If p=7, then what is the value of 8×p−68×p-6?
A
6

B
9

C
50

D
56

a. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives

[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]

[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]

and so

[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]

Set this equal to zero and solve for t :

[tex]1-e^{2t} = 0[/tex]

[tex]1 = e^{2t}[/tex]

[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]

[tex]0 = 2t \ln(e)[/tex]

[tex]0 = 2t[/tex]

[tex]t=0[/tex]

This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).

b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,

[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

We have

[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]

and we've already committed dx/dt. So

[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]

Substitute the first and second derivative into the differential equation:

[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]

[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]

[tex]4e^{6t} -e^{2t}= 0[/tex]

[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]

[tex]4e^{4t} - 1 = 0[/tex]

[tex]4e^{4t} = 1[/tex]

[tex]e^{4t} = \dfrac14[/tex]

[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]

[tex]4t \ln(e) = -\ln(4)[/tex]

[tex]4t = -\ln(4)[/tex]

[tex]t = -\dfrac{\ln(4)}4[/tex]

Answer:

Step-by-step explanation:

Total Number of possible outcomes = 52

Getting a jack from a deck of 52 cards for a certain event (A) = 4

The Probability (A) = 4/ 52

= 1 / 13 = 0.07

Hope you like it please mark as brainliest.

Answer:

Step-by-step explanation:

x y

−1 −2

2 3

3 1

6 −2

Answer:

no

Step-by-step explanation:

6 and -2 is not a function

Answer:

x=11

Step-by-step explanation:

3x-11=22

3x-11+11=22+11

3x=33

3x/3=33/3

x=11

Step-by-step explanation:

3x = 22 + 11

3x = 33

3x = 33/3

3x = 11

Answer: 1/2

Step-by-step explanation:

Slope is the number in front of x

Answer:

The slope of the line or m is represented by 1/2. x and y are coordinates on the line and -5 represents the y-intercept. The used for this equation is y = mx + b. M = slope and b is the y-intercept

Step-by-step explanation:

Hope I made sense to you.

[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=2x - 5 \quad \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5-2}\implies \cfrac{[2(5)-5]~~ - ~~[2(2)-5]}{3} \\\\\\ \cfrac{5-(-1)}{3}\implies \cfrac{5+1}{3}\implies 2[/tex]

Answer: 12

2 + 10

12

:)

Answer: 12

Step-by-step explanation: just add 2 to 10

Answer:

line them up straight with the bottom number and the top number.

Answer:

130/81

simplified: 1 49/81

Step-by-step explanation:

I did the math

Answer:

w = win

Step-by-step explanation:

w=13

Answer:

w = 13

Step-by-step explanation:

16w - w = 15w

15w - 12w = 3w

3w - 2w = w

w = 13

Answer:

Part A, write out the equation by subtracting the vertex from x and y, then set it equal to the radius square. All of this information is given in the picture. Then the domain is all the x's and the range is all the y's starting at the center and going out 10 in each direction since 10 is the radius.

Step-by-step explanation:

Use the circle formula that you learned in lesson 3.02 using the given points. Remember this quiz was open note and your formula should be in your notes. Also, it should be familiar to you from Geometry and middle school math where you first learned about circles:)

Answer:

[tex]x>4[/tex]

Based on this, we know the correct number line will be an empty bubble with a line going to the right of 4.

Step-by-step explanation:

[tex]x-8>-4[/tex]

add 8 to both sides of the inequality

[tex]x>4[/tex]

Answer:

Option "C" none of these is the correct answer.

Step-by-step explanation:

The subset of the set {7, 8, 9} must have the elements of this set only.

Hope this helps :)

After doing some quick calculations, we can determine that X = −35.9

I hope this helps! :)

Answer:

x = -35.9

Step-by-step explanation:

Subtract both sides by 11.2                                                                                                 11.2 - 11.2 equals zero leaving x on one side.

x = - 24.7 - 11.2

A negative minus another negative number is a larger negative number.

x= -24.7 - 11.2 = -35.9

x = -35.9

Answer:

35

Step-by-step explanation:

if not correct I'm very very sorry I tried my best for this</3

Answer:

O - point

CD- chord

AB- diametre

I dont know PO sorry

Answer:

O is the center.

AB is the diameter.

OP is a radius.

CD is a tangent.

By the way the combination of letters is the two points that it relates too.

Step-by-step explanation:

hope this helps. . .<3

Step-by-step explanation:

if you observe the graph the y values increase as the x value increase.

so it has a possitive association.

if the value of y increase as the value of the x increase then data has positive association.

270 = 2 x 3 x 3 x 3 x 5 = 2 x 3^3 x 5

ok done. Thank to me :>

Answer:

2x3x3x3x5

Step-by-step explanation:

if your doing this on time4learning lesson type 5x2x3x3x3 to get it right it worked for me but it didnt work in any other order

Answer:

I don't know..,.............,,.,.......,

Answer:

The slope of a line perpendicular to a vertical line is zero.

Step-by-step explanation:

Answer:

1.)

a.)The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.

b.)Medications such as naproxen, ibuprofen, and acetaminophen are most effective in reducing pain and swelling associated with muscle-related lower back pain. However, OTC medication is less likely to alleviate symptoms that stem from nerve compression or disc problems.

Step-by-step explanation:

I HOPE ITS HELP YOU

Answer:

Neither because x can't equal 3 and equal 2 at the same time and 2x + 5y doesn't equal 3x + 5y. 3x is > 2x by one x

Step-by-step explanation:

Hope this answer works for you!

Answer:

range is { - 17, 1, 22 }

Step-by-step explanation:

Substitute the values from the domain (input) into f(x) for range

f(- 4) = 3(- 4) - 5 = - 12 - 5 = - 17

f(2) = 3(2) - 5 = 6 - 5 = 1

f(9) = 3(9) - 5 = 27 - 5 = 22

range is { - 17, 1, 22 }

Answer:

C. y=3x-4

Step-by-step explanation:

I just know trust me

Answer:

this is the correct answer happy

Can you give me some hint please

a = 18

d = 16 - 18 = -2

an = a + (n - 1) × d

an = 18 + (n - 1) × (-2)

an = 18 - 2n + 2

an = -2n + 20