose... w different dinner combo meals.
1
2
3
4
Choose...
12
45
60
75
5
6
7

Answers

Answer:

Your Answer Is 60

Step-by-step explanation:

I Took The Test Just Now

The number of different combo meals are possible in a restaurant which is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 60.

What is arrangement?

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is the n!. Here, n is the number of objects.

A restaurant is serving a special dinner combo meal that includes a drink, a main dish, and a dessert.

Dinner includes 4 drinks,5 main types of dishes.3 types of desserts.

The number of different combo meals are possible can be find out by simply multiplying all the meals. Thus,

[tex]n=4\times5\times3\\n=60[/tex]

Thus, the number of different combo meals are possible in a restaurant which is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 60.

Learn more about the arrangement here;

https://brainly.com/question/6032811

#SPJ2

As a hurricane approaches, the air temperature changes −7.8°F every hour.

Which value represents the change in air temperature over 1.25 hours?

−9.75°F

−9.05°F

−6.55°F

−6.24°F

Answers

The change in air temperature over 1.25 hours is -9.75°F

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the rate of change and b is the initial value of y.

As a hurricane approaches, the air temperature changes −7.8°F every hour. The amount of change after 1.25 hours is:

Change = −7.8°F every hour * 1.25 hours

Change = -9.75°F

Therefore the change in air temperature over 1.25 hours is -9.75°F

Find out more on linear equation at: https://brainly.com/question/14323743

what is the hypotenuse of a right triangle with a and b related by the statement a=b-5.

Answers

Answer:

c = 5b ±sqrt(-10(b+a)+2)

Step-by-step explanation:

By using the Pythagoras theorem,

c² = a² + b²

a = b-5

b = a+5

c² = (b-5)² + (a+5)²

c² = b²-10b+25 + a²+10a+25

c² = b²-10b-10a+50

c² = b²-10(b+a)+50

c = 5b ±sqrt(-10(b+a)+2)

Hayley is considering two gym membership plans. The plans are detailed here. Plan One: $40 for a monthly pass plus $4 for each gym visit Plan Two: $12 for each gym visit. Which equation expresses the situation in the form of y=mx+b where x is the number of gym visits per year and y is the total cost per month for Plan One?

y=40x+4

y=4x+40

y=12x

y=3x+50

please help

Answers

Answer:

Plan One: y=4x+40

Plan Two: y=12x

Step-by-step explanation:

If the diameter of a circle is [tex]\sqrt{144}[/tex] then what is the radius?

Answers

Hey there!

√144

= 12^2

= 12 * 12

= 144

Therefore, your answer should be: 12

Side note: There’s many ways to find the result of the square root but I just made it “easier” to solve and tackle future problems like this on your own.

Anyways

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

−10sin(x)=−4csc(x)+3

Answers

-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0 or 5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2 or sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ or x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ or x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ or x = π + arcsin(4/5) + 2nπ

(where n is any integer)

Right triangles 1, 2, and 3 are given with all their angle measures and approximate side lengths. Use one of the triangles to approximate the ratio (KL)/(JL).

- 0.64
- 0.77
- 0.83
- 1.2

Answers

Answer:

[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex] = 0.83

Step-by-step explanation:

The key understanding here is that ΔJKL is similar to triangle 3 based on the AA criterion (they both have a right angle and a 40° angle).

We can find [tex]\frac{KL}{JL}[/tex] by setting up a proportion statement that includes KL, JL, and the lengths of their corresponding sides in triangle 3.

We can use this proportion:

[tex]\frac{KL}{6.4}[/tex] = [tex]\frac{JL}{7.7}[/tex]

[tex]\frac{KL}{6.4}[/tex] ⇒ opposite to 40° angle

KL, JL ⇒ ΔJKL

[tex]\frac{JL}{7.7}[/tex] ⇒ adjacent to 40° angle

6.4, 7.7 ⇒ triangle 3

[Now see the attachment]

Now we can rewrite the equation to show the ratios of the side lengths within each triangle.

[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex]

[tex]\frac{KL}{JL}[/tex] ⇒ ΔJKL

KL, 6.4 ⇒ adjacent to 40° angle

[tex]\frac{6.4}{7.7}[/tex] ⇒ triangle 3

JL, 7.7 ⇒ adjacent to 40° angle

Answer: it’s 0.82

Step-by-step explanation:

In the month of January, a certain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of
4.8% per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell
this year?

Answers

Answer:

11∑N=1 9000 (1.048)^n

Step-by-step explanation:

First month = a = 9,000burgers

Common ratio = r = 1 + 0.48 = 1.048

Total number of months = n = 11; from February to December.

Formula to determine the number of burgers the restaurant expects to sell this year:

= 11∑N=1 9000 (1.048^n)

Answer:

Step-by-step explanation:

3=2x
Solve this equation.
Then verify IT.

Answers

[tex] \huge \bf \: Question : [/tex]

[tex]3 = 2x[/tex]

This is an equation. We need to find the value of X and verify it.

[tex] \huge \bf \: Solution : [/tex]

Let's find out the value of X :-

[tex] \sf \implies \: 3 = 2x[/tex]

Firstly, over turn the equation :-

[tex]\sf \implies2x = 3[/tex]

Then, Divide both sides of this equation by 2 :-

[tex]\sf \implies \: \dfrac{2x}{2} = \dfrac{3}{2} [/tex]

Cancel 2/2 on this equation and Leave x :-

3/2 can't be cancelled.

[tex]\sf \implies \: \dfrac{ \cancel2x}{ \cancel2} = \dfrac{3}{2} [/tex]

[tex]\sf \implies \: x = \dfrac{3}{2} [/tex]

Hence the value of x is 3/2.

________________________________

[tex] \bf \huge \: Verification : [/tex]

Put the value of x on this equation :-

[tex]\sf \implies \: 3 = 2x[/tex]

On Putting 3/2 instead of x :-

As we know that x is multiplied with 2 so,

[tex]\sf \implies \: 3 = 2 \times \dfrac{3}{2} [/tex]

Simplify this equation(Cancel 2 and 2) :-

[tex]\sf \implies \: 3 = \cancel2 \times \dfrac{3}{ \cancel2} [/tex]

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

[tex]\sf \implies \bf \: L HS = RHS[/tex]

[tex] \boxed {\bf\huge Hence, verified.}[/tex]

______________________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

7/10 of guest were over 25 what is the percentage

Answers

70% of the guests were over 25

Simplify 4 to the seventh power over 5 squared all raised to the third power . (4 points)

a
4 to the tenth power over 5 to the fifth power

b
4 to the fourth power over 5

c
4 to the twenty-first power over 5 to the sixth power

d
12 to the seventh power over 15 squared

Answers

Answer: The answer is C, 4 to the 21st over 5 to the 6th power.

Sophia was measuring the height of her Christmas tree. The
first part she measured was 36 inches tall. The second part
was 2 feet tall. How tall was her Christmas tree?

Answers

Answer:

60 inches or 5 feet

Step-by-step explanation:

36 inches + 2 feet (24 inches) = 60 inches, also 5 feet

can some1 please help:(

Answers

A) -2/5

hope it helps ....❤

what decimal represents the fraction 1/4

Answers

Answer:

0.25

Step-by-step explanation:

1/4 is equal to 1.00 split into 4 equal parts. 0.25*4 = 1.00 , meaning that each 1/4 is equal to 0.25

Answer:

0.25.

Step-by-step explanation:

We divide 1 by 4:

4) 1. 00

0.25

50 mm = how many cm?

Answers

Answer:

5cm

Step-by-step explanation:

50mm ÷ 10 = 5cm

-2 - 1 + 4 I need the help please

Answers

Answer:

it's 1

Step-by-step explanation:

hope this helps 1

the answer is 1

-2+-1= -3
4-3

p/18+7=9 what is the value of p

Answers

Answer:

p=36

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:

p/18+7-(9)=0

Simplify p/18

(p/18+7)-9=0

7= 7/1= 7*18/18

p+7*18/18=p+126/18

(p+126)/18-9=0

9=9/1=9*18/18

(p+126)-(9*18)/18=p-36/18

p-36/18=0

p-36=0

p=36

Hope this helped :)

Can someone please help me.

Answers

Answer:

make that 30 percent int a fraction and u should know what to do

Step-by-step explanation:

Other Questions

Read the following passage from "The Setting Sun and the Rolling World."He himself had taken chances before, in his own time, but he felt too much of a father. He had worked and slaved for his family and the land hadnot betrayed him. He saw nothing now but disaster and death for his son out there in the world. Lions had long since vanished but he knew ofworse animals of prey...What does the land likely represent to Old Musconi?O A security, protection, familyB. opportunity, risk, rewardC. frustration, disappointment, childrenD. suffering, loneliness, betrayal what do you waste the most of and how could you repurpose it into something that is beneficial? What did critics of capitalism propose as alternatives? How did they address the plight of workers? Solve for x.8x - 5 = 6x + 8x + 10 Read the following summary of a play's main character:Olivia has gotten a new job. She is charming butdisorganized and has next to no ability to follow aschedule. Tomorrow is her first day.Which of the following stage directions best convey the basic elements ofthis character? According to Dalton's atomic theory, atomsa: of different elements combine in simple whole-number ratios to form compoundsb: can be divided into protons, neutrons, and electronsc: of all elements are identical in size and massd: can be destroyed in chemical reactions if you cannot resist eating chocolate what part of the brain are you using Help help math math I never was good at math, so i wanted to ask someone for help,I'm doing 8th grade math, and this is the problem:-11 + 9b = 25If you can help me I will be very grateful! Mr. Cooper determined functions to represent his distance traveled in miles, d, in terms of the number of hours, 1, of driving on two types ofhighways. He found that on a state highway the function was d = 45t, and on a U.S. highway, the function was d = 601.If Mr. Cooper drove for 1.5 hours on each type of highway, how much farther did he drive on the U.S. highway than on the state highway?Enter the answer in the box. a veces me pregunto si hago bien en respetar los mandamientos Which information can a star chart provide?the distance from Earth to the nearest starthe distance from Earth to the nearest starthe locations of the North and South Polesthe locations of the North and South Polesthe distance an object is compared to the horizonthe distance an object is compared to the horizonthe locations of constellations at different times during the year in a typical roman family, what was a typical job for the wife? the most common patterns of minority treatment include assimilation, segregation, subjugation, and legal protection. The minute hand of a clock has a length of 12 cm, and the hour hand has a length of 8 cma) How far does the tip of the minute hand travel in one hour?b) How far does the tip of the hour hand travel in 12 hours?c) How far does the tip of each hand travel in one week? Miguel glues a ribbon border around the edges of a 5-inch by 8-inch picture to create a frame. What is the total length of ribbon Miguel uses? pls ansswerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr Evaluate the expression 2-8 2-7= which group would have made these arguments in 1787? free- soldiers anti federalists loyalist federalists Explain the purpose of pencils.

2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2atHint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.​

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2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2at

Hint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.