Plss help i dont understand

The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = \(x^2 - 2xy + 3y^2\), we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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Answer:

x=2

Step-by-step explanation:

Add 3

2x=4

divide by 2

x =2

Answer:

x=7/10

Step-by-step explanation:

2/5=4/10

11/10=x+4/10

11/10-4/10=x

7/10=x

Answer:

x=7/10 or 0.7

Step-by-step explanation:

I turned the fractions into decimals

so

1.1=x+0.4

subtract 0.4 from 1.1 to get 0.7

Turn it into a fraction which is 7/10

The width of the opening is 2x, which equals 2(4√2) = 8√2 feet. To solve this problem, we'll use the properties of a paraboloid of revolution.

Given that the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, we have the vertex of the parabola at (0, 2). We also know the focus of the parabola is at the light source, which is at (0, 0).
Since the parabola opens downward, its equation is of the form (x - h)² = -4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus.
In our case, h = 0, k = 2, and p = 2. So the equation becomes x² = -4(2)(y - 2) or x² = -8(y - 2).
At the opening, the paraboloid is 4 feet deep, so y = -2. Substituting this value into the equation, we get:
x² = -8(-2 - 2) => x² = 32
Now, we find the width by solving for x:
x = ±√32 => x = ±4√2

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The width of the opening of the searchlight is 2√32 feet.

To find the width of the opening of the searchlight, we'll first determine the equation of the parabola and then use that to find the width.
Identify the vertex and focus:

The vertex is at the base of the searchlight (0, 0) and the focus is 2 feet from the base along the axis of symmetry,

so it's located at (0, 2).
Determine the equation of the parabola:

Since the parabola opens upward, its equation will be in the form \((x-h)^2 = 4p(y-k),\)

where (h, k) is the vertex and p is the distance from the vertex to the focus.

In this case, h = 0, k = 0, and p = 2,

so the equation is \(x^2 = 4(2)(y) or x^2 = 8y.\)
Find the width at the depth:

Since the depth of the searchlight is 4 feet, we'll find the width at y = 4. Substitute y = 4 in the equation:

\(x^2 = 8(4)\), which gives \(x^2 = 32\).

To find the width, we need the distance between the two points where x is positive and negative, so x = ±√32.
Calculate the width of the opening:

The width of the opening is the difference between the positive and negative values of x, which is 2√32.

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Explanation

To answer this given question, we will make use of the Empirical rule of normal distribution

The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

The image below helps gives a clearer understanding

So in our case, since the mean is 189 mg/dL and the standard deviation is 23

Then we will have the following values at

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The option b "The area under the curve is 1." and the option d "It is symmetrical" are true about the probability function for a t distribution.

When the sample size is small and the population standard deviation is unknown, the t-distribution is used in statistics.

Option b confirms that the total area under the t-distribution curve is 1, indicating that the sum of probabilities for all possible outcomes is also equal to 1.

Option d confirms the symmetry of the t-distribution, implying that the curve is balanced on both sides of the mean. The mean, median, and mode of a symmetrical distribution are all equal.

To summarize, the t-distribution is a useful tool in statistics when working with small sample sizes because it accounts for the uncertainty in the population standard deviation.

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No, the LDA classifier and the Bayes classifier would not necessarily give similar boundaries when trained on a large amount of training data from an arbitrary distribution.

The LDA (Linear Discriminant Analysis) classifier assumes that the input features are normally distributed and that the class covariances are equal. It finds linear boundaries that maximize the separation between classes based on these assumptions. On the other hand, the Bayes classifier makes decisions based on the class conditional probabilities and prior probabilities of the classes. It can handle arbitrary distributions and does not make assumptions about the class covariances. Therefore, even with a large amount of training data, if the distribution of the data does not conform to the assumptions of LDA (e.g., non-normal distributions or unequal class covariances), the LDA classifier may not give similar boundaries to the Bayes classifier.

The LDA and Bayes classifiers may not give similar boundaries when trained on data from an arbitrary distribution, as the LDA classifier relies on specific assumptions about the data distribution that may not hold true in practice.

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Answer:

The board should be 4.7 feet long.

Step-by-step explanation:

To find the remaining piece, you just multiply 1.1 by 2.3 which is 2.53. That's the length of the remaining piece.

Then you add all the pieces together.

1.1+1.1+2.53 =

4.73

Round and add label.

4.7 feet

5% of $1100 = 55

Year given = 7

So, 55 × 7 = 385

She would get after 7 years all total  = (1100 + 385) = $1485

Answer:

It is NOT c

Step-by-step explanation:

I clicked c and it was wrong lol.

Answer:

its D

Hope this helps ⊂◉‿◉つ

Answer:

$13,450

Step-by-step explanation:

The fixed costs of production, are the costs incurred that are independent from the production volume, that is, regardless of how many spinners the company produces, those costs will remain the same. If 'x' is the number of spinners produced, interpreting the cost function, we can see that it costs $1.28 to produce each spinner and that there is a cost that does not rely on production of $13,450. Therefore, the fixed cost of production is $13,450.

Answer:

It would be the last graph (c). It would look like the image below.

Explanation:

Since 3 is negative the answer would have a graph with a line going like this \.

Answer:

a. connect the point (0 , 3) with A

b. connect the origin (0 , 0) with B

c. For A: y = 0.5x +3

For B: y = 0.5x

Step-by-step explanation:

y = ax + b is the general rule for any straight line

a being the slope and b being the y intercept, a is given to be 0.5

y = 0.5x + b, substitute the coordinates of point A

4 = 0.5 *2 +b hence b = 4 - 0.5 *2 = 4 - 1 = 3

so y = 0.5 x + 3 is the equation of the line passing through A

since the second line that passes through B is parallel to the first, hence it has the same slope of 0.5

same procedure, substitute coordinates of B

2 = 0.5 * 4 + b hence b = 2 - 0.5 *4 = 2 - 2= 0

so y = 0.5 x is the equation of the line passing through B

Answer: 9 + 1.50m

Step-by-step explanation:

From the question, we are informed that the minimum cost for an Uber ride is $9 and that a fee of $1.50 will be added for each additional mile.

A piece wise function to model the situation will be:

= 9 + 1.50m

where m = every additional mile

For example, if a person takes 4 additional miles, this will be calculated as:

= 9 + 1.50m

= 9 + 1.50(4)

= 9 + 6

= $15

Answer:

u kind of forgot the attachment bestie

Answer:

option c (third one down)

Step-by-step explanation:

well its not a or d cause -10 times -3 is a positive number and then using law of exponents add the values of exponent and u get b as the only one that makes sense:)

The value of the quantity after 97 years, considering a growth rate of 0.55% per decade, to the nearest hundredth, is 8,649.28.

We have,

The continuous growth formula:

\(A = P e^{rt}\)

Where:

A is the final value of the quantity

P is the initial value of the quantity = 8200

r is the growth rate (as a decimal) = 0.55% = 0.55/100 = 0.0055

t is the time in years = 97 years

e is the mathematical constant approximately equal to 2.71828

Since a decade is a period of 10 years, divide the given time of 97 years by 10.

Number of decades = 97 years / 10 = 9.7 decades

Substitute.

\(A = P e^{rt}\\A = 8200 \times e^{0.0055 * 9.7}\)

\(A = 8200 \times e^{0.05335}\)

A = 8200 * 1.05479

A = 8649.278

A = 8649.28

Therefore,

The value of the quantity after 97 years, considering a growth rate of 0.55% per decade, to the nearest hundredth, is 8,649.28.

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Answer:

\(4.3^{9}\)

Step-by-step explanation:

\((4.3^{1})\)\((4.3^{2})\)\((4.3^{2})\)\((4.3)^{2}\)\((4.3^{2})\)  If I expand this out a little, it might be easier to see.  If I do not have an exponent, it is understood that there is only one of those factors so the exponent is 1.

\((4.3^{2})^{4}\)  means that we are taking\(4.3^{2}\) four times.

The Product of Power Principle tells us that when we are multiplying by same base we add the exponents.

\(4.3^{9}\) or 506953 Rounded to the nearest whole number

By using GCF and distributive Property, it is obtained that

3550 = 5 \(\times\) 710 as a product

What is Greatest Common Factor and distributive property?

Greatest Common factor (GCF) of two numbers a and b is the greatest number that divides both a and b.

Distributive property is the property over both addition and multiplication.

If a, b and c are three numbers, then distributive property is given by

\(a \times (b + c) = a \times b + a \times c\)

3550 = 3000  + 550

Now,

\(3000 = 2\times 2 \times 2\times 3\times 5 \times 5 \times 5\\550 = 2 \times 5 \times 5 \times 11\)

GCF of 3000 and 550 = 5

3550 = 5 \(\times\) 600 + 5 \(\times\) 110

3550 = 5 \(\times\) (600 + 110) [Distributive Property]

3550 = 5 \(\times\) 710

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Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

According to the information, the lateral area of the room is 112m²; the area to be painted is 109.4m²; the volume is 185.76m³ and the floor area is 46.44m².

To calculate the area of the lateral surface of the room we must find the area of all the sides and then add it as shown below:

To find the area of the surface to be painted, excluding windows and doors, we must find the area of the doors and windows and subtract it from the total lateral area as shown below:

To find the volume of the room, we must multiply the height, by the length, by the width as shown below:

To find the surface area of the floor we must multiply the length of the width by the length of the length as shown below:

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Answer:

\( {12}^{2} \times {6}^{2} = {(12 \times 6)}^{2} = {72}^{2} \)

Answer:Richter scale measures intensity of earthquake as power of 10. The intensity of the Chilean earthquake( year 1960) was approx 316.23 times greater than the earthquake in Haiti (year 2010)How to measure the greatness of earthquakes from Richter scale's intensities?Suppose that the first measured earthquake was of  intensity (on Richter scale)Suppose the second measured earthquake was of   intensity(on Richter scale).It is a fact that each unit of the the Richter scale measurement increases as the power of 10.So if b = a + 1, then the second earthquake was 10 times greater than the first earthquake.If we have b = a + x, then we have:Second earthquake was  times greater than the first earthquake.As it was given that the earthquake in Haiti was of 7.0 intensity on Richter scale, and that the Chilean earthquake was about 9.5 intensity on Richter scaleThe difference is 9.5 - 7 = 2.5

Step-by-step explanation:

The distance that would be between the cities on a map that has a scale of 3 inches:17 miles is 9 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The two cities are 51 miles away from each other.

3 inches:17 miles

Now,

17 miles = 3 inches

Multiply 3 on both sides.

17 x 3 miles = 3 x 3 inches

51 miles = 9 inches

Thus,

There would be 9 inches between the cities on the map.

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