The length of a rectangle is shown below:

On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair negative 2, 3, and the point B is on ordered pair 3, 3.

If the area of the rectangle to be drawn is 30 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?

C(3, −2), D(−2, −2)
C(3, −3), D(−2, −3)
C(−3, 3), D(−3, −2)
C(−2, 3), D(−2, −2)

Possible triangles that satisfy the given conditions are:

Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5

Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5

Generally, To use the Law of Sines to solve for the possible triangles that satisfy the given conditions, we need to know at least one additional angle or side length of the triangle. The Law of Sines states that:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths of the triangle and A, B, and C are the corresponding angles opposite those sides. Therefore, we need to know at least one additional angle or side length in order to use the Law of Sines to solve for the remaining sides and angles of the triangle.

If we let B1 and B2 be the two possible values of angle B, then we can use the Law of Sines to find the corresponding values of angles A1 and A2 and sides a1 and a2 as follows:

a1/sin(A) = c/sin(B1) a2/sin(A) = c/sin(B2)

Solving these equations for a1 and a2, we get:

a1 = c * sin(A) / sin(B1) a2 = c * sin(A) / sin(B2)

Since we are given that a = 36 and c = 44, we can substitute these values into the above equations to find the values of a1 and a2.

a1 = 44 * sin(31) / sin(B1) a2 = 44 * sin(31) / sin(B2)

Now, we can use the Law of Sines to find the corresponding values of angles A1 and A2.

A1 = arcsin(a1 * sin(B1) / c) A2 = arcsin(a2 * sin(B2) / c)

Substituting the values of a1 and a2 that we found earlier and the given value of c, we get:

A1 = arcsin(36 * sin(B1) / 44) A2 = arcsin(36 * sin(B2) / 44)

To find the possible values of angles B1 and B2, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we have:

B1 + A1 + C1 = 180 degrees B2 + A2 + C2 = 180 degrees

Substituting the values of A1 and A2 that we found earlier, we get:

B1 + arcsin(36 * sin(B1) / 44) + (180 - 31 - B1) = 180 degrees B2 + arcsin(36 * sin(B2) / 44) + (180 - 31 - B2) = 180 degrees

Solving these equations for B1 and B2, we find that the possible values of B1 and B2 are:

B1 = 63.5 degrees B2 = 116.5 degrees

Therefore, the possible triangles that satisfy the given conditions are:

Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5

Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5

Note that these values should be rounded to one decimal place as requested.

Read more about Law of Sines

https://brainly.com/question/17289163

#SPJ1

Answer:

Step-by-step explanation:

c

The monthly payment for the $11,000 loan for 6 years with an annual interest rate of 3.1% is $181.20.

From the information, we have a $11,000 loan for 6 years with an annual interest rate of 3.1%. The interest will be:

= Principal × Rate × Time.

= $11000 × 3.1% × 6.

= $2046

The monthly payment will be:

= ($11000 + $2046) / (6 × 12)

= $13046 / 72

= $181.20

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

The factor that produces the corresponding dimensions of cylinder B is: 3/2.

Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.

To find the scale factor of similar solids, you can use the formula:

scale factor = (size of the similar solid) / (size of the original solid)

For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:

scale factor = (16 cubic units) / (64 cubic units) = 1/4

This means that the smaller solid is 1/4 the size of the larger solid.

Given the following:

Circumference of the base of cylinder A = 4π units [the radius = 2 units]

Area of the base of cylinder B = 9π units² [the radius = 3 units]

Scale factor = radius of the base of cylinder B / radius of the base of cylinder A

Scale factor = 3/2

Learn more about similar solids on:

https://brainly.com/question/16599646

#SPJ1

Complete Question:

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

Step-by-step explanation:

Press ''CTRL + /'' to access the list of features.

Find the “Text Formatting” section.

Choose “Superscript” from the list of options.

On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.

Step-by-step explanation:

1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.

2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.

3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.

4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.

Answer:

The park has 20 climbing activities.

Step-by-step explanation:

Given, 

Total activities = 50

Percent of climbing activities = 40%

Number of climbing activities = 40% of total activities

Number of climbing activities =  40/100 * 50

Number of climbing activities = 0.40 * 50 = 20

Hope this helps!!

The correct statement is: the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.

The correct answer is an option (c)

In this question we have been given a statement 'the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______'

We need to select a correct choice to complete the given statement.

Also, we need to give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.

We know that by Alternate Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.

Consider the following figure.

A pair of alternate interior angles: ∠4 and ∠6

a pair of corresponding angles:  ∠2 and ∠6

and a pair of alternate exterior angles: ∠2 and ∠8

Therefore, the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.

Learn more about the corresponding angles here:

https://brainly.com/question/29114209

#SPJ4

Maya has a solution that volume is 3.8 liters. She needs more 20.12 liters solution.

What is solution?

A particular kind of homogenous mixture made up of two or more substances is known as a solution. A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture.

Given that Maya has a solution with volume 3.8 liters.

The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the times sign or the dimension sign.

Times means multiplication.

She requires 4.3 times more than she currently possesses..

She needs = 4.3 × 3.8 = 16.32 liters.

The total amount she needs is 16.32 + 3.8

Addition process:

  1

16.32

+3.80

______

20.12

To learn more about algebraic operation, click on below link:

https://brainly.com/question/29294489

#SPJ1

The value of the function instance h (-3) as required to be determined given the function declaration; h(x) = −3x + 15 is; 24.

It follows from the task content that the value of the function instance h (-3) is to be determined given the function h (x) = -3x + 15.

Since the given function is; h (x) = -3x + 15.

The value of the function instance; h (-3) can be determined by evaluating as follows;

h (-3) = -3 (-3) + 15

h (-3) = 9 + 15

h (-3) = 24.

On this note, the value of the function instance h (-3) as required is; 24.

Read more on function evaluation;

https://brainly.com/question/2284360

#SPJ1

The value of y is 16.

When one quantity's value increases compared to another's decrease or vice versa, it is said that the two are inversely proportionate.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.

Inverse proportionality will be represented by the symbol '∝'. When two values x and y are Inverse proportional to each other then

             x ∝ 1/y

Here we have

y varies inversely with the square root of x

=>  [tex]y\propto\frac{1}{\sqrt{x} }[/tex]

=>  [tex]y\ = \frac{k}{\sqrt{x} }[/tex]  

=> [tex]\sqrt{x} y = k[/tex] ----- (1)

At x = 64, and y = 12  

=> √64 × 12 = k

=> k = (8) × 12

=> k = 96  

Thus the proportionality constant k = 96

Now Take x = 36 and k = 96 in equation (1)

=> √36 × y = 96

=>  6 × y = 96

=>  y = 16

Therefore,

The value of y is 16.

Learn more about Inverse proportionality at

https://brainly.com/question/17086612

#SPJ1

Answer:

1280 cm³

I presume you are looking for the solution steps and these are below

Step-by-step explanation:

If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.

The height of the pyramid can be computed using the Pythagorean theorem

Let a be each side, h the height and s the slant height

[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]

The volume, V of a square pyramid of side a and height h is given by the formula:

[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]

[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]

The volume of the pyramid is 1280 cubic cm.

Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.

Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.

So we need the values for area of the base and height of the pyramid.

Area of the square base=16×16 sq. cm.= 256 sq. cm.

Again we can apply the relation to find the value of height,

(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²

So, putting the values we get,

[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]

⇒ [tex]289 = (height)^2+64[/tex]

⇒ [tex](height)^2= 225[/tex]

⇒ [tex]height = 15cm[/tex]

Now by appyling the volume of the pyramid we get,

Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.

To learn more about Volume of pyramid,

https://brainly.com/question/22875296

https://brainly.com/question/27195620

Answer:

100

Step-by-step explanation:

0 20 40 60 100

5. l

10. l

15. l

20. l

Answer:

Step-by-step explanation:

because there is no change in slope. The graph will always be strait in this

The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13

What is Ascending Order?

Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.

Solution:

Given the order is -19, 13, -15, -8, -11, -13

Arranging them in the Ascending Order

-19, -15, -13, -11, -8, 13

In the above arrangement the given numbers are arranged into ascending order

To learn more about Ascending Order from the given link

https://brainly.com/question/282796

#SPJ1

Slope-intercept form: [tex]y=mx+b[/tex]

Parallel lines always have the same slopes and different y-intercepts.

We're given:

Because parallel lines have the same slopes, this line therefore has a slope of -3.

[tex]y=-3x+b[/tex]

Now, plug in the given point to solve for b:

[tex]3=-3(-1)+b\\3=3+b\\b=0[/tex]

Therefore:

[tex]y=-3x[/tex]

[tex]y=-3x[/tex]

The value of the given integral [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] is 2/75.

The given integral is [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex].

We have to evaluate the given integral.

The given integral is definite integral. To evaluate the given integral we firstly solve the integral then we put the value in the solved integral to find the value.

We solving the integral [tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

Let u = 2e^{5t}+3

Now differentiating

du/dt = 10e^{5t}

e^{5t}dt = du/10

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int\frac{1}{u^2}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int{u^{-2}}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-2+1}/(-2+1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-1}/(-1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/u)+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/2e^{5t}+3)+C

Now;

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5t}+3}\right]^{\text{In}3/5}_{0}[/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5({\text{In}3/5})}+3}-\frac{1}{2e^{5(0)}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{({\text{In}3})}+3}-\frac{1}{2e^{0}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2\cdot3+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{6+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[1/9 - 1/5]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[5-9/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[-4/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 2/75

To learn more about definite integral link is here

brainly.com/question/29685762

#SPJ4

The right question is:

Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer.

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

The value of the function after evaluation is , f(x)=0 . Hence it is neither a minima nor a maxima.

f(x) =(x + 5)^4; x = - 5

=(-5+5)^4

=(0)^4

=0

The critical value is crucial for accurately portraying a range of properties in statistics. The critical value can be helpful for proving or disproving ideas when they are tested, in addition to validity and accuracy.

If you're taking a statistics course or are just interested in how these concepts work, it is essential to comprehend critical value and how to compute it before analyzing other statistical functions, such as margin of error and significance.

When calculating the margin of error for a set of data, statisticians utilize a measurement known as the critical value.

To learn more about critical value

brainly.com/question/14508634

#SPJ4

The system of inequalities represents this solution is:

6c + 7.5d ≥ 75

d + c ≤ 15.

A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Money from walking neighbor's dog = $6 per hour

Money from car wash = $7.5 per hour

Total Number of hours of work not more than 15 hours

Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car

So, money from walking neighbor's dog = 6c

and money from car wash = 7.5d

Therefore total money saved = 6c + 7.5d

∵ Total Number of hours of work is not more than 15 hours

⇒ d + c ≤ 15

∵ Tom needs to make at least $75 to cover prom expenses

⇒ 6c + 7.5d ≥ 75

The system of inequalities represents this solution is:

6c + 7.5d ≥ 75 ;

d + c ≤ 15.

To learn more about inequality refer to:

brainly.com/question/14506583

#SPJ1

The complete question is as follows:

To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?

The best reason to prefer the least-squares regression line that uses to predict is the Standard Deviation of the residuals is smaller.

Least Squares Regression:

Least squares is a mathematical technique that allows analysts to determine the best way to fit a curve to a graph of data points. It is commonly used to make scatterplots easier to interpret and is associated with regression analysis. Least squares is now available as part of most statistical software programs.

There are two least-squares regression lines, one to predict log(y) using x and the other to use for prediction.

a. A small value of means that the variance is explained poorly compared to the model that predicts instead, and thus the model is a poorer model. Therefore, there is no compelling reason to choose a model that predicts logic in.

b. If the standard deviation of the residuals is not too high, there will be less variability between the actual and predicted values, and thus the model will be more accurate. Therefore, there are compelling reasons to favor a model that predicts.

C. The magnitude of the slope has no effect on whether a model is good or bad, so it's not the best reason to favor a model that expects log y and  x.

d. The presence of more random variation in the number of residuals does not necessarily indicate a superior model. The reason for this is that the variation between the expected and actual values ​​is large, which can lead to large variability. This means that there is no compelling reason to prefer a model that uses to predict log y. It is normal that the distribution of residuals of residuals does not affect model quality. As a result, this is not the best reason.

Learn more about Least Square Regression:

https://brainly.com/question/29243226

#SPJ4

The square root representing in the statement is 25.

In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4²= 16.

A square root of a number is a value that, when multiplied by itself, gives the number or a factor of a number that, when multiplied by itself, gives the original number.

Given that, if I have 5 fishes and 25 fishermen what would be the square root

We need to identify the squared number in the statement, in between 5 and 25 we know 25 = 5²

Which means, 25 is the square of 5

Or, 5x5 = 25

Hence, the answer square root number is 25

For more references on square root, click;

https://brainly.com/question/29286039

#SPJ1

The answer of the limit is -3

The correct statement is Jen is that driving faster than Paris.

Jen's journey home is represented by the equation y=58x+422.

Paris covers ,

324 miles in 5 hour

Therefore, her speed is,

324/5

= 64.8 miles/hr

Jen's rate is expressed as,  y=58x+422.

Here , distance covered is 422 miles.

After comparing their speed we can conclude that , Jen is faster.

Distance word problems are a sort of algebra word problem that is very prevalent. They involve a scenario in which you must determine how quickly, far, or long one or more things have gone.

These are frequently referred to as train problems since one of the most well-known varieties of distance problems involves determining when two trains travelling in opposite directions cross paths.

Distance, pace, and time are the three fundamental components of movement and travel.

To learn more about distance

brainly.com/question/15172156

#SPJ4

A constant term in mathematics is a term in an algebraic equation whose meaning is constant or cannot change because it has no modifiable variables. For example, in the quadratic polynomial x² + 2x + 3 = 0, the term 3 is a constant.

Answer: y=2(x+1)^2 +7

Step-by-step explanation:

The equation for a parabola is y=a(x-h)^2+k

(h,k) would be the vertex but when writing the equation, the sign in front of the h has to be the opposite of the x-value in the vertex (note: the minus sign in front of the h just means opposite of, not always negative) So in this situation since the 1 is negative, it would be positive in the equation

The a represents the distance from the vertex to the focus.

In order to solve this problem you just sub in the opposite of h and the normal value of k and then the a would be two since that is the distance between the focus and the vertex.

This would make your answer 2(x+1)^2 +7

The calculation of  el valor de "x, y, and z" is "2, 3, 1"

Equation [1] must be solved for the variable z.

[1] z = -x - y + 6

/ Replace this in equation [2]'s variable z.

[2] 2x - y + 3•(-x -y +6) = 3

[2] -x - 4y = -13

Add this to the equation [3]'s variable z.

[3] 4x + 5y - 10•(-x -y +6) = 13

[3] 13x + 14y = 72  Equation [2] must be solved for x.

[2] x = -4y + 13

/ Replace the value of x in equation [3] with this.

[3] 14•(-4y+14) + 15y = 73  [3] - 41y = -122

Equation [3] must be solved for the variable y.

[3] 41y = 122

[3] y = 3  We already know the following:

y = 3, z = -x-y+6, and x = -4y+14 To find x, use the value of y.

x = -4+3 = 1  To find z, use the x and y values.

z = -(2)-(3)+6 = 1

Answer: "x, y, and z" = "2, 3, 1"

To lean more about el valor de refer to:

https://brainly.com/question/14498579

#SPJ1

Regression analysis will indicate about the underlying population and the model.

It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we  will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.

Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.

To learn more about Regression analysis

https://brainly.com/question/3297603

#SPJ4

The probability of drawing two numbers from both jars whose product is even = 5/9.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Total number of outcomes =9

Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)

The probability of drawing two numbers from both the jars whose product is even = 5/9

To know more about probability visit: brainly.com/question/11234923

#SPJ4

The probability that the product of the two two-digit numbers is less than 200 is given as follows:

43/8010.

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.

There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:

90 x 89 = 8010.

(the numbers have to be different)

The desired outcomes which result in a product of less than 200 are of given as follows:

Hence the number of desired outcomes is given as follows:

9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.

Meaning that the probability is of:

43/8010.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

As per the cylindrical coordinate, the value of E is (0, 2π/5)

In math, coordinates refers the set of values that show an exact position.

Here we have given that  x² + y² = 9, above the plane z = 0, and below the cone z² = 36x² + 36y²

And we need to find the value of E.

While we looking into the given question, we have identified that in cylindrical coordinates the region E is described by

=> 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r.

Here the given equation will go through the double integral, then we get,

=> ∫∫∫ₓ x² dV

And it can be rewritten based on the differentiation,

=> ∫₂⁰ ∫¹₀ ∫²₀ (r cos θ)² r dz dr dθ

=>  ∫₂⁰ cos² θ dθ

=> ∫¹₀ 2r⁴ dr = 2π/5

To know more about coordinates here.

https://brainly.com/question/27749090

#SPJ4

Answer:

Step-by-step explanation:

Simplifying square roots

Example

Let's simplify \sqrt{75}

75

​

square root of, 75, end square root by removing all perfect squares from inside the square root.

We start by factoring 757575, looking for a perfect square:

75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5

2

×375, equals, 5, times, 5, times, 3, equals, start color #11accd, 5, squared, end color #11accd, times, 3.

We found one! This allows us to simplify the radical:

\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} \\\\ &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} \\\\ &=5\cdot \sqrt{3} \end{aligned}

75

​

​

=

5

2

⋅3

​

=

5

2

​

⋅

3

​

=5⋅

3

​

​

So \sqrt{75}=5\sqrt{3}

75

​

=5

3

​

square root of, 75, end square root, equals, 5, square root of, 3, end square root.

Want another example like this? Check out this video.

Practice

PROBLEM 1.1

Simplify.

Remove all perfect squares from inside the square root.

{\sqrt[]{12}}=

12

​

=root, start index, end index, equals

Explain

Want to try more problems like these? Check out this exercise.

Simplifying square roots with variables

Example

Let's simplify \sqrt{54x^7}

54x

7

​

square root of, 54, x, start superscript, 7, end superscript, end square root by removing all perfect squares from inside the square root.

First, we factor 545454:

54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 654=3⋅3⋅3⋅2=3

2

⋅654, equals, 3, dot, 3, dot, 3, dot, 2, equals, 3, squared, dot, 6

Then, we find the greatest perfect square in x^7x

7

x, start superscript, 7, end superscript:

x^7=\left(x^3\right)^2\cdot xx

7

=(x

3

)

2

⋅xx, start superscript, 7, end superscript, equals, left parenthesis, x, cubed, right parenthesis, squared, dot, x

And now we can simplify:

\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}

54x

7

​

​

=

3

2

⋅6⋅(x

3

)

2

⋅x

​

=

3

2

​

⋅

6

​

⋅

(x

3

)

2

​

⋅

x

​

=3⋅

6

​

⋅x

3

⋅

x

​

=3x

3

6x

​

​

Practice

PROBLEM 2.1

Simplify.

Remove all perfect squares from inside the square root.

\sqrt{20x^8}=

20x

8

​

=square root of, 20, x, start superscript, 8, end superscript, end square root, equals

Explain

Want to try more problems like these? Check out this exercise.

More challenging square root expressions

PROBLEM 3.1

Simplify.

Combine like terms and remove all perfect squares from inside the square roots.

2\sqrt{7x}\cdot 3\sqrt{14x^2}=2

7x

​

⋅3

14x

2

​

=2, square root of, 7, x, end square root, dot, 3, square root of, 14, x, squared, end square root, equals

Explain

Want to try more problems like these? Check out this exercise.