Find the missing side. Round to the nearest tenth.
18
x
50°

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

To know more about rate of change, refer here:

https://brainly.com/question/29181688#

#SPJ11

The discount given on the cost of the meal is $15

When a government imposes an obligational fee or financial charge on an individual or group in order to raise funds for public projects that support the best facilities and infrastructure, the action is referred to as a tax.

step1

According to the question, we are given the following information

The original cost of the meal = $75

Off coupon = 20%

step2

Required

The number of coupons given

coupon amount = 0.2 * 75

coupon amount = $15

Hence the discount given on the cost of the meal is $15

To learn more about discounts refers to;

brainly.com/question/26618117

#SPJ1

If the original price was $75 and Fatima used a 20% coupon, then Fatima saved $15.

    0.20 x 75 = 15

This means the cost of the meal that was taxed was a $60 meal.

Now we also know that after tax, the price of the meal came back to a $75 cost.  This means that the amount of tax was also $15, but it's a $15 tax on a $60 meal, so this is a 25% tax.

    $15 tax / $60 meal = 0.25 = 25%

The trick here is that in the beginning, the savings is based on the $75 meal, while the tax is based on a $60 meal, so the percentages are not the same.

The orthogonal projection of v onto the subspace w is the vector (88/121, 0).

The orthogonal projection of v onto the subspace w spanned by the vectors ui can be found using the formula: projw(v) = (v•u1/||u1||^2)u1, where "•" represents the dot product and "|| ||" represents the magnitude.

Plugging in the values given, we have:

projw(v) = (8,-5)•(11,0)/(11^2+0^2)(11,0) = (88/121, 0)

Therefore, the orthogonal projection of v onto the subspace w is the vector (88/121, 0).

To understand this concept better, it is important to note that the orthogonal projection of a vector onto a subspace is a vector that lies entirely within that subspace and is the closest vector to the original vector in terms of Euclidean distance.

In other words, the projection vector is the "shadow" of the original vector onto the subspace. In this case, we are projecting the vector v onto the subspace spanned by u1, which means we are finding the closest vector to v that can be written as a linear combination of u1.

To know more about linear click here

brainly.com/question/30444906

#SPJ11

The recursive formula which correctly represents the given formula; g ( n ) = g ( n − 1 ) + 5.

It follows from the task content that the expression which represents the recursive formula.

By observation, the common difference, d of the arithmetic progression is; 5.

On this note, the recursive formula can be written as follows;

g ( n ) = g ( n − 1 ) + 5.

Consequently, the required recursive formula for the given arithmetic progression is; g ( n ) = g ( n − 1 ) + 5.

Read more on recursive formula;

https://brainly.com/question/15403068

#SPJ1

Answer:

22 cm

Step-by-step explanation:

A hexagon has six sides. Since it is a regular hexagon, all of the sides have equal length, so we can multiply the length of one side, 3.6 by 6 to get the perimeter. 3.6 x 6 = 21.6. To the nearest centimeter, the upper bound is 22.

When three people divide $18 in a ratio of 3:1:2, Malachy will receive $9, Gavin will receive $6, and Gavin will receive $3.

Malachy and Gavin will each receive $9, while Gavin will receive $6. Malachy will receive three times as much money as Gavin. This is because the ratio of Malachy's share to Gavin's share is 3:1.

The ratio of the amounts that Malachy, Gavin, and Gavin share is 3:1:2, which adds up to a total of 6 parts. This means that the total amount of money they share can be divided into 6 equal parts.

To find the value of each part, we can divide the total amount by 6$18 / 6 = $3

So each part is worth $3.

Now we can find out how much money each person gets by multiplying their share in the ratio by the value of each part: Malachy: 3 parts x $3/part = $9

Gavin: 1 part x $3/part = $3

Gavin will get twice as much money as Malachy, which means he will receive 2/6ths of the money, or $6. Lastly, the remaining $3 will go to Gavin.

To learn more about Ratio :

https://brainly.com/question/12024093

#SPJ11

Out of 52 cards, there is only one Queen of Hearts. Hence, then, the probability = 47/52

5 cards can be chosen from a deck of 52 cards in ⁵²C₅

In order to avoid choosing a queen of hearts, we must choose 5 cards. There is only one queen of hearts in a deck of 52 cards. There are still 51 cards left, and 5 of them can be chosen in ⁵²C₅.

Therefore, the likelihood that a five-card poker hand does not include the queen of hearts is equal to ⁵¹C₅/⁵²C₅

47/52

Know more about probability

https://brainly.com/question/5858025

#SPJ4

The full question

What is the probability that a five-card poker hand does not contain the queen of hearts?

Answer:

Step-by-step explanation:

- 4x^3 / (- 4) = 32 / (- 4)

x should and cannot be negative or it shouldn't be for example (- x) = 90

cubic root (x^3) = cubic root (- 8)

x = cubic root (- 8)

x = 2i

what is "i"?

It is an imaginary number as you cannot square, cubic, or whatever root with a negative in it. so instead you must add "i" to remove the negative as a replacement and indicator that it was a negative number.

The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

Learn more about integrals here:

https://brainly.com/question/31059545

#SPJ11

Answer:

$7.50 are earned per hour

Step-by-step explanation:

5x = 37.50

divide both sides by 5

x = 7.50

Answer:

70 dollars

Step-by-step explanation:

he has only 70%left of his initial savings so that make 70%*100=7*10=70usd

Answer:

A

Step-by-step explanation:

Joint variation is given by:

\(y=kxz\)

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

\(360=k(4)(10)\)

Solving for k:

\(40k=360\Rightarrow k=9\)

Therefore, our equation is:

\(y=9xz\)

Then when x = 5 and z = 12:

\(y=9(5)(12)=540\)

The answer is A.

Parry Company's ROI for year 2 is 33.47%.

To calculate Parry Company's ROI (Return on Investment) for year 2, we need to use the formula:

ROI = (Net Operating Income / Total Assets) × 100

Given the information:

Net Operating Income for year 2 = $930,000

Total Assets at the end of year 1 = $2,775,888

Using these values in the formula, we can calculate the ROI for year 2:

ROI = (930,000 / 2,775,888) × 100

ROI = 0.3347 × 100

ROI = 33.47%

We must apply the following method to get Parry Company's ROI (Return on Investment) for year 2:

ROI is calculated as (Net Operating Income/Total Assets) / 100.

With the knowledge:

Total Assets at the end of Year 1 were $2,775,888, while Net Operating Income for Year 2 was $930,000.

We may determine the ROI for year 2 using the following numbers in the formula:

ROI = (930,000 / 2,775,888) × 100

ROI = 0.3347 × 100

ROI = 33.47%

For similar questions on ROI

https://brainly.com/question/30561521

#SPJ8

Answer:

Here you go!

Step-by-step explanation:

a line of symmetry is a line of which both sides are the same

Answer:

6

Step-by-step explanation:

Line of symmetry : a line drawn through the shape for which either side of the line is a reflection of the other.

There are 6 lines of symmetry for this shape.

(see attached diagram)

Answer:

A = 78.46 square yards

Step-by-step explanation:

A = (C^2)/4π

A = ((31.4 )^2)/4π

A = 78.46

hope this helps, pls mark brainliest :D

Answer:

your answer is going to be 3097.48

The type of queuing model applying for the  arrival rate of customers follows a poisson distribution is "M/M/2".

When consumers arrive at random to obtain a service and the service time is also a random variable, a queuing model is an appropriate model to represent the situation.

For the stated question-

Thus, the kind of queuing model uses is "M/M/2".

To know more about the queuing model, here

https://brainly.com/question/29557688

#SPJ4

Check the picture below.

Answer: 14

Step-by-step explanation:

Take the values at either end of the box (80 and 66) and subtract.

Answer:

f(t) = -.03t + 0.45

Step-by-step explanation:

The incidence rate of active cases of tb for the 6-month period was  0.00014

An incidence rate describes how quickly disease occurs in a population.

Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.

So for this question

The number of new  active cases of tb occurring between January 1 and June 30, 2012 was 26

Population at risk  in Baltimore is 183,000

Incidence rate = 26/183,000

The incidence rate of active cases of tb for the 6-month period was           0.00014 or 14 per 100,000 population.

To know more about incidence rate

https://brainly.com/question/22366057

#SPJ4

Using the perimeter of a rectangle, it is found that she can make a deck of 122 ft wide.

The perimeter of a rectangle of length l and width w is given by:

\(P = 2(l + w)\)

In this problem:

Then:

\(P = 2(l + w)\)

\(280 = 2(10 + 8 + w)\)

\(36 + 2w = 280\)

\(2w = 244\)

\(w = \frac{144}{2}\)

\(w = 122\)

She can make a deck of 122 ft wide.

You can learn more about the perimeter of a rectangle at https://brainly.com/question/10489198

Translation is a term that defines a type of transformation in mathematics, specifically in geometry. It is defined as the movement of an object from one place to another in a two-dimensional coordinate plane without altering its shape, size, and orientation.

It is a type of rigid motion that is used in various fields of mathematics, especially in algebra and geometry. In the given (-1, 4) —> (6, -2) scenario, the translation is described below:

Part a: Since the value of x is increasing from -1 to 6, the first blank is filled with 7 (6 - (-1) = 7), which represents a right translation.

Part b: Since the value of y is decreasing from 4 to -2, the first blank is filled with 6 (4 - (-2) = 6), which represents a down translation.

Therefore, the translation can be described as (7, -6), i.e., the point is moved 7 units to the right and 6 units down.

To know more about Translation visit:

brainly.com/question/11211420

#SPJ11

The trigonometric ratios have been determined and the angles T and U are complementary.

Trigonometric Ratios are ratios of the side of a right-angled triangle. These are used to find the missing sides and angles of a right-angled triangle.

A right-angled triangle is a triangle with a measure of one of the angles as 90 degrees.

The triangle TUV is a right-angled triangle, the sides of the triangle are t, u, and v.

Part 1:

The angle T is not equal to angle U.

But by the angle sum property,

T + U + V = 180

T + U = 90

Both the angles are complementary.

Part 2:

The trigonometric ratios are as follows:

sin T = t/v

cos T = u/v

sin U = u/v

cos U = t/v

Part 3:

From the data in part 2,

Options C and D are the correct statements.

sin T = cos U

cos T = sin U

Part 4:

sin 37 = cos ( 90-37)

sin 37 = cos 53

To know more about Trigonometric Ratios

brainly.com/question/1201366

#SPJ1

Answer:

2 days!

Step-by-step explanation:

So, we have 50 + 35x = 70 + 25x.

Solving, we obtain 10x = 20, so x = 2.

Your answer is 2 days.

If this answer helped you, please tell me! :)

Answer:

5q+5p=4+8p

= 5q+5p-8p=4

= 5q-3p=4

Answer:

Research that verifies the number of people who preferred the pillow.

Sorry, if I'm wrong.