Which equation is this model?

The equation of the tangent line is y = -x + 3 and the equation of the normal line is y = x - 1.

Given the equation 2x³ + 2y³ = 9xy

To find the tangent line at point (2,1), we need to find the derivative of the equation:

6x² + 6y²dy/dx - 9y - 9xydy/dx = 0

Solving for dy/dx, we get:

dy/dx = (9y - 6x²)/(6y² - 9x)

At point (2,1), x = 2 and y = 1.

Substituting these values in the above equation, we get:

dy/dx = (9 - 24)/(6 - 18)dy/dx = -1

The slope of the tangent line is -1 at point (2,1).

Now, we can use the point-slope form of a line to find the equation of the tangent line:

y - 1 = -1(x - 2)

y = -x + 3

The slope of the normal line is the negative reciprocal of the slope of the tangent line.

Hence, the slope of the normal line is 1.

Using the point-slope form of a line, the equation of the normal line at point (2,1) is:

y - 1 = 1(x - 2)

y = x - 1

Therefore, the equation of the tangent line is y = -x + 3 and the equation of the normal line is y = x - 1.

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The argument is valid. The argument is valid based on the direct truth-table method.

To test the validity of the argument, we can use the direct truth-table method. Let's break down the argument and construct the truth table for the given premises and the conclusion:

Premises:

G ⊃ H

R ≡ G

~H v G

Conclusion:

R • H

Constructing the truth table:

We have three propositions: G, H, and R. Each proposition can have two truth values, true (T) or false (F). Therefore, we need 2^3 (8) rows in the truth table to evaluate all possible combinations.

By evaluating the truth table, we find that in all rows where the premises (1, 2, 3) are true, the conclusion (R • H) is also true. There is no row where the premises are true, but the conclusion is false. Therefore, the argument is valid.

The argument is valid based on the direct truth-table method. This means that if the premises (G ⊃ H, R ≡ G, ~H v G) are true, then the conclusion (R • H) must also be true.

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Answer:

This fraction is in simplest form:

=2/5

Solution

In order to simplify a fraction there must be:

1. A number that will divide evenly into both the numerator and denominator so it can be reduced. No such number exists for 2 and 5.

or

2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 2 is not greater than 5.

This fraction is in simplest form:

=2/5

Hope this helps!

Need to learn more about fractions? I'm your guy! :D

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

B. 6 cm

Step-by-step explanation:

\(\text{Take the volume of a sphere and solve for r.}\\V=\frac{4}{3}\pi r^3\\\text{We already know that the volume is 113, so substitute that value.}\\113=\frac{4}{3}\pi r^3\\\text{Divide both sides by 4/3 pi.}\\\frac{113}{\frac{4}{3}\pi}=r^3\\\text{Divide 113 by 4/3 pi.}\\r^3=26.98\\\text{For a more accessible value, round up.}\\r^3 \approx27\\\text{Take the cube root of both sides.}\\r=3\)

Now that the radius is known, all we have to do is multiply it by 2 to get the diameter. Here the answer is simply 3 * 2, or 6.

Answer:

B. 6 cm

Step-by-step explanation:

You can use the formulas \(d=(\frac{6V}{\pi } )^{\frac{1}{3} }\) or \(d = \sqrt[3]{\frac{6V}{\pi } }\) to solve for diameter using volume. I will use the first forumla for this problem.

1. Substitute 113 for "V":

\(d=(\frac{6(113)}{\pi }) ^{\frac{1}{3} }\)

2. Multiply in the parenthesis:

\(d=(\frac{678}{\pi } )^{\frac{1}{3} }\)

3. Divide by pi (3.14):

678 ÷ 3.14 = 215.923567

\(d=215.9^{\frac{1}{3} }\)

4. Apply the exponent:

d = 5.99907...

d = 6 cm

hope this helps!

The perimeter of the floor of the office building  which was given as 127.5 feet is equal to 42.5 yards.

Perimeter of the floor in an office building is equal to 127.5 feet.

Convert perimeter of the floor of the given office building in feet into yards:

Number of feet in one yard = 3 feet

3 feet = 1 yard

⇒ 1 feet = ( 1 / 3 ) yard

⇒ 127.5 feet = ( 127.5 ) ×   ( 1 / 3 ) yards

⇒127.5 feet = ( 127.5 / 3 ) yards

⇒127.5 feet = ( 42.5 ) yards

Therefore, the perimeter of the floor of the given office building is equal to 42.5 yards.

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The value of the ratio t:m:w in its simplest form is 3:8:28.

To simplify the ratio t:m:w, we need to find the common factor between t, m, and w.

Using the given ratios, we can write t:m:w as (3x):(8x):(28y), where x is the common factor between t and m and y is the common factor between m and w.

From the given ratio t : m = 3:8, we can say that t is equal to 3 and m is equal to 8.

Similarly, from the given ratio m:w = 4:7, we can say that m is equal to 4 and w is equal to 7.

So, we have

t : m = 3:8 and m:w = 4:7

Multuiply second by 2

t : m = 3:8 and m:w = 8:14

So, we have

t : m : w = 3 : 8 : 14

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Answer:

The pair of slacks would be

C. $20.30

I hope that this helps! ^‿^

Answer:

\( - 6 + \frac{1}{4} x + 3( \frac{1}{4} x + 6) \\ \\ = - 6 + \frac{1}{4} x + \frac{3}{4} x + 18 \\ \\ = - 6 + x + 18 \\ = x + 12\)

Answer:

\( = - 6 + \frac{1}{4x} + 3( \frac{1}{4x} + 6) \\ = - 6 + \frac{1}{4x} + \frac{3}{4x} + 18 \\ = 12 + \frac{4}{4x} \\ = 12 + \frac{1}{x} \\ = \frac{12x + 1}{x} \)

The capacity to overcome opposition or hesitancy to accept is referred to as convincing.

Convincing can also be described by other words like cogent, sound, telling, and valid.

Despite the fact that all of these words have the same meaning—"having such force as to compel serious attention and typically acceptance”—convincing denotes the ability to go over resistance or hesitation to accept.

When you say that someone or something is compelling, you indicate that they persuade you that something is real, accurate, or true.

Three fundamental strategies for persuading a listener to agree with you are ethos, logos, and pathos.

A more appropriate translation today may be "picture."

The audience's perception of the speaker's character, according to Aristotle, is referred to as ethos.

Therefore, the capacity to overcome opposition or hesitancy to accept is referred to as convincing.

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The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Answer:

3,958 kjksjjdkskdjdjd

Answer:

90

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

Answer:

I can try

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.

Answer:

hope it helps...

Step-by-step explanation:

In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or their combination.

PLEASE FOLLOW ME

Answer:Rigid just means that the whole shape goes through the same transformation, so with rotations, reflections, and translations, the shape should not change at all, just in a different place or orientation.

Answer: Veronica is not correct

Explanation:

The AAA theorem, aka the AA theorem, only applies to similar triangles. We cannot use it to prove two triangles are congruent or not. We would need to know info about at least one pair of sides. So based on this diagram, we don't have enough information to know if triangle HAT is congruent to triangle PAM or not.

A similar example to this is to consider two equilateral triangles. Let's call them triangle A and triangle B. If equilateral triangle A has side lengths of 2, and has side lengths of 10, we can see that the triangles are not congruent. However, the triangles are similar because the corresponding angles equal one another. One triangle is a scaled copy of the other. This example is a counterexample as to why the AAA theorem is not a valid congruence theorem.

Answer:

-4

Step-by-step explanation:

g(-1) = 3(-1)² - 2(-1) + 7 / 2(-1) + 5

= 3-(-2)+7 / -2+5

= 5+7/-3

= 12/-3

= -4

An articulated ladder should be utilized in a stepladder design for working on stairs. This structure is especially built for stairway safety and stability, with movable legs that can be placed to different heights to suit uneven stairs and give a level area for standing.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area of a planar figure is the space contained by its border. The number of unit squares that cover the surface of a closed form is the figure's area. The area is the region defined by an object's form.

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Answer:

x = 15°

Step-by-step explanation:

the inscribed angle APB is half the measure of the central angle AOB , so

x = \(\frac{1}{2}\) × 30° = 15°

Answer:  AE = 5

Step-by-step explanation:

I sketched the triangle based on the information provided.

since ∠A = 90° and is divided into three equal angles, then ∠BAD, ∠DAE, and ∠CAE = 30°

Since AB = 5 and BC = 10, then ΔCAB is a 30°-60°-90° triangle which implies that ∠B = 60° and ∠C = 30°

Using the Triangle Sum Theorem, we can conclude that ∠ADB = 90°, ∠ADE = 90°, ∠ AED = 60°, AND ∠ AEC = 120°

We can see that ΔAEC is an isosceles triangle. Draw a perpendicular to divide it into two congruent right triangles. Label the intersection as Z. ΔAEZ and ΔCEZ are 30°-60°-90° triangles.

Using the 30°-60°-90° rules for ΔABC we can calculate that AC = 5√3.

Since we divided ΔAEC into two congruent triangles, then AZ = \(\dfrac{5\sqrt 3}{2}\)

Now use the 30°-60°-90° rules to calculate AE = 5

Answer:

D

Step-by-step explanation:

They should both level out at the same height considering the volume of hydrochloric acid used.

Answer:

D

Step-by-step explanation:

Answer:

- 0.3

Step-by-step explanation:

Slope Intercept Form:

y = mx + b

Slope:

m = slope

Equation:

- 0.3x + 3.7

Slope = - 0.3

Hope This Helps :)

Step-by-step explanation:

Hey there!

Let the width be x. Then the length will be 3x - 7.

Perimeter (p) = 38cm.

We have;

Perimeter (p)= 2(length+wide)

38 = 2(3x-9+x)

38 = 8x - 18

38+18 = 8x

X = 56/8

Therefore, x = 7cm

3x-9 = 3*7-9

= 12cm.

Therefore, wide= 7cm and length= 12cm.

Hope it helps...

The number of possible sandwiches does is 6.

What is combination ?

In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.

Given ,

Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.

The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.

factorial of n! = n*(n-1) !

The number of possible sandwiches does  =  3!

=3*2 = 6.

Therefore, The number of possible sandwiches does is 6.

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Answer:

15/4

Step-by-step explanation:

to find the slope with two coordinates use

y2 - y1 / x2 - x1

first find the difference between the ys

the 2nd y point is 5, and the 1st y point is -10, so subtract them from each other

5 - (-10) = 5 + 10 = 15

then find the difference between the xs

the 2nd x point is -1, and the 1st x point is -5, so subtract them from each other

-1 - (-5) = -1 + 5 = 4

now put the difference in ys over the difference in xs

15 / 4

So thats your slope

A line graph is used when an independent variable is a continuous quantitative variable. A line graph is a type of chart used to represent data over time with the help of lines connecting various data points.

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Answer:

yfyffyfyfyg

Step-by-step explanation:

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