Use the tangent plane to approximate a function of two variables at a point. Use a tangent plane to approximate the value of the following function at the point (4.1, 4.9). Give your answer accurate to 4 decimal places. f(x, y) = /73 – 2a? – y?

The remainder when f(x) = x³ - 5x² + 4x - 10 is divided by (x + 5) is (b) -280

The functions are given as

f(x) = x3 − 5x2 + 4x − 10 is divided by (x + 5)

Rewrite them as

f(x) = x³ - 5x² + 4x - 10 is divided by (x + 5)

Set the divisor to 0

So, we have

x + 5 = 0

Determine the value of x

This gives

x = -5

By the remainder theorem

Substitute x = -5 in the function f(x)

So, we have

f(-5) = (-5)³ - 5(-5)² + 4(-5) - 10

Evaluate the expression

f(-5) = -280

By the remainder theorem, this represents the remainder

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Answer:

x = 6

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

however, x > 0 , then x = 6

The approximate circumference of spaceship Earth is 160m

The formula for calculating the volume of a sphere is given as;

V = 4/3 πr³

Given that;

Now, substitute the values

65417 = 1. 3 ×3.14r³

Multiply the values

65417 = 4. 082r³

Make r the subject

r³ = 16025. 722

Find the cube root

r = 25. 2m

The circumference is expressed as;

Circumference = 2πr

Substitute the values, we have;

Circumference = 2× 3.14 × 25.2

Circumference = 160 m

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Answer:

is this mnps?

Step-by-step explanation:

Answer: \(107939\ BTU\)

Step-by-step explanation:

Given

Propane produced heat energy of \(2470\ BTU/ft^3\)

The volume of the tank is \(43.7\ ft^3\)

The energy produced by this propane tank is

\(\Rightarrow 2470\times 43.7=107939\ BTU\)

Answer:

Length- 14 Width- 100

Step-by-step explanation:

First: 7x2=14

Then: 114-14=100

Hope this helps

-Mercury

Answer:

42

Step-by-step explanation:

the ratio 2:4 can be reduced to 1:2,

where the number of girls corresponds to the 1 and the number of boys corresponds to the 2.

If there are 14 girls, then there must be 28 boys (14 x 2 = 28).

Now to get the total number we need to add the total number of boys and girls together.

So 14 + 28 = 42

Hope it helps :)

Answer:

32

Step-by-step explanation:

14 + 28 = 32

2 x 7 = 14

4 x 7 = 28

Answer:

  h = 10 13/14 units

Step-by-step explanation:

You want the height from the side of length 14 of a parallelogram with side length 17 and height 9.

The area of a parallelogram is the same, no matter which side is used as the "base". This means ...

  A = bh = 17(9) = 14(h)

  h = 17·9/14 = 10 13/14 . . . . units

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Answer:

25 quarters and 64 dimes

Step-by-step explanation:

25 times 25 = 6.25    Remaining 64 coins are dimes

64 times 10 = 6.40

Add to get 12.65 in 89 coins

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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2.1 To show that all partial derivatives of u and v exist at (x, y) = (0, 0) and satisfy the Cauchy-Riemann equations, we need to calculate the partial derivatives of u and v and check their existence and the Cauchy-Riemann conditions.

The function is given as u(x, y) = xy and v(x, y) = x² + y².

Partial derivatives of u:

∂u/∂x = y

∂u/∂y = x

Partial derivatives of v:

∂v/∂x = 2x

∂v/∂y = 2y

All partial derivatives exist at (x, y) = (0, 0) since they are simple functions and do not have any singularities.

Now, let's check if the Cauchy-Riemann equations are satisfied:

∂u/∂x = ∂v/∂y

y = 2y

This equation holds true for all values of y, including y = 0.

∂u/∂y = -∂v/∂x

x = -2x

This equation also holds true for all values of x, including x = 0.

Therefore, all partial derivatives of u and v exist at (x, y) = (0, 0), and they satisfy the Cauchy-Riemann equations.

2.2 To show that f is not continuous at (0, 0) and hence not differentiable at (0, 0), we can examine the behavior of f as (x, y) approaches (0, 0).

The function f(x, y) = u(x, y) + iv(x, y) = xy + i(x² + y²)

As (x, y) approaches (0, 0), both u(x, y) = xy and v(x, y) = x² + y² approach 0. However, f(x, y) = xy + i(x² + y²) approaches 0 + i(0) = i(0) = 0i = 0, which is a different value.

Therefore, f is not continuous at (0, 0), and hence it is not differentiable at (0, 0).

2.3 To investigate whether f is analytic or not, we need to check if it is differentiable in a neighborhood around every point.

Since we have already shown that f is not differentiable at (0, 0), it implies that f is not analytic because differentiability is a necessary condition for analyticity.

2.4 To investigate whether f has a harmonic complex conjugate or not, we need to check if u and v satisfy the Laplace's equation (∇²u = 0 and ∇²v = 0) and if they satisfy the Cauchy-Riemann equations.

The Laplace's equation is not satisfied by u(x, y) = xy because ∇²u = ∂²u/∂x² + ∂²u/∂y² = 0 + 0 ≠ 0.

Therefore, f does not have a harmonic complex conjugate.

2.5 To show that the function f(x, y) = x² - y² - iy is harmonic, we need to demonstrate that it satisfies the Laplace's equation (∇²u = 0 and ∇²v = 0).

For u(x, y) = x² - y², we have ∇²u = ∂²u/∂x² + ∂²u/∂y² = 2 - 2 = 0.

For v(x, y) = -y, we have ∇²v = ∂²v/∂x² + ∂²v/∂y² = 0 + 0 = 0.

Both u and v satisfy the Laplace's equation, indicating that f(x, y) = x² - y² - iy is a harmonic function.

To determine the harmonic conjugate of f, we can integrate the partial derivative of v with respect to x and y, and obtain the imaginary part of the function:

h(x, y) = ∫ (∂v/∂y) dy = ∫ 0 dy = C(y)

Where C(y) is an arbitrary function of y.

The harmonic conjugate of f is given by:

g(x, y) = u(x, y) + ih(x, y) = x² - y² + iC(y)

Therefore, the harmonic conjugate of f(x, y) = x² - y² - iy is g(x, y) = x² - y² + iC(y), where C(y) is an arbitrary function of y.

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To show that all partial derivatives of u and v exist at (x, y) = (0, 0) and satisfy the Cauchy-Riemann equations, we need to calculate the partial derivatives of u and v and check their existence and the Cauchy-Riemann conditions.

The function is given as u(x, y) = xy and v(x, y) = x² + y².

Partial derivatives of u:

∂u/∂x = y

∂u/∂y = x

Partial derivatives of v:

∂v/∂x = 2x

∂v/∂y = 2y

All partial derivatives exist at (x, y) = (0, 0) since they are simple functions and do not have any singularities.

Now, let's check if the Cauchy-Riemann equations are satisfied:

∂u/∂x = ∂v/∂y

y = 2y

This equation holds true for all values of y, including y = 0.

∂u/∂y = -∂v/∂x

x = -2x

This equation also holds true for all values of x, including x = 0.

Therefore, all partial derivatives of u and v exist at (x, y) = (0, 0), and they satisfy the Cauchy-Riemann equations.

2.2 To show that f is not continuous at (0, 0) and hence not differentiable at (0, 0), we can examine the behavior of f as (x, y) approaches (0, 0).

The function f(x, y) = u(x, y) + iv(x, y) = xy + i(x² + y²)

As (x, y) approaches (0, 0), both u(x, y) = xy and v(x, y) = x² + y² approach 0. However, f(x, y) = xy + i(x² + y²) approaches 0 + i(0) = i(0) = 0i = 0, which is a different value.

Therefore, f is not continuous at (0, 0), and hence it is not differentiable at (0, 0).

2.3 To investigate whether f is analytic or not, we need to check if it is differentiable in a neighborhood around every point.

Since we have already shown that f is not differentiable at (0, 0), it implies that f is not analytic because differentiability is a necessary condition for analyticity.

2.4 To investigate whether f has a harmonic complex conjugate or not, we need to check if u and v satisfy the Laplace's equation (∇²u = 0 and ∇²v = 0) and if they satisfy the Cauchy-Riemann equations.

The Laplace's equation is not satisfied by u(x, y) = xy because ∇²u = ∂²u/∂x² + ∂²u/∂y² = 0 + 0 ≠ 0.

Therefore, f does not have a harmonic complex conjugate.

2.5 To show that the function f(x, y) = x² - y² - iy is harmonic, we need to demonstrate that it satisfies the Laplace's equation (∇²u = 0 and ∇²v = 0).

For u(x, y) = x² - y², we have ∇²u = ∂²u/∂x² + ∂²u/∂y² = 2 - 2 = 0.

For v(x, y) = -y, we have ∇²v = ∂²v/∂x² + ∂²v/∂y² = 0 + 0 = 0.

Both u and v satisfy the Laplace's equation, indicating that f(x, y) = x² - y² - iy is a harmonic function.

To determine the harmonic conjugate of f, we can integrate the partial derivative of v with respect to x and y, and obtain the imaginary part of the function:

h(x, y) = ∫ (∂v/∂y) dy = ∫ 0 dy = C(y)

Where C(y) is an arbitrary function of y.

The harmonic conjugate of f is given by:

g(x, y) = u(x, y) + ih(x, y) = x² - y² + iC(y)

Therefore, the harmonic conjugate of f(x, y) = x² - y² - iy is g(x, y) = x² - y² + iC(y), where C(y) is an arbitrary function of y.

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Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

Answer:

y =1

Step-by-step explanation:

6(2y−9)=-42

Divide each side by 6

6/6(2y−9)=-42/6

2y -9 = -7

Add 9 to each side

2y -9+9 = -7+9

2y =2

Divide by 2

2y/2 = 2/2

y =1

The value of B+U+S+T+E+D is 20. B represents the number 2, U represents the number 3, S represents the number 19, T represents the number 20, E represents the number 5, and D represents the number 4. When these numbers are added together, they equal 20.

BUSTED is an acronym for 'Believing Uncovering Solving Troubles Everywhere Dynamicly'. It is a popular phrase used by the characters in the Scooby-Doo cartoons. It is a phrase used to express the moment when the mystery is solved and the bad guy is caught.

BUSTED is an important part of the Scooby-Doo cartoon series. It expresses the moment when the mystery is solved and the bad guy is caught. It is also a great way to encourage children to believe in themselves and to use their own detective skills to solve a mystery. The value of B+U+S+T+E+D is 20, and it is a fun way to teach kids math and problem solving skills.

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Answer:B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

An interval on the graph above that is increasing include the following: B. -2 < x < 2.

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

On the other hand (conversely), if the output value (range) is decreasing when the input value (domain) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph above, we can reasonably infer and logically deduce that it is increasing over the interval -2 < x < 2.

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Answer:

So basically you have to multiply.

Step-by-step explanation:

If one US Dollar is equal to 100 bells then how many US Dollars would you need to get to 186,000 bells?

Mk Let's use our brains here.

Let's just convert everything to bells real quick. No dollars.

100 bells times what equals 186,000?

100 x ?  = 186,000

That Number is 8600

100 x 8600 = 186,000

So now that we have that number, how many US dollars is equal to 8600?

It's 86!

Because 100(bells) x 86(dollars) = 8600 bells'

So your answer is 86 dollars

Hope this helped!

- Unbrand -

(If this is wrong sorry, I'm not that good at math! :(. )

E. NO correct choices. The volume of the solid obtained by rotating the region R about the horizontal line y = 1 is (64π/3) cubic units.

To find the volume of the solid obtained by rotating the region R about the horizontal line y = 1, we can use the method of cylindrical shells.

The region R is bounded by the curve y = \(5 - x^2\) and the horizontal line y = 1. Let's first find the intersection points of these two curves:

\(5 - x^2\)  = 1

\(x^2\) = 4

x = ±2

So, the region R is bounded by x = -2 and x = 2.

Now, consider a vertical strip within R with width Δx. The height of the strip is the difference between the two curves: ( \(5 - x^2\) ) - 1 = 4 - \(x^2\). The thickness of the strip is Δx.

The volume of this strip can be approximated as V = (height) * (thickness) * (circumference) = (4 - \(x^2\)) * Δx * (2πy), where y represents the distance between the line y = 1 and the curve ( \(5 - x^2\) ).

To find the volume, we integrate this expression over the interval [-2, 2]:

V = ∫[-2,2] (4 - \(x^2\)) * (2πy) * dx

To express y in terms of x, we rewrite the equation y =  \(5 - x^2\)  as x^2 = 5 - y, and then solve for x:

x = ±√(5 - y)

Now, substitute this expression for y in terms of x into the integral:

V = ∫[-2,2] (4 - \(x^2\)) * (2π(1 + x)) * dx

Evaluating this integral:

V = 2π ∫[-2,2] (4 - \(x^2\))(1 + x) dx

Now, expand the expression inside the integral:

V = 2π ∫[-2,2] (4 + 4x - \(x^2\) - \(x^3\)) dx

V = 2π [8 + 8 - (8/3) - 4] - [-8 + 8 - (-8/3) - 4]

V = 2π [24/3 - 4/3] - [-8/3 - 4/3]

V = 2π [20/3] - [-12/3]

V = 2π [32/3]

V = (64π/3)

Therefore, the volume of the solid obtained by rotating the region R about the horizontal line y = 1 is (64π/3) cubic units.

None of the given answer choices match this result, so the correct choice is E. NO correct choices.

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The z-score associated with a 95% confidence level is approximately 1.96.

The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.

Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.

Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula

z = invNorm(1 - α/2)

where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:

z = inv Norm(1 - 0.05/2)

= inv Norm(0.975) ≈ 1.96

Therefore, the z-score is 1.96

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Answer:1 5/7

Step-by-step explanation:

Answer:

12/7 or 1 5/7

Step-by-step explanation:

it's would be 1 5/7

Based on the data, the area of the triangle would be 88 ² units.

To find the area of the triangle in the image we must take into account the measurements shown. In this case it has a height of 11 units and a base of 16 units. To find the area we must apply the following formula:

In that case, we have to replace the base and height values and perform this operation as shown below:

According to the above, the area of this triangle is 88 units².

Note: This question is incomplete Here is the complete information:

Attached image

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Answer:d

Step-by-step explanation:

To build a garden of 4 feet Deja needs 12 small bricks.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The first garden is 4 feet long the bricks Deja is using are each 1/3 of a foot long.

Therefore, the number of bricks required is,

= 4/(1/3).

= 4×(3/1).

= 12 bricks.

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Answer:

its the first one. hope this helps

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The missing value in the puzzle is 29

The missing value in the puzzle can be obtained thus :

Take the Square of the value at the top of the triangle , A

Multiply the two bottom values , C

Subtract C from A to obtain the value in the middle of the triangle.

Hence,

A = 8² = 64

C = 7 * 5 = 35

Middle value = 64 - 35 = 29

Therefore, the missing value in the puzzle is

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