please use calculus 2 and show all work thank you
Evaluate (f¹)' (2) for the function f(x) = √√√x³ + x² + x + 1. Explain your reasoning and write the solution in exact form. Do not use a decimal approximation.

Given the trigonometric identity: sin (π/2 + x) = cos x. We are to show that it can be derived from compound angle formulas for sine and cosine functions.

In order to prove the identity using the compound angle formulas, we have to start by recalling the formulas for sin(A + B) and cos(A + B).The compound angle formulas are given as:$$\begin{aligned}\sin (A+B)&=\sin A\cos B+\cos A\sin B\\\cos(A+B)&=\cos A\cos B-\sin A\sin B\end{aligned}$$

Let us set A = π/2 and B = x. Hence, A + B = π/2 + x. Then, we can write:$$\begin{aligned}\sin \left(\frac{\pi}{2}+x\right)&=\sin\frac{\pi}{2}\cos x+\cos\frac{\pi}{2}\sin x \\&= \cos x\end{aligned}$$And, $$\begin{aligned}\cos\left(\frac{\pi}{2}+x\right)&=\cos\frac{\pi}{2}\cos x - \sin\frac{\pi}{2}\sin x \\&= -\sin x\end{aligned}$$

Therefore, sin(π/2 + x) = cos x, as desired.

Know more about trigonometric:

https://brainly.com/question/29156330

#SPJ11

Answer:

1) 345    2) 62    3) 36    4) 51     5) 96      6) 142

Step-by-step explanation:

I hope you and your 3rd or 4th grader self enjoy the answers i gave you.

Answer:

RS = 17

Step-by-step explanation:

Given S lies on RT , then

RS + ST = RT , that is

RS + 3 = 20 ( subtract 3 from both sides )

RS = 17

Answer:

7/16 = 0.4375

Step-by-step explanation:

sry

Answer:

Step-by-step explanation:

Total cost is $26 add x-pieces each $1.50:

Answer:

x = 8/√3

Step-by-step explanation:

We solve that above question using the trigonometric function of sin

Sin theta = Opposite/Hypotenuse

Theta = 60°

Opposite = 4

Hypotenuse = x

Hence,

Sin 60 = 4/x

Cross Multiply

sin 60 × x = 4

x= 4/sin 60

in rational form

sin 60 = √3/2

Hence, x = 4/ √3/2

= 4 ÷ √3/2

= 4 × 2/√3

= 8/√3

the mean score for a critical reading test, using Excel, the probability that a random sample of 500 students will have a mean score of more than 590 can be calculated to be approximately 0.408.

To calculate the probabilities using Excel, we can utilize the standard normal distribution. First, we need to convert the sample means to z-scores by using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the sample mean of more than 590, we can calculate the probability of z being greater than the corresponding z-score using the formula "=1-NORM.S.DIST(z-score,TRUE)". In this case, the z-score is (590 - 580) / (115 / sqrt(500)), which gives approximately 0.408.

Similarly, for the sample mean of less than 575, we calculate the probability of z being less than the corresponding z-score using the formula "=NORM.S.DIST(z-score,TRUE)". The z-score is (575 - 580) / (115 / sqrt(500)), which gives approximately 0.084.

Therefore, the probability that a random sample of 500 students will have a mean score of more than 590 is approximately 0.408, and the probability that the sample mean is less than 575 is approximately 0.084.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

Answer:

It is 1, or A:  adding the two middle numbers

Step-by-step explanation:

When you think of it, here's an example:

15

23

55

34

Add 23 and 55:

23+55=78

We've got this now:

15

78

34

Now, all you've gotta do is find the mediam.

Hope this helped, and please mark as Brainliest <3

Answer:

[tex]P(A\ and\ B) = 44\%[/tex]

Step-by-step explanation:

Given

Represents the event as follows:

A = [tex]Elon\ Musk[/tex] will offer you a [tex]free\ trip[/tex] into space in the next month\

B = Scientists from [tex]Area\ 51[/tex] will [tex]start\ selling[/tex] pet aliens next month

So, we have:

[tex]P(A) = 41\%[/tex]

[tex]P(B) = 27\%[/tex]

[tex]P(A\ or\ B) = 24\%[/tex]

Required

Determine [tex]P(A\ and\ B)[/tex]

This is calculated as:

[tex]P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)[/tex]

So, we have:

[tex]P(A\ and\ B) = 41\% + 27\% - 24\%[/tex]

[tex]P(A\ and\ B) = 44\%[/tex]

Answer:

120°

Step-by-step explanation:

To find the measure of angle t in the pentagon, we can use the property that the sum of the interior angles of a pentagon is equal to 540 degrees.

So, we can set up an equation:

80° + 90° + 130° + 120° + t = 540°

Simplifying the equation:

420° + t = 540°

Next, we can isolate the variable t by subtracting 420° from both sides of the equation:

t = 540° - 420°

t = 120°

Therefore, the measure of angle t in the pentagon is 120 degrees.

Hope this helps!

The conditional probability that the process is in state 0 (or 1), given that absorption had not yet taken place. Therefore, P(X3 = 0, T > 3) = 0.075.

The Markov chain starts at time zero in state Xo = 0 and the transition probability matrix of Markov Chain is as follows: 0 1 2 0 0.7 0.2 0.1 P= 1 0.3 0.5 0.2 2 0 0 1

P(X3 = 0, T > 3).We know that the probability of moving from state i to state j in two steps is given by P2(i, j).

Thus, the probability of moving from state i to state j in three steps is given by P3(i, j). We have P2(i, j) = P(i, ·)P(j, ·) = Σk P(i, k)P(k, j).

For a 3-step transition probability, we use the equation P3 = P2P = P2 (P2) and so on. Therefore,P3(1, 2) = P2(1, 1)P(1, 2) + P2(1, 2)P(2, 2) + P2(1, 3)P(3, 2) = (0.7)(0.3) + (0.2)(0.5) + (0.1)(0) = 0.235

Similarly,P3(1, 0) = P2(1, 0)P(0, 0) + P2(1, 1)P(1, 0) + P2(1, 2)P(2, 0) = (0)(0.7) + (0.3)(0) + (0.235)(0.2) = 0.047

Since we are interested in finding P(X3 = 0, T > 3), we need to find the probability that absorption had not yet taken place at time 3 and that the process is in state 0 at time 3, which can be expressed as:

P(X3 = 0, T > 3) = P(X3 = 0, X4 ≠ 2) = P(X3 = 0, X4 = 0) + P(X3 = 0, X4 = 1)

We know that T is the first time that the process reaches state 2 and the process will reach and be absorbed into state 2.

Thus, T is the absorption time for state 2 and it has a geometric distribution with parameter P2(2, 2) = 1, which implies that P(T = t) = (1 – 1)P2(2, 2) = 0 for all t < 1.

Therefore, P(X3 = 0, X4 = 0) = P(X3 = 0, X4 = 0, T > 3)

              = P(X3 = 0, T > 3)P(X4 = 0 | X3 = 0, T > 3) = P(X3 = 0, T > 3)P(0, 0) / P(X3 = 0, T > 3)P(0, 0) + P(X3 = 1, T > 3)

               P(1, 0) + P(X3 = 2, T > 3)

               P(2, 0) = (0.047)(1) / [(0.047)(1) + (0.235)(0.7) + (0)(0.2)]

              = 0.067

Therefore, P(X3 = 0, T > 3) = P(X3 = 0, X4 = 0) + P(X3 = 0, X4 = 1) = (0.067)(0.7) + (0.235)(0.2) = 0.075.

Therefore, P(X3 = 0, T > 3) = 0.075.

Learn more about Markov chain rule:https://brainly.com/question/30465344

#SPJ11

If z = xy⁷ − x²y, x = t² + 1, y = t² − 1, then using chain rule the value of dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)

To find dz/dt using the chain rule, we need to differentiate z with respect to t while considering the relationship between z, x, y, and t.

Given:

z = xy⁷ − x²y

x = t² + 1

y = t² − 1

We can start by finding dz/dx and dz/dy separately and then use the chain rule to combine them to find dz/dt.

First, let's find dz/dx:

Differentiating z with respect to x, keeping y constant:

dz/dx = (d/dx)(xy⁷) - (d/dx)(x²y)

Using the product rule for differentiation:

dz/dx = y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)

Next, let's find dz/dy:

Differentiating z with respect to y, keeping x constant:

dz/dy = (d/dy)(xy⁷) - (d/dy)(x²y)

Using the product rule again:

dz/dy = x(y⁷ + 7y⁶(dy/dy)) - x²

Since dy/dy = 1, we can simplify dz/dy as:

dz/dy = xy⁷ + 7xy⁶ - x²

Now, let's use the chain rule to find dz/dt:

dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)

Substituting the expressions we found earlier for dz/dx and dz/dy, and using dx/dt = 2t and dy/dt = 2t:

dz/dt = (y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx))(2t) + (xy⁷ + 7xy⁶ - x²)(2t)

Simplifying this expression gives us dz/dt in terms of t, x, and y:

dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)

This is the complete calculation for finding dz/dt using the chain rule.

To learn more about chain rule click on,

https://brainly.com/question/32367259

#SPJ4

Complete question is:

Use the chain rule to find dz/dt. z = xy⁷ − x²y, x = t² + 1, y = t² − 1

Answer:

Y=2x^2

Step-by-step explanation:

The following equations represent a parabola with vertex (0,0): y=2x², x=-2y² and x=2y².

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

A parabola also can be represented by a quadratic equation. The vertex of an up-down facing parabola of the form ax²+bx+c is [tex]x_v=\frac{-b}{2a}[/tex] . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex.

The another form for describing a parabola is [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], where h and k are the vertex coordinates.

You should analyse each one of the options, considering the equations that can be represented a parabola.

Letter A - y=2x²

The coefficients of the quadratic equation are:

a=2, b=0, c=0

Then,

[tex]x_v=\frac{-b}{2a}\\ \\ x_v=\frac{-0}{2*2}=0[/tex].

If x-coordinate of vertex is equal to 0, from y=2x²you can:

[tex]y_v=2x^2\\ \\ y_v=2*0^2=0[/tex]

Therefore, the given equation ( y=2x²) represents a parabola with vertex (0,0).

Letter B - x=-2y²

From equation [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], you can rewrite the given equation parabola for vertex (0,0) in:

[tex]4p(x-0)=(y-0)^2\\ \\ 4*\frac{-1}{8} x=y^2\\ \\ \frac{-1}{2} x=y^2\\ \\ x=-2y^2[/tex]

Therefore, the given equation ( x=-2y²) represents a parabola with vertex (0,0).

Letter C - x=2y²

From equation [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], you can rewrite the given equation parabola for vertex (0,0) in:

[tex]4p(x-0)=(y-0)^2\\ \\ 4*\frac{1}{8} x=y^2\\ \\ \frac{1}{2} x=y^2\\ \\ x=2y^2[/tex]

Therefore, the given equation ( x=2y²) represents a parabola with vertex (0,0).

Letter D - y=-2

The degree of equation is not equal 2. Therefore, it does not represent a parabola.

Only the equations of letter A, B and C represent a parabola with vertex (0,0). See the attached image.

Read more about the vertex of parabola here:

https://brainly.com/question/4551229

Answer:

well

Step-by-step explanation:

please add the image

Applying the knowledge of fractions, half of 1/2 cake = 1/4 cake.

We are asked to find how many parts of are there in half of one-half of a cake.

Thus:

half = 1/2

1/2 of 1/2 cake = 1/2 × 1/2 (of = multiplication)

= (1 × 1)/(2 × 2)

= 1/4

Therefore, applying the knowledge of fractions, half of 1/2 cake = 1/4 cake.

Learn more about fractions on:

https://brainly.com/question/78672

Answer:

if r= to 13.8 so the answer is 598.28

The equation of the tangent plane to the parametric surface at the point (2, 5, 0) is x + 20y + z - 102 = 0.

To find the equation of the tangent plane to the given parametric surface at the point (2, 5, 0), we need to compute the partial derivatives and evaluate them at the given point.

The parametric surface is defined by the equations:

x = u + v

y = 5u^2

z = u - v

First, we find the partial derivatives with respect to u and v:

∂x/∂u = 1

∂x/∂v = 1

∂y/∂u = 10u

∂y/∂v = 0

∂z/∂u = 1

∂z/∂v = -1

Next, we evaluate the partial derivatives at the given point (2, 5, 0):

∂x/∂u = 1

∂x/∂v = 1

∂y/∂u = 10u = 10(2) = 20

∂y/∂v = 0

∂z/∂u = 1

∂z/∂v = -1

At the point (2, 5, 0), the partial derivatives are:

∂x/∂u = 1

∂x/∂v = 1

∂y/∂u = 20

∂y/∂v = 0

∂z/∂u = 1

∂z/∂v = -1

The equation of the tangent plane can be written as:

(x - x₀) (∂x/∂u) + (y - y₀) (∂y/∂u) + (z - z₀) (∂z/∂u) = 0,

where (x₀, y₀, z₀) is the given point.

Substituting the values, we have:

(x - 2)(1) + (y - 5)(20) + (z - 0)(1) = 0.

Simplifying further, we get:

x - 2 + 20(y - 5) + z = 0.

Expanding and rearranging the terms, the equation of the tangent plane to the parametric surface at the point (2, 5, 0) is:

x + 20y + z - 102 = 0.

Learn more about tangent plane here

https://brainly.com/question/30619505

#SPJ11

Answer:

a) 1/2, 0.5, 50% b)3/4, 0.75, 75% c) 1/12, 0.08333, 8.333% d) 5/12, 41.6667%, 0.416

Step-by-step explanation:

Answer:

a] 1/2 b] 5/6 c] 1/6 d] 5/4

Step-by-step explanation:

no of even no present/total numbers and so on

try it later

Here are the characteristics of Quadratic Functions

Axis of symmetry

x and y-intercepts

Zeroes

vertex

Point symmetric to y-intercept

Hi there!

[tex]\large\boxed{(-\infty, \infty)}}[/tex]

We are given the function:

[tex]f(x) = a\sqrt[3]{bx-c}+d[/tex]

This is the transformation form of a cubic root function. Recall these properties of cubic root functions:

Domain: -∞ < x < ∞ (all real numbers)

Range: -∞ < x < ∞ (all real numbers)

Therefore, the range of the given function is all real numbers, or on (-∞, ∞).

The $130,000 would be considered as Statistic.

In statistics, a population refers to the entire group of individuals or items of interest, while a sample is a subset of the population. A parameter is a numerical value that describes a characteristic of a population.

In this scenario, the survey results are based on a sample of 10,000 graduates out of a total population of 200,000 graduates. The average salary of $130,000 is calculated from the data collected within this sample. Since it is derived from the sample, it is considered a statistic.

A parameter would be used to describe the average salary of the entire population of 200,000 graduates if data were collected from all of them. However, in this case, the given information only pertains to the subset of the sample.

LEARN MORE ABOUT Statistic here: brainly.com/question/31538429

#SPJ11

According to the Empirical rule, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. The correct option is b. 16.5 years and 38.1 years.

The given question states that a researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. We are to find the range of age at which approximately 95% of women had their first child, according to the empirical rule.

There are three ranges for the empirical rule as follows:

Approximately 68% of the observations fall within the first standard deviation from the mean.

Approximately 95% of the observations fall within the first two standard deviations from the mean.

Approximately 99.7% of the observations fall within the first three standard deviations from the mean.

Now, we will apply the empirical rule to find the age range at which approximately 95% of women had their first child. The mean age is 27.3 years and the standard deviation is 5.4 years, hence:

First, find the age at which 2.5% of women had their first child:

µ - 2σ = 27.3 - (2 × 5.4) = 16.5

Then, find the age at which 97.5% of women had their first child:

µ + 2σ = 27.3 + (2 × 5.4) = 38.1

Therefore, approximately 95% of women had their first child between the ages of 16.5 years and 38.1 years. Hence, the correct answer is option b. 16.5 years and 38.1 years.

To know more about Empirical rule, refer to the link below:

https://brainly.com/question/30404590#

#SPJ11

Answer:

65,000 grams

Step-by-step explanation:

Because 1000 grams is in 1 kilogram, you would multiply the 65 kilograms by 1,000 to convert it to grams.

So to convert 65 kilograms to grams you would do:

65 * 1,000 = 65,000 grams

Yikes i dont know this but thanks for the coins C:

Using Green's theorem the flux of the field F across the ellipse is 0, indicating that there is no net flow across the ellipse.

To find the flux of the field F = a × i - 3y × j outward across the ellipse, we can use Green's theorem. Green's theorem relates the flux of a vector field across a closed curve to the circulation of the field around the curve.

Let's denote the ellipse as C, which is parameterized by x = a cos(t) and y = b sin(t), where a and b are the semi-major and semi-minor axes of the ellipse, and t varies from 0 to 2π.

Calculate the curl of the vector field F:

∇ × F = (∂Fₓ/∂y - ∂Fᵧ/∂x) k

= (-3)k

Determine the area enclosed by the ellipse using Green's theorem:

The flux of F across the ellipse is equal to the circulation of F around the ellipse:

∮C F · dr = ∬R (∇ × F) · dA

Since the curl of F is -3k, the flux simplifies to:

∮C F · dr = ∬R (-3k) · dA

= -3 ∬R dA

= -3A

Therefore, the flux of F across the ellipse is -3 times the area enclosed by the ellipse.

Find the area enclosed by the ellipse:

The equation of the ellipse is given as x = a cos(t) and y = b sin(t).

To find the limits of integration, we note that t varies from 0 to 2π, which represents one complete revolution around the ellipse.

∬R dA = ∫₀²π ∫₀²π (a cos(t))(b) dt

= ab ∫₀²π cos(t) dt

= ab [sin(t)]₀²π

= ab (sin(2π) - sin(0))

= 0

Therefore, the area enclosed by the ellipse is 0.

Learn more about Green's theorem at

https://brainly.com/question/30763441

#SPJ4

A solution to the differential equation xy' - 3y = 6 is y = -2/x. This is a particular solution that satisfies the given differential equation.  Therefore, y = -2/x is a solution to the differential equation xy' - 3y = 6.

To find a solution to the differential equation xy' - 3y = 6, we need to solve the equation and find a function that satisfies it. We can begin by rearranging the equation:

xy' - 3y = 6

To solve this linear first-order ordinary differential equation, we can use the method of integrating factors. The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -3:

IF = e^(-3x)

Multiplying both sides of the equation by the integrating factor, we have:

e^(-3x)xy' - 3e^(-3x)y = 6e^(-3x)

This can be rewritten as:

(d/dx)(e^(-3x)y) = 6e^(-3x)

Integrating both sides with respect to x, we get:

e^(-3x)y = ∫(6e^(-3x))dx

Simplifying the integral and applying the constant of integration, we have:

e^(-3x)y = -2e^(-3x) + C

Dividing both sides by e^(-3x), we obtain:

y = -2 + Ce^(3x)

The constant C can take any value. By choosing C = 0, we have y = -2/x, which is a particular solution to the given differential equation. Therefore, y = -2/x is a solution to the differential equation xy' - 3y = 6.

Learn more about differential equation here:

https://brainly.com/question/25731911

#SPJ11

It does not determine the observed interaction effects between variables.

In the case of multiple linear regression, the option that is not determined is:

Variable interactions that have been observed to have effects.

Option 1: Multiple linear regression can estimate the observed relationship between predictor and outcome variables after adjusting for confounding relationships and option 2: it can determine the potential confounding effects from lurking variables. Furthermore, numerous direct relapse can evaluate the causal connections among indicator and result factors adapting to jumbling connections (choice 3).

However, the potential observed interaction effects between variables cannot be determined by multiple linear regression on its own. Association impacts happen when the connection between two indicators and the result variable isn't added substance however relies upon the mix of the indicator values. In order to evaluate the effects of interactions, additional analysis methods like including interaction terms and carrying out specific interaction tests are required.

To know more about  linear regression refer to

https://brainly.com/question/32505018

#SPJ11

Answer:

the answer is D

Step-by-step explanation:

y=[tex]x^{2}[/tex]+1

Answer:

A

Step-by-step explanation:

It is talking about a positive number

Answer:

a

Step-by-step explanation:

Answer: A

Step-by-step explanation: