OU
Prove algebraically that 0.5 =
Write your proof in the box, below, and use x in the working.
The concluding line has been written for you.
Therefore x =
olu

The area of the surface obtained by rotating the curve x = 20 cos(3θ), y = 20 sin(3θ), where 0 ≤ θ ≤ π/2, about the x-axis is calculated using the formulA for surface area of revolution

To find the area of the surface, we can use the formula for the surface area of revolution. Given a curve defined parametrically by x = f(θ) and y = g(θ), where α ≤ θ ≤ β, the surface area obtained by rotating the curve about the x-axis is given by:

A = ∫[α,β] 2πy √(1 + (f'(θ))²) dθ

In this case, we have x = 20 cos(3θ) and y = 20 sin(3θ), with 0 ≤ θ ≤ π/2. Taking the derivatives, we find f'(θ) = -60 sin(3θ) and g'(θ) = 60 cos(3θ).

Plugging these values into the surface area formula and simplifying, we get:

A = ∫[0,π/2] 2π(20 sin(3θ))(√(1 + (-60 sin(3θ))²)) dθ

Evaluating this integral will give us the exact value of the surface area of the rotated curve about the x-axis within the given range of θ.

Learn more about integral here: https://brainly.com/question/31433890

#SPJ11

Answer:

A) experiment B) Survey C) observational study

Step-by-step explanation:

A could either be experiment or observation but you are experimenting with different types of music and plants so experiment makes more sense to me.

B is a survey because you are asking a group about a topic and recording the answer which is essentially a survey.

C is an observation because you are checking to see improvement, no improvement, or stays the same ie: meaning you have to observe what happens before and after

Three mathematical concepts Sets, relation, function a strong tool for storing and analysing data is relational data.It is based on three crucial mathematical ideas. The correct answer is b. a domain a tuple

Relation and functions what they do Understanding the ideas in Mathematics a strong tool for storing and analysing data is relational data. It is built on sets, relations, and functions, three fundamental ideas in mathematics. In a relational database, sets are collections of items like tables, columns, and rows.

Relations are the connections between items in a set, such as the connections between database columns and rows. Functions are the rules that specify how objects and the connections between them interact, such as the rules that specify how a query behaves. Relational data can be arranged and managed with the use of these mathematical ideas in order to store and analyse data effectively.

Complete question:

On which three mathematical concepts is the relational data structure based? Select all that apply.

a. a variable

b. a domain a tuple

c. a relation

d. a table

e. an equation

To know more about Mathematical relation visit:

https://brainly.com/question/30278753

#SPJ4

Solving the distance-time problem here, the taken time to reach the restaurant is 196 seconds (approx.)

This is a distance-time problem.

To solve this problem the required formula is, d/t = v or, d/v = t,

where d is the represented distance and t denotes the required time, and v is denoted as the velocity or speed.

Here v, velocity is 32 feet/second, and d, distance is 6271 feet.

So, the taken time to reach the restaurant is 6271/32 = 196 seconds (approx.)

To know more about distance-time problems, refer to the following link:

https://brainly.com/question/26608770

#SPJ4

Fuel consumption determines the number of gallons of fuel needed to travel a certain distance. To travel 2625 miles, the tank must be filled 75 / 15 = 5 times.

To solve the given problem, we need to make use of the concept of fuel consumption. This concept determines the number of gallons of fuel needed to travel a certain distance. Hence, let's first calculate the car's fuel consumption to travel one mile.

Step 1: Fuel consumption to travel one mile The car gives 35 miles per gallon. Hence, fuel consumption to travel one mile = 1 / 35 gallon = 0.0286 gallons

Step 2: Number of times the tank must be filled To travel 2625 miles, the total fuel required = 0.0286 x 2625 = 75 gallons Given, the tank capacity = 15 gallons Hence, the tank must be filled 75 / 15 = 5 times to travel 2625 miles.

To know more about distance Visit:

https://brainly.com/question/13034462

#SPJ11

On a sequence diagram, a message does represent a service request. A sequence diagram is a type of interaction diagram in Unified Modeling Language (UML) .So the answer to your Question is True.

UML illustrates the interactions between objects or components within a system over a specific period of time. It visualizes the flow of messages between objects to depict the order of and the timing of these interactions. In a sequence diagram, messages are used to represent communication between objects. Messages can be synchronous, where the sender waits for a response before proceeding, or asynchronous, where the sender does not wait for a response. In the context of a service-oriented architecture, a message can represent a service request being sent from one object or component to another. By using messages to represent service requests, sequence diagrams provide a clear and visual representation of the interactions and flow of information within a system. They help in understanding the sequence of steps involved in a process and the dependencies between different components or objects.

Learn more about Unified Modeling Language (UML)  here:

https://brainly.com/question/30504439

#SPJ11

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

To learn more about dimensions please click on below link.

https://brainly.com/question/8286598

#SPJ1

t=46°

u=134°

v=23°

w=23°

Answer:

Solution given;

v=w [base angle of triangle]

<SPQ+<SRQ=180°[sum of opposite angle of a cyclic quadrilateral is 180°]

81+v+53+w=180°

134°+v+v=180°

2v=180°-134°

v=46/2

v=23°

w=v=23°

In triangle ∆ PQR

v+w+u=180°[sum of interior angle of a triangle]

23+23+u=180°

u=180°-46°

u=134°

again

In triangle ∆ PSR

t+81+53=180°

t=180°-134°

t=46°

Answer:

t and u are supplementary as opposite angles of a cyclic quadrilateral.

v and w are equal as opposite angles to equal sides.

1000 respondents were surveyed about whether they preferred hybrid teaching, online teaching, or attending classes in person. The relative frequency of the online teaching proponents was 0.252. The number of respondents who preferred online teaching is 252.

To find out how many respondents preferred online teaching, you can use the relative frequency as a proportion of the total number of respondents.

.252 = (number of respondents who preferred online teaching) / 1000

To find the number of respondents who preferred online teaching, you can cross-multiply and solve for that value:

.252 * 1000 = number of respondents who preferred online teaching

number of respondents who preferred online teaching = 252

So, 252 respondents preferred online teaching.

You can learn more about relative frequency at

https://brainly.com/question/3857836

#SPJ4

Answer:

your answer should be. 9+20=29

Answer:

-5 = -90/18

this will be your answer my friend

Answer:

Step-by-step explanation:

227.07

Answer:

2010 miles.

Step-by-step explanation:

Victoria fell asleep 13% into the trip. if 261=13%, then you want to know how many miles in 1%. so you divide 261 by 13 and get 20.1 so you know one percent of the trip is 20.1 miles, so if you want to know 100% of the trip, then you multiply 20.1 by 100, to get 2010.

a) Decision rule: t less than -1.314

b) Test statistics = -2.785

c) Reject H0

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The American Water Works Association reports that the per capita water use in a single-family home is 77 gallons per day.

Legacy Ranch is a relatively new housing development.

The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences.

(a) So, the decision rule is,

t is less that -1.314.

(b) Test statistics = (73 - 77) / (7.6 / √28)

    Test statistics = -2.785

(c)  The decision regarding H0 is, Reject H0.

Hence,

a) Decision rule: t less than -1.314

b) Test statistics = -2.785

c) Reject H0

To know more about standard deviation, click on the link

https://brainly.com/question/475676

#SPJ4

Using Distance formula ,

\(\bold{d(AB) = \sqrt{ (x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } }\\ \\\bold{5 = \sqrt{(5 - 1) {}^{2} + (2 - y) {}^{2} }} \\ \\\bold\blue{ squaring \: both \: sides\:,} \\ \\\bold{ 25 = (5 - 1) {}^{2} + (2 - y) {}^{2} }\\ \\\bold{ 25 = (4) {}^{2} + (4 + y {}^{2} - 4y)}\\ \\ \bold{25 = 16 + y {}^{2} - 4y + 4}\\ \\ \bold{25 = y {}^{2} - 4y + 20}\\ \\\bold{ y {}^{2} - 4y - 5 = 0}\\ \\\bold{ y {}^{2} - 5y + y - 5 = 0} \\\\\bold{ y(y - 5) + 1(y - 5) = 0}\\ \\\bold{ (y + 1)(y - 5) = 0 }\\\\\bold{ y = - 1 \: or \: y = + 5}\)

therefore ,

possible coordinates of A are either ( 1 , -1 ) or ( 1 , 5 )

hope helpful~

the two triangles are not similar.

The cost of the tiles and carpet will be $1,600 and $640, respectively.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The area of the bedroom is given as,

A = (5 x 1/4 x 16) x (4 x 1/4 x 16)

A = 20 x 16

A = 320 square feet

A = 320 / 9

A = 35.56 square yards

Ceramic tile costs $5 per square foot. Then the cost of tiles is given as,

⇒ 320 x 5

⇒ $1,600

The carpet costs $18 per square yard. Then the cost of the carpet is given as,

⇒ 35.56 x 18

⇒ $640

The cost of the tiles and carpet will be $1,600 and $640, respectively.

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

#SPJ1

Based on simultaneous equations, Kaun has deposited in each account the following:

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

The total deposit in the two accounts = R 5,400

The annual interest in Account A = 3% or 0.03

The annual interest in Account B = 2% or 0.02

The total interest earned from both accounts for the year = R 140

Let Account A be designated as a and Account B be designated as b.

a + b = 5,400 ... Equation 1

0.03a + 0.02b = 140 ... Equation 2

Eliminate a by multiplying Equation 1 by 0.03:

0.03a + 0.03b = 162 ... Equation 3

Subtract Equation 2 from Equation 3:

0.03a + 0.03b = 162

-

0.03a + 0.02b = 140

= 0.01b = 22

b = 2,200

From Equation 1, substitute b:

a + 2,200 = 5,400

a = 3,200 (5,400 - 2,200)

Check:

In equation 2:

0.03a + 0.02b = 140

0.03(3,200) + 0.02(2,200) = 140

96 + 44 = 140

140 = 140

Learn more about simultaneous equations at https://brainly.com/question/185757

#SPJ1

Data frame can be created in R to display the values of x and Z. Then, an R-program can be written to calculate the corresponding values of Z when x takes specific values such as 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.

Here is an example of an R-program that creates a data frame and evaluates the function Z for the given values of x:

# Create a data frame

x <- c(2, 4, 6, 8, 10, 12, 14, 16, 18, 20)

df <- data.frame(x = x, Z = numeric(length(x)))

# Evaluate Z for each value of x

for (i in 1:length(x)) {

 df$Z[i] <- 3*x[i]^2 + 4*x[i] / sqrt((x[i]+4)*(x[i]-4))

}

# Display the data frame

print(df)

This program creates a data frame df with two columns: x and Z. It then uses a for loop to iterate over each value of x and calculates the corresponding value of Z using the given function. Finally, the program prints the data frame, displaying the values of x and Z for the specified x values.

Learn more about R-program here:

https://brainly.com/question/32629395

#SPJ11

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

False

Step-by-step explanation:

Required

State if the product of rational numbers and integer is an integer

The statement is false and the proof is as follows

Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;

Take for instance: 0.2, 0.5, 2.25, etc.

When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;

1. It can result to an integer:

For instance;

\(0.2 * 5 = 1\)

\(0.5 * 4 = 2\)

\(2.25 * 8 = 18\)

2. It can result in a decimal number

For instance;

\(0.2 * 3 = 0.6\)

\(0.5 * 5 = 2.5\)

\(2.25 * 7 = 15.75\)

From (1) above, we understand that the product can result in an integer.

Hence, the statement is false

Answer:

The answer is A.

Step-by-step explanation:

First, divide two by nine. The result is the decimal zero point two repeating.

Second, the digit that repeats is two. So, since two is one digit, the answer is A.

Answer:

Answer is A

Step-by-step explanation:

I took the quiz sis

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

To learn more about to determine the volume of a cylinder, check: https://brainly.com/question/9624219

#SPJ2

Answer:

85

Step-by-step explanation:

The q1 is 7-, q2 is 77.5 and the third quartile range is 85

Answer:

I can't answer this question.

Step-by-step explanation:

There is no "shown spinner", so I have no clue as to what the answer is or could be. Maybe try attaching a photo?

Answer:

A) 60

B) 72/300

C) 150

Step-by-step explanation:

A) P(green) = ⅕

⅕ × 300 = 60

B) purple: 72

45+37+52+94+72 = 300

Therefore, 72/300

C) 1000 × (45/300)

150

Answer:

37 shares

Step-by-step explanation:

Answer:

37 shares

Step-by-step explanation:

Answer:

w=pa

Step-by-step explanation:

Answer:

D.77

Step-by-step explanation:

Since the mean is the average first you

Add up all the values

74+75+80+76+75+81+78 = 539

Divide the product by the number of values

539÷7=77

Answer:

Fractions

Step-by-step explanation:

the first step would be to conveery 50 into 100. put 40/50 in a fraction and mutiply by two.

\(\frac{40}{50}\) x \(\frac{2}{2}\) = \(\frac{80}{100}\). convert this to a percent. therefore, mark's average in english is an 80%. do the same with his math .

Answer: D

Step-by-step explanation: