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.​

2. Calculate An Expression For Dy/dx And D2y/dx2 In Terms Of T If The Parametric Pair Is Given As Tan(x)

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

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......

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 :)

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:

a

Step-by-step explanation:

-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

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:)

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

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

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

Answers

Answer:

20 cm is the answer.

20

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

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:

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:

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

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:

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

−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)

50 mm = how many cm?

Answers

Answer:

5cm

Step-by-step explanation:

50mm ÷ 10 = 5cm

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

Answers

Answer:

y=0.25x-6

Step-by-step explanation:

PLEASE HELP ME RN PLEASE ​

Answers

Answer:

1.

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

2.

[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

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

Answers

70% of the guests were over 25
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.

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)

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:

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

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

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

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

Answers

Answer:

(27000)(27225)

Step-by-step explanation:

Answer:

6/11

Step-by-step explanation:

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

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

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:

can some1 please help:(

Answers

A) -2/5

hope it helps ....❤

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

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