The second derivative form of xe3x

Check the picture below.

let's recall that, the arc made from 0 to π is just half a circle or namely a semi-circle, so any fraction of π refers to that arc

\(\cfrac{11\pi }{18}\qquad \textit{really means}\qquad \cfrac{11}{18}\qquad \textit{of that semi-circle}\)

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

Put Plot R at 2. Put Plot S at 1 1/2

Step-by-step explanation:

For Plot S:

- 7/2 - 3/4 - ( -1/4 - 2/12)

-7/2 - 3/4 -(- I/4 - 5/2

-7/2 - 3/4 - (-11/4)

-7/ - 3/4 + 11/4

Answer: -3/2

For Plot R:

7/2 - (-3/4) - (-1/4 + 2 1/2)

7/2 + 3/4 -(- 1/4 + 2 1/2)

7/2 + 3/4 - (-1/4 + 5/2)

7/2 + 3/4 - 9/4

Answer: 2

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The value of the y-intercept of the function is 6.

Zeroes of the function are the value for which the value of the function becomes 0 and Graphically, it is a point on the plane where the given function cuts the x-axis or makes the x-intercept (i.e. value of y=0).

In the given function,

f(x)=-(x+1)(x-3)(x+2)

if we have to make this function = 0, we have to either put x=-1, x=3 or x=-2

So, the answer is -2

Similarly, the y-intercept is the point where the curve made by the function cuts the y-axis or its value of x coordinate becomes 0.

So, if we put x=0 in the function, i.e.

f(0)=-(0+1)(0-3)(0+2)

we get the value of y-intercept = 6

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Answer:

Step-by-step explanation:

hi, Green should have smelled more tranquil, but somehow it just tasted rotten.

Doris enjoyed tapping her nails on the table to annoy everyone.

His son quipped that power bars were nothing more than adult candy bars.

Trash covered the landscape like sprinkles do a birthday cake.

Answer:

14 :)

Step-by-step explanation:

Answer:

Speed= 67.5 miles per hour

Step-by-step explanation:

Google maps has told Juanita that her car trip will be 32 miles.

Juanita has already gone 14 miles.

Remaining miles left to travel

= 32-14

Remaining miles left to travel

= 18 miles

She has only 16 minutes to reach her destination.

The required speed for her to reach her destination

= Distance/time

Her time = 16 minutes

Her time = 16/60

Her time =4/15 hours

Speed= distance/time

Speed= 18 /(4/15)

Speed=18* 15/4

Speed= 67.5 miles per hour

Juanita needs to drive at 67.5 miles per hour to arrive in 16 more minutes

The total distance (D) is given as:

\(\mathbf{D = 32miles}\)

She has traveled 14 miles;

So, the remaining distance (d) is:

\(\mathbf{d = D -14}\)

This gives

\(\mathbf{d = 32 -14}\)

\(\mathbf{d = 18}\)

Speed is calculated as:

\(\mathbf{Speed = \frac{distance}{time}}\)

Where: distance = 18 miles and time = 16 minutes

So, we have:

\(\mathbf{Speed = \frac{18\ miles}{16\ minutes}}\)

Convert time to hour

\(\mathbf{Speed = \frac{18\ miles}{16/60\ hour}}\)

So, we have:

\(\mathbf{Speed = \frac{18 \times 60\ miles}{16\ hour}}\)

\(\mathbf{Speed = \frac{1080\ miles}{16\ hour}}\)

Divide

\(\mathbf{Speed = 67.5\ miles/ hour}\)

Hence, the speed is 67.5 miles per hour

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Answer:

1). \(\text{log}_4(5x^2+2)=\text{log}_4(x + 8)\)

2). log(x - 1) + log5x = 2

3). ln(x + 5) = ln(x - 1) + ln(x + 1)

4). \(e^{x^2}=e^{4x+5}\)

Step-by-step explanation:

1). ln(x + 5) = ln(x - 1) + ln(x + 1)

   ln(x + 5) = ln(x - 1)(x + 1)  [Since ln(a×b) = ln a + lnb]

   (x + 5) = (x- 1)(x + 1)

   x + 5 = x² - 1

   x² - x - 6 = 0

   x² - 3x + 2x - 6 = 0

   x(x - 3) + 2(x - 3) = 0

   (x + 2)(x - 3 ) = 0

   x = -2, 3

   But x = -2 is an extraneous solution.

  Therefore, x = 3 is the only solution.

2). \(e^{x^2}=e^{4x+5}\)

  x² = 4x +5

  x² - 4x - 5 = 0

  x² - 5x + x - 5 = 0

  x(x - 5) + 1(x - 5) = 0

  (x + 1)(x - 5) = 0

  x = -1, 5

  Therefore, solution set is (-1, 5)

3). \(\text{log}_4(5x^2+2)=\text{log}_4(x + 8)\)

   5x² + 2 = (x + 8)  

   5x² - x - 6 = 0

   5x² - 6x + 5x - 6 = 0

   x(5x - 6) + 1(5x - 6) = 0

   (x + 1)(5x - 6) = 0

   x = -1, \(\frac{6}{5}\)

4). log(x - 1) + log5x = 2

    log(x - 1)(5x) = 2

    5x(x - 1) = 10² [if loga = b, \(a=10^{b}\)]

    5x² - 5x - 100 = 0

    x² - x - 20 = 0

    x² - 5x + 4x - 20 = 0

    x(x - 5) + 4(x - 5) =0

    (x - 5)(x + 4) = 0

    x = -4, 5

But x = -4 is an extraneous solution.

Therefore, x = 5 is the only solution.

Answer:

57+20= 90 (false)

40+39= 79 (true)

Answer:

14 * 9(-9) - 8 = 1142               9 - 45(-3) + 7 = 151

Step-by-step explanation:

14 * 9(-9) - 8 = 1142               9 - 45(-3) + 7 = 151

(This one is true)                  (This one is false)

Answer:

100 pieces of rope

Step-by-step explanation:

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

Answer:

x = 25, y = 9

Step-by-step explanation:

Since the triangles are congruent then corresponding angles and sides are congruent, thus

∠ O = ∠ P , substitute values

6y - 14 = 40 ( add 14 to both sides )

6y = 54 ( divide both sides by 6 )

y = 9

and

NG = IT , that is

x - 2y = 7 ( substitute y = 9 into the equation )

x - 2(9) = 7

x - 18 = 7 ( add 18 to both sides )

x = 25

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Answer: .8

How?

24 : 30 = 4/5

4/5 = .8

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

E=12t+30 C=7t+75

Evelyn has more in savings than Cooper when  t > 9 weeks.Step-by-step explanation:

Answer:

j=30

Step-by-step explanation:

Answer:

C,

Step-by-step explanation:

A and D is incorrect because they are negative correlation

and B is incorrect because a correction of 0.95 means all values are close to each other, but B values are scattered much more that C values

so answer C

The correct options include:

b. In the fifth year Mariah's balance will be higher than Colton's

c. Mariahs beginning balance was 400 and coltons beginning balance was 500.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, from the table

(0, 500), (1, 550), (2, 600), (3, 650) and (4, 700)

The equations for the given points is y=500+50t

Put t=0, 1, 2, 3, 4 in f(t)=400(1.15)t

When t=0, f(0)=$0

When t=1,

f(1)=400×1.15×1

= $460

When t=2,

f(2)=400×1.15×2

= $920

When t=3,

f(3)=400×1.15×3

= $1380

When t=4,

f(4)=400×1.15×4

= $1840

Fifth year:

The balance in Mariah account is

f(t)=400(1.15)t

⇒ f(5)=400×1.15×5

= $2300

The balance in Colton account is

y=500+50t

⇒ y=500+50(5)

= $750

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Answer:

The answer is 4 with the remainder of 5.

Step-by-step explanation:

29 divided by 6, 6 goes into 29 4 times which is 24.

6 x 4 = 24

29 - 24 = 5

So, 4 r5.

Answer:tony stark

Step-by-step explanation:shake it out west

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The 2 numbers are 32 and 27.

Step-by-step explanation:

32 plus 27 equals 59.

32 minus 27 equals 3.

So, the answer is 32 and 27.

Hope this helps! :)

Answer:

F(C)<250

Step-by-step explanation:

To solve the problem we need to remember that a function is a relationship between an input usually called "x" (domain) and an output, usually called "y" and it's also the range of the function.

F(X)=y

We are given a relationship (a function) between the ferryboat trips "c" and the number of cars transported per day.

f(C)=C/20

Hence, the range of the function knowing that there are not more than 5000 cars transported by the ferryboat (daily) the range is all the numbers that are less or equal to 250.

F(C)<250

:)!

Answer:

1.043

Step-by-step explanation:

Decimal multiplier to increase by x% is computed as:-

100% + x%

The decimal multiplier to increase by 4.3% would be

100% +4.3% = 104.3%

To remove% we divide the number by 100, so the number will become

Hence, The decimal multiplier to increase by 4.3% = 1.043

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Hope this Helps

Answer:

Step-by-step explanation:

D