HELLOOOOOOOO
ok ik this might be a little too much but can you still pls help!
:) :) :) :) :)

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

\(\textsf{B)} \quad \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}\\\end{minipage}}\)

Given expression:

\((2x^2y^3+y)^7\)

Therefore:

Therefore:

\(\displaystyle (2x^2y^3+y)^7=\sum^{7}_{k=0}\binom{7}{k} (2x^2y^3)^{7-k}(y)^{k}\)

To find the 4th term in the binomial expansion, substitute k = 4 into the equation:

\(\implies \displaystyle \sum^{7}_{k=0}\binom{7}{4} \left(2x^2y^3\right)^{7-4}\left(y\right)^{4}\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{(7-4)!4!} \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(35 \cdot 8x^6y^9y^4\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(280x^6y^{13}\right)\right)\)

Therefore, the expression that correctly shows how to use the binomial theorem to determine the 4th term in the expansion is:

\(\displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{8(4 - 2^6)}{4}}\)

\(\mathsf{2^6}\\\mathsf{\rightarrow2\times2\times2\times2\times2\times2}\\\mathsf{\rightarrow 4\times4\times4}\\\mathsf{\rightarrow 16\times4}\\\mathsf{\rightarrow \bf 64}\)

\(\mathsf{= \dfrac{8(4 - \bf 64)}{4}}\)

\(\mathsf{4 - 64}\\\mathsf{\rightarrow \bf -60}\)

\(\mathsf{= \dfrac{8(\bf -60)}{4}}\)

\(\mathsf{8(-60)}\\\mathsf{\rightarrow \bf -480}\)

\(\mathsf{= \dfrac{-480}{4}}\\\\\mathsf{\rightarrow \dfrac{-480\div4}{4\div4}}\\\\\mathsf{\rightarrow- \dfrac{\bf 120}{1}}\\\\\mathsf{\rightarrow \bold{-120}\div 1}}\\\\\mathsf{\rightarrow \bf -120}\)

\(\huge\text{Therefore, your answer is: \boxed{\mathsf{-120}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

the correct rigid transformation is a translation 3 units to the left and 6 units up. Option D

To determine the correct rigid transformation, we need to analyze the given options and identify the one that preserves the size and shape of the original figure.

Option A, a 45° rotation clockwise about the origin, would change the orientation of shape 2 and is unlikely to result in congruence with shape 1.

Option B, a translation 6 units to the left and 8 units up, does not preserve the relative positions of the points in shape 2. Therefore, it would not make shape 2 congruent to shape 1.

Option C, a reflection across the x-axis, would change the orientation of shape 2 and is also unlikely to result in congruence.

Option D, a translation 3 units to the left and 6 units up, preserves the relative positions of the points in shape 2. This transformation would result in shape 2 being congruent to shape 1, as it moves shape 2 to the same position and orientation as shape 1.

Therefore, the correct rigid transformation is a translation 3 units to the left and 6 units up.

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a. We want to approximate e⁴⁷², so we substitute x = 4⁷² into the Taylor series expansion:

e⁴⁷² ≈ 1 + (4⁷²) + ((4⁷²)²)/2! + ((4⁷²)³)/3!

b. The absolute error in the approximation using the Taylor polynomial |1.3480 x 10²⁰⁶.

Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem.

a. To approximate the quantity e⁴⁷² using a Taylor polynomial with n = 3, we can use the Taylor series expansion of the exponential function:

eˣ = 1 + x + (x²)/2! + (x³)/3! + ...

For our case, we want to approximate e⁴⁷², so we substitute x = 4⁷² into the Taylor series expansion:

e⁴⁷² ≈ 1 + (4⁷²) + ((4⁷²)²)/2! + ((4⁷²)³)/3!

b. To compute the absolute error in the approximation, we need the exact value of e⁴⁷². Since e is a transcendental number, its exact value cannot be expressed as a finite decimal or fraction. However, we can use a calculator to obtain an approximate value for e⁴⁷² and then calculate the absolute error.

Using a calculator, we find that e⁴⁷² ≈ 1.3480 x 10²⁰⁶.

To calculate the absolute error, we subtract the approximate value obtained from the Taylor polynomial from the exact value:

Absolute error = |Exact value - Approximate value|

Absolute error = |1.3480 x 10²⁰⁶ - (approximated value using the Taylor polynomial)|

Please note that the calculation of the absolute error requires knowing the exact value of e⁴⁷², which cannot be determined exactly. The above calculation provides an example of how the absolute error can be computed if the exact value is given.

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The complete question is:

a. Approximate the given quantity using a taylor polynomial with n=3.

b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.

e⁴⁷²

The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

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Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

Answer:

1755.98

Step-by-step explanation:

1755.97809915

1 cent is 1 hundredth of a dollar, so to round to the nearest cent means to round to the nearest hundredth.

The 7 in boldface is the hundredths place.

Drop all digits to the right of the 7.

1755.97

dropped digits: 809915

Look at the leftmost digit that was dropped (in boldface). If it is from 0 to 4, you are done, and the answer is 1755.97. If the leftmost digit that was dropped is from 5 to 9, the hundredths digit goes up by 1. Here, the first digit that was dropped is an 8, so the 7 in the hundredth place goes up 1 to 8.

Answer: 1755.98

The labor hours required for the eighth satellite are calculated to be 51,200 based on a learning curve value of 0.5120 and an expected improvement curve of 80%.

The learning curve concept suggests that as the cumulative production doubles, the labor hours required to produce each unit decrease by a certain percentage. In this case, the learning curve value for the eighth unit is given as 0.5120, which means that the labor hours needed for the eighth satellite is 51.20% of the labor hours required for the first unit.

To calculate the actual number of labor hours, we multiply the learning curve value by the total labor hours required for the first unit. Given that the total labor hours for the first unit is 100,000, we can calculate the labor hours for the eighth satellite as follows: 0.5120 * 100,000 = 51,200.

Therefore, based on the given learning curve value and the expected improvement curve of 80%, the number of labor hours for the eighth satellite is determined to be 51,200.

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Answer:

Cos x = \(\frac{base}{hypotenuse}=\frac{\sqrt{3} }{2}\)

Tan x = \(\frac{perpendicular}{base} = \frac{1}{\sqrt{3} }\)

Step-by-step explanation:

Sin x = \(\frac{perpendicular}{hypotenuse} = \frac{1}{2}\)

So, Perp = 1 and hyp = 2

Putting this in Pythagorean theorem to get the base

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

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

base ² = 4-1

base² = 3

Taking square root on both sides

Base = \(\sqrt{3}\)

Now

Cos x = \(\frac{base}{hypotenuse}=\frac{\sqrt{3} }{2}\)

Tan x = \(\frac{perpendicular}{base} = \frac{1}{\sqrt{3} }\)

Answer: $88.

Step-by-step explanation:

given data:

The cost of the dress for the prom = $22

label of the rack the dresss was on = 50%.

lowest marked price for the dress = 75%.

Solution:

if the lowest marked price of the cloth was already 75%.

and the current cost of the clothe is $22

the original cost of the cloth would be

100% – 75% = 0.25%

= $22 * 100 / 0.25%

= $88.

The original cost of the dress was $88

Answer:

$88

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

Answer:

LO=6

Step-by-step explanation:

MO/KO=NO/LO

5/10=3/LO

5LO=30

LO=6cm

The value of the variables m and n are 3/2 and 4 respectively

First, we need to know that quadratic functions are defined as functions having its degree as 2.

The general formula for a quadratic function is expressed as;

ax² + bx + c

In standard form, we have;

ax² + bx + c = 0

From the information given, we have that the two functions have the same root, then, we have;

The value of n = 4

For the value of m, we have (-b/a)

-5x/m = -10x/3

cross multiply

m = 3(-5x)/-10x

m = 3/2

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

The ratio of hours spent at soccer practice to hours spent at a birthday party can be represented as 2 for every 3

To provide an accurate ratio, I would need the specific number of hours spent at both soccer practice and the birthday party.

Once you provide that information, you can create the ratio by putting the two numbers in the form 2 for every 3.

For example, if you spent 3 hours at soccer practice and 2 hours at a birthday party, the ratio would be 3:2. This means that for every 3 hours spent at soccer practice, you spent 2 hours at the birthday party.

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The table shows how many hours Sara spent at several activities one Saturday.

Activity "Hours

Soccer practice 2

Birthday party 3

Science project 1

What is the ratio of hours spent at soccer practice to hours spent at a birthday party?

Choose 1 answer:

1 for every 2

B

2 for every 1

2 for every 3

3 for every 2

The required solution of the equation is (2,5). The correct option is A. (2,5).

\(y=x+3.....(1)\\2x+y=9......(2)\)

putting the value of y from eq. 1 in eq. 2 we get,

\(2x+x+3=9\\3x=9-3\\3x=6\\x=2\)

putting the value of x=2 in eq. 1 we get,

\(y=2+3\\y=5\)

Hence, the required solution of the equation is (2,5).

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The magazine asks its readers to complete a survey and respond by mailing.

The fact that the survey could be biased can only be that occurs a problem with the delivery.

With this argument, we can discard the other options, having in mind the context.

Then, the correct answer is A.

Answer:

10x + 25 less than or equal to (the sign) $55

Step-by-step explanation:

Answer:

The inequality is 10x + 25 \(\geq\) 55

Step-by-step explanation:

This would be the possible inequality, because it says that "EACH" shirt costs 10$ meaning that Kelsey may buy multiple, which is why you would want to put 10x (for every shirt she buys they each cost 10 dollars) and PLUS she wants a pair of sneakers, so add 25 $

She has only 55$ to spend, so here MAXIMUM amount she can spend is 55$ which means, she can only buy whatever she wants for 55$ or lower.

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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The y-intercept of a line in the xy-plane is (0,1) as shown in attached graph given int the question.

To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis. This means that the y-intercept is the value of y when x is equal to zero. Therefore, we can read off the y-intercept directly from the equation of the line. To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis.

In the given graph we can see that the line intersects the point 1 on y axis.

Therefore, y-intercept of a line in the xy-plane is (0,1).

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Answer:

Where's the question?

Step-by-step explanation:

From the use of the angle of elevation, the length of ladder is 47 feet.

The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.

We know that we have to use the idea of the angle of elevation in this case. We know that;

Cos 65 = 20/x

x is the length of the ladder

x =20/Cos 65

x = 20/0.4225

x = 47 feet

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Answer:

a repeating term of .3

Step-by-step explanation:

1/3 = 1 divided by 3

1 divided by 3 = .33333333333333333333

that is called a repeating term

\(\frac{1}{3}\) = .3

Answer: 1/3 is .3333333 on going

it cant be a whole number

Answer:

61% close to 3/5 but its just 61/100

Step-by-step explanation:

First add up all the times rolled in or equal to number 4 rolled

thats 61 now we need to find the total which when added is an even 100 so its a 61% chance

Answer:

64

Step-by-step explanation:

Y/2 + 8 = 40

subtract 8 from both sides

Y/2 = 32

Multiply 2 on both sides

Y = 64

Answer:

True option is B. AA' = BB'

Step-by-step explanation:

Because,

Point A translated into Point A'

Point B translated into Point B'

Sorry if there's wrong :)

Answer:

30/x - 10

Step-by-step explanation:

Quotient of 30 and a number is 30/x

10 less is -10

Answer:

30/x - 10

Step-by-step explanation:

We first take 30 and divide by x, and then we subtract 10 from that result.

i)  The firm's Total Cost function is TC =\(2Q^3 - 5Q^2 + 12Q + C\), where C is the constant of integration representing fixed costs.

ii) The profit-maximizing level of output, when the firm's fixed costs are zero, is approximately 4.41 units.

i) To find the firm's Total Revenue (TR) function, we need to multiply the quantity (Q) by the price. In this case, the price is given by the marginal revenue function (MR).

Given that MR = 100 - 2Q, the total revenue can be calculated as:

TR = Q * MR

  = Q * (100 - 2Q)

  = 100Q - \(2Q^2\)

So, the firm's Total Revenue function is TR = 100Q - 2Q^2.

To find the firm's Total Cost (TC) function, we need to integrate the marginal cost function (MC) with respect to Q.

Given that MC = \(6Q^2 - 10Q + 12,\) the total cost can be calculated as:

TC = ∫(MC) dQ

 \(= ∫(6Q^2 - 10Q + 12) dQ\)

  \(= 2Q^3 - 5Q^2 + 12Q + C\)

So, the firm's Total Cost function is TC =\(2Q^3 - 5Q^2 + 12Q + C\), where C is the constant of integration representing fixed costs.

ii) To find the profit-maximizing level of output, we need to determine the quantity (Q) at which marginal cost (MC) equals marginal revenue (MR). In this case, MR is given by 100 - 2Q.

Setting MC equal to MR, we have:

MC = MR

\(6Q^2 - 10Q + 12 = 100 - 2Q\)

Simplifying the equation, we get:

\(6Q^2 + 8Q - 88 = 0\)

To solve this quadratic equation, we can use the quadratic formula:

\(Q = (-b ± √(b^2 - 4ac)) / (2a)\)

Applying the values a = 6, b = 8, and c = -88, we get:

\(Q = (-8 ± √(8^2 - 4*6*(-88))) / (2*6)\)

Q = (-8 ± √(64 + 2112)) / 12

Q = (-8 ± √2176) / 12

Since we are looking for a positive quantity, we take the positive square root:

Q = (-8 + √2176) / 12

Calculating this value, we find:

Q ≈ 4.41

Therefore, the profit-maximizing level of output, when the firm's fixed costs are zero, is approximately 4.41 units.

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