please write clear and bold72. [3 marks] For y = 3x² - x + 6, find the differential and evaluate for x = 2 and dx = = 0.1.

Answer:

60

Step-by-step explanation:

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

Answer:

(1,8) and (1,2) are 6 units apart

The integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder \(z=y^{2}\) and below the paraboloid \(z=8-2x^{2} -y^{2}\) is 128/9.

The first step is to find the bounds of integration. The region in the first octant (x,y,z≥0) is bounded by the planes x=0, y=0, and z=0.

The parabolic cylinder z=y2 is bounded by the planes x=0 and \(z=y^{2}\). The paraboloid \(z=8-2x^{2} -y^{2}\) is bounded by the planes x=0, y=0, and z=8.

The next step is to set up the integral. The integral is:

\(\int\limits {0^{1} } \int\limits {0^{\sqrt{x} } }\int\limits {y^{8}-2x^{2} -y^{2} 8xzdxdy\)

We can evaluate the integral by integrating with respect to z first. The integral with respect to z is:

\(8x^{2} (8-2x^{2}-y^{2} )-8xy^{2} -y^{8} -2x^{2} -y^{2}\)

Simplifying this expression, we get the equation:

\(8x^{2} (8-2x^{2}-y^{2} )-8xy^{2}\)

We can now integrate with respect to x. The integral with respect to x is:

\(4(8-2x^{2}-y^{2} )^{2} -4xy^{2}-0^1\)

Simplifying this expression, we get the equation:

\(4(8-2x^{2}-y^{2} )^{2} -4xy^{2}\)

We can now integrate with respect to y. The integral with respect to y is:

\(4\frac{(8-2-y)^{3} }{3} -4y^{3} -0^1\)

Simplifying this expression, we get the equation:

\(\frac{128}{9}\)

Therefore, the integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder \(z=y^{2}\) and below the paraboloid \(z=8-2x^{2} -y^{2}\) is \(\frac{128}{9}\).

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The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.

The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.

Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.

Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.

This question should be provided with answer choices, which are:

The correct answer is A.

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Answer:

\(5^{1/2}\)

Step-by-step explanation:

Answer: 25 weeks

Step-by-step explanation:

Let W represent the number of weeks

Judy equation is

12W + 300

Cassie equation is

20W + 100

Now let's solve it! Our system of equation is

12W + 300 = 20W + 100

Subtract 300 from both sides

12W = 20W -200

Subtract 20W from both sides

-8W = -200

W = 25 weeks

So, it takes 25 weeks for Judy and Cassie to have the same amount saved.

Answer:

let judy = 300 + 12W

cassie = 100 + 20W

300 + 12W =  100 + 20W

300 - 100 = 20W - 12W

200 = 8W

W = 25

300 +  12(25) = 100 + 20(25)

300 + 300 = 100 + 500

600 = 600

Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.

THE GRAPH IS IN THE PICTURE,line graph

Step-by-step explanation:

For the inverse of a relation to be a function itself, the original relation must be one-to-one or injective. This ensures that each element in the domain corresponds to a unique element in the range.

If there are repeated elements in the domain or range, the inverse relation would not satisfy the definition of a function.

In order for the inverse of a relation to be a function itself, the original relation must be one-to-one or injective. This means that each element in the domain corresponds to a unique element in the range.

A one-to-one or injective relation ensures that there are no repeated elements in the domain or range. If there are repeated elements, the inverse relation would not satisfy the definition of a function because it would have multiple outputs for a single input, violating the requirement of a well-defined function.

To clarify, if a relation is not one-to-one, it means that there exist two or more elements in the domain that map to the same element in the range. In such cases, the inverse relation would have multiple outputs for these elements, making it not a function.

Therefore, the condition for the inverse of a relation to be a function is that the original relation must be one-to-one or injective.

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Answer:

(3, - 28)

Step-by-step explanation:

f(x) = 4x² - 24x + 8

\(x = - \frac{ - 24}{2 \times 4} \)

x = 3

f(3) = -28

= (3, -28)

Answer:

Interval notation of x<3 is (-∞,3)

Interval notation of x>=5 is [5,+∞)

Step-by-step explanation:

x<3

Since you did not enter an equal sign, this translates to ) since we will not be including the number 3

Based on the < you entered, the left side of the interval notation will extend to negative infinity, which is denoted as -∞

(-∞,3)

----------------------

x>=5

Because you entered an equal sign, this translates to [ since we include the number 5.

Based on the ≥ you entered, the right side of the interval notation will extend to positive infinity, which is denoted as +∞

[5,+∞)

The sum of all the entries of a matrix whose null space consists of all linear combinations of vectors is zero.

To find the sum of all the entries of a matrix whose null space consists of all linear combinations of vectors, follow these steps:

Therefore, the sum of all the entries of a matrix whose null space consists of all linear combinations of vectors is zero.

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Answer:

Step-by-step explanation:

5x + 4 = 0.5×38

5x + 4 = 19

5x = 19 - 4

5x = 15

 x = 3

Answer:

1.5 feet

Step-by-step explanation:

Answer:

1.5 feet or 3/2 feet

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Given the function f(x) = -(-x)

we want to evaluate f(-3)

What we do simply here is substitute the value of -3 for x in the equation

That would be ;

f(-3) = -(-(-3)) = -(3) = -3

Answer:

true

Step-by-step explanation:

because x-2 is like f(x)

Using the Newton-Raphson method with an initial guess of xo = 1.2, the calculated value for one real root of tan x = 4x, rounded to six decimal places, is approximately 1.186824.

To find a real root of the equation tan x = 4x using the Newton-Raphson method, we start with an initial guess xo = 1.2.

The Newton-Raphson iteration formula for finding the next approximation xn+1 from xn is given by xn+1 = xn - f(xn)/f'(xn), where f(x) represents the function tan x - 4x and f'(x) represents the derivative of f(x).

Iterating through the Newton-Raphson formula, we update the approximation using the equation xn+1 = xn - (tan xn - 4xn) / (sec² xn - 4), where sec² xn represents the square of the secant of xn.

After performing the iterations until convergence, the calculated value for the real root of tan x = 4x, rounded to six decimal places, is approximately 1.186824.

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Answer:

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

Step-by-step explanation:

Your welcome ;)

The maximum rate of change of function f at the given point occurs in the direction of the gradient vector.

To find the maximum rate of change of a function f at a given point, we need to compute the gradient of the function and evaluate it at that point. The gradient represents the direction of steepest ascent, and its magnitude indicates the maximum rate of change.

By finding the partial derivatives of f with respect to each variable and evaluating them at the given point, we obtain the components of the gradient vector. The maximum rate of change occurs in the direction of this gradient vector. Without the specific function and point, it is not possible to determine the exact maximum rate of change or its direction.

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then it is a perpendicular

Answer: x = 2 - 1/2 y

Step-by-step explanation:

12x + 6y = 24

12x = 24 - 6y

x = 2 - 1/2 y

Answer:

The first is organize your data set and after that determinate if the length (the total data) is odd or even dependent of that find the middle value. This is the traditional algorithm for find the median of whatever data set.

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Good Luck! I double checked my answer!

Answer:

37

Step-by-step explanation:

Hey There!

They want us to find the hypotenuse using the Pythagorean Theorem

The Pythagorean Theorem says

\(a^2+b^2=c^2\)

or that the two legs ( shorter side) square, added together equal the hypotenuse square

Note: This only works with right triangles

so basically

\(hypotenuse^2=35^2+12^2\\35^2=1225\\1262=144\\144+1225=1369\\\sqrt{1369} =37\)

Therefore the missing side length equals 37

hope this helps!

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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Answer:

1000

Step-by-step explanation:

Answer:

10000 or 40000 pls mark this answer as brain list

Answer:

Approximately 45%.

Step-by-step explanation:

We know that Steve's team played in total 33 games. Out of the 33, they won 15 of them.

So, as a fraction of the total won over the total games, we can write:

\(\displaystyle\frac{15}{33}\)

So, by dividing, the percent the team won is:

\(\displaystyle\frac{15}{33}=0.\overline{45}=0.454545...\approx0.45=45\%\)

The team won approximately 45% of its games.

Therefore , the solution of the given problem of slope comes out to be

slope m = 1/5.

How steep a line is defined by its slope. A gradient overflow is a feature of a gradient-based equation. The slope is calculated by dividing the average horizontal differences (run) between two locations by the vertical difference (rise) between the same two locations. The hill type of an equation is used to represent the problem of a fixed path and is written as y = mx + b. The line's y-intercept lies where the grading is m, a = b, where (0, b). The slope y and y-intercept are the following for the trigonometric functions y = 3x - 7: (0, 7). Where the line's slope is m and b is where the y-intercept is located.

Here,

Given:

Section A: If y=2(x)1/2 If f'(a)=a-1/2 and f'(a)=y'=dy/dx=x-1/2, then m=a-1/2.

For point (x1, y1), section b) point slope y-y1=m(x-x1), x=a, y-4=4-1/2 (x-4)

y=1/2(x-4)+4

y=1/2x-2+4

y=1/2x+2

Y-10=25-1/2 at point (25,10) (x-25)

y=1/5(x-25)+10

y=1/5x-5+10

y=1/5x+5

Therefore , the solution of the given problem of slope comes out to be

slope m = 1/5.

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Answer:

3/18, or simplified, he has a 1/6 chance of grabbing an adventure book.

Step-by-step explanation:

6 + 5 + 4 + 3 = 18. There's 3 adventure books, which makes it so that he has a 3/18 chance of it being an adventure book. How did I simplify? 18 ÷ 3 = 6, 3 ÷ 3 = 1.

Answer:

$14.41

Step-by-step explanation:

5.45+10.14=15.59 30-15.59=14.41