What is the y value of -2?

According to the question The volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

To find the volume of the solid obtained by rotating the region bounded by the curves \(x = 6 - 3y$, $x = 0$, and $y = 3$\) about the \($y$\)-axis, we can use the method of cylindrical shells.

The height of each cylindrical shell is the difference between the two curves, which is given by \($(6 - 3y) - 0 = 6 - 3y$\)

The radius of each cylindrical shell is the distance from the \($y$\)-axis, which is simply \($y$\).

The differential volume of each cylindrical shell is then given by \(dV = 2\pi y(6 - 3y) \, dy$.\)

To find the total volume, we integrate the differential volume from \(y = 0$ to $y = 3$:\)

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

To solve the integral, let's integrate the expression step by step:

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

Expanding the expression, we have:

\($V = \int_{0}^{3} 12\pi y - 6\pi y^2 \, dy$\)

Integrating term by term, we get:

\($V = \left[6\pi \left(\frac{1}{2}y^2\right) - 2\pi \left(\frac{1}{3}y^3\right)\right] \bigg|_{0}^{3}$\)

Simplifying further:

\($V = \left[3\pi y^2 - \frac{2}{3}\pi y^3\right] \bigg|_{0}^{3}$\)

Plugging in the limits of integration:

\($V = \left[3\pi \cdot 3^2 - \frac{2}{3}\pi \cdot 3^3\right] - \left[3\pi \cdot 0^2 - \frac{2}{3}\pi \cdot 0^3\right]$\)

Simplifying:

\($V = \left[27\pi - 27\pi\right] - \left[0 - 0\right]$\)

\($V = 0$\)

Therefore, the volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

To know more about integration visit -

brainly.com/question/30543110

#SPJ11

Answer:

as the sum of 2 opposite interior angles is equal to the sum of the exterior angle.

So here, X is the exterior angle.

and the measure of 2 opposite interior angles are 82° and 29°

Answer:

Answer:

\(x = 40 \: \: degrees\)

Step-by-step explanation:

\(3x + 20 + x = 180 \\ 4x + 20 = 180 \\ 4x = 180 - 20 \\ 4x = 160 \\ \frac{4x}{4} = \frac{160}{4} \\ x = 40 \: \: degrees\)

Katy's house is 8 kilometers from Pedro's house.Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house

Since Katy would have to walk due north to get to Pedro's house and due east to get to Austen's house, we can visualize a right-angled triangle with Katy's house as the right angle. Let's label the distance between Katy's house and Pedro's house as x. According to the given information, the distance between Katy's house and Austen's house is 10 kilometers, and the distance between Austen's house and Pedro's house is 6 kilometers. Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house:

x^2 + 6^2 = 10^2

x^2 + 36 = 100

x^2 = 100 - 36

x^2 = 64

x = √64

x = 8

Katy's house is 8 kilometers away from Pedro's house.we can visualize a right-angled triangle with Katy's house as the right angle.Using the Pythagorean theorem, we can calculate the distance between Katy's house and Pedro's house

To know more about   Pythagorean theorem follow the link:

https://brainly.com/question/343682

#SPJ11

Answer:

its -1 since the equation is all real numbers

Answer:

Your answer is -1.

Step-by-step explanation:

The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Here, we have,

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                            = (16!) / ( 16 - 2 )!2!

                                            = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                       = 10! / (8!)(2!)

                                                       = 45

Required Probability = 45 / 120

                                  = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                     = 2 × 14

                                                     = 28

Required Probability = 28/ 120

                                  = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

Learn more about probability here

brainly.com/question/30034780

#SPJ4

The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

learn more about domain here:

https://brainly.com/question/17043620

#SPJ1

Answer:

76

Step-by-step explanation:

Answer:

20 age This is right answer

Answer:

Smaller angel is 77.5 degrees

The larger angel is 102.5 degrees

For the series ∑(n=1)∞ \(1/9^n\), the Root Test indicates that it converges.

For the series ∑(n=1)∞ \(1/n^n\), the Root Test indicates that it converges.

The Root Test is used to determine the convergence or divergence of a series by examining the limit of the nth root of the absolute value of its terms. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if it is equal to 1 or inconclusive, the test does not provide a definitive result.

For the series ∑(n=1)∞ 1/9^n, we apply the Root Test by calculating the limit of the nth root of the absolute value of the terms:

lim┬(n→∞)⁡√\((|1/9^n|)\) = lim┬(n→∞)⁡\((1/9)^(1/n) = 1/9\)

Since the limit is less than 1, specifically 1/9, the Root Test tells us that the series ∑(n=1)∞ 1/9^n converges. Therefore, the correct answer is "O converges."

Similarly, for the series ∑(n=1)∞ \(1/n^n\), we evaluate the limit:

lim┬(n→∞)⁡√\((|1/n^n|)\) = lim┬(n→∞)⁡\((1/n^n)\)= 0

Since the limit is 0, which is less than 1, the Root Test tells us that the series ∑(n=1)∞ 1/n^n converges. Therefore, the correct answer is "O converges."

Learn more about Root Test here:

https://brainly.com/question/29461191

#SPJ11

Therefore, x=7.

The general solution of the given first-order linear differential equation is y = Ce^(-3x^2) + 4x, where C is an arbitrary constant.

The general solution of the first-order linear differential equation y' + 6xy = 24x is given by y = Ce^(-3x^2) + 4x, where C is an arbitrary constant.

To solve this differential equation, we'll use an integrating factor. The integrating factor for the given equation is e^(∫6xdx) = e^(3x^2), where we integrate 6x with respect to x.

Multiplying both sides of the differential equation by the integrating factor, we have:

e^(3x^2)(y' + 6xy) = e^(3x^2)(24x)

By applying the product rule on the left-hand side, we can simplify the equation:

(e^(3x^2)y)' = 24x * e^(3x^2)

Integrating both sides with respect to x, we get:

∫(e^(3x^2)y)'dx = ∫(24x * e^(3x^2))dx

Integrating the left-hand side gives us e^(3x^2)y, and integrating the right-hand side requires a substitution u = 3x^2, du = 6xdx:

e^(3x^2)y = ∫24x * e^(3x^2)dx

e^(3x^2)y = ∫4du

e^(3x^2)y = 4u + C'

e^(3x^2)y = 4(3x^2) + C'

e^(3x^2)y = 12x^2 + C'

Finally, solving for y, we have:

y = (12x^2 + C') * e^(-3x^2)

To match the general solution form, we can let C = C' * e^(-3x^2). Therefore, the general solution of the given first-order linear differential equation is:

y = Ce^(-3x^2) + 4x, where C is an arbitrary constant.

Learn more about differential equation here

https://brainly.com/question/1164377

#SPJ11

To calculate the company's annual holding cost, we need to multiply the annual average inventory by the holding cost per unit.

First, we need to calculate the annual average inventory. The formula for the average inventory is (Q/2), where Q represents the order quantity.

Given:

Annual requirements (Demand) = 7500 units

Ordering cost = BD 12

Order quantity (Q) = 150, 300, 45000 (Assuming these are different order quantities)

Holding cost per unit = BD 0.5

For each order quantity, we can calculate the annual average inventory using the formula (Q/2). Then, we multiply the average inventory by the holding cost per unit.

For order quantity Q = 150:

Average Inventory = Q/2 = 150/2 = 75 units

Holding Cost = Average Inventory * Holding cost per unit = 75 * 0.5 = BD 37.5

For order quantity Q = 300:

Average Inventory = Q/2 = 300/2 = 150 units

Holding Cost = Average Inventory * Holding cost per unit = 150 * 0.5 = BD 75

For order quantity Q = 45000:

Average Inventory = Q/2 = 45000/2 = 22500 units

Holding Cost = Average Inventory * Holding cost per unit = 22500 * 0.5 = BD 11250. Now, we sum up the holding costs for each order quantity:

Annual Holding Cost = BD 37.5 + BD 75 + BD 11250 = BD 11362.5 Therefore, the company's annual holding cost is BD 11362.5.

Learn more about Holding Cost  here:

https://brainly.com/question/31236493

#SPJ11

The solution of the inequality are n  ≤ -7 and n ≥ -12.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality individually.

n + 2 ≤ −5 and  n + 6 ≥ −6

Hence,

n + 2 ≤ − 5

subtract 2 from both sides of the inequality

n + 2 - 2 ≤ − 5 - 2

n  ≤ -7

n + 6 ≥ −6

subtract 6 from both sides of the inequality

n + 6 ≥ −6

n + 6 - 6 ≥ −6 - 6

n ≥ -12

Therefore, n  ≤ -7 and n ≥ -12

learn more compound inequality here:https://brainly.com/question/29951684

#SPJ1

Answer:

18

Step-by-step explanation:

1/2 x 12 x 3

1 x 12 x 3/2 -divide all by 2

12 x 3/2 - simplify

36/2

answer: 18

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To learn more about   significant figures click here:

brainly.com/question/31437050

#SPJ11

Answer:

The 8th term of the sequence is 896/2187.

Step-by-step explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

\(\displaystyle x_{n} = a\left(r\right)^{n-1}\)

Where a is the initial term and r is the common ratio.

Substitute:

\(\displaystyle x_{n} = 7\left(\frac{2}{3}\right)^{n-1}\)

To find the 8th term, let n = 8. Substitute and evaluate:

\(\displaystyle \begin{aligned} x_{8} &= 7\left(\frac{2}{3}\right)^{(8) - 1} \\ \\ &= 7\left(\frac{2}{3}\right)^{7} \\ \\ &= 7\left(\frac{128}{2187}\right) \\ \\ &= \frac{896}{2187} = 0.4096...\end{aligned}\)

In conclusion, the 8th term of the sequence is 896/2187.

Answer:

total angles in triangle = 180

180 = 44+56+ y

y = 180-44-56

y = 80°

now to find z and x

we know the 2 straight lines are parallel (indicated by arrows)

x = 56°

z = 44°

how?

alternate angles theorem

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Answer:

the answer is 10% if it is simple interest you're talking about.

Answer:

One solution (See explanation for the number)

Step-by-step explanation:

Let's see..

3(x-2)+7x=0.5(6x-2)

3x-6+7x=3x-1

10x-6=3x-1

10x=3x+5

7x=5

x=5/7

Hope this helps :)

There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

WHAT IS COMBINATION ?

Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.

To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial (i.e. n multiplied by all the positive integers less than n).

In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:

C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))

Simplifying this expression, we get:

C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1

C(14, 10) * C(4, 4) = 1001 * 1

C(14, 10) * C(4, 4) = 1001

So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

To know more about combination visit :-

https://brainly.com/question/11732255

#SPJ1

Answer:

5 + 10\(\sqrt{3}\)

= 22.3205080757

Step-by-step explanation:

Answer:

≈ 13,7 inches

Step-by-step explanation:

Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC

Answer:

the answer is -1/4x which isn't on there

Step-by-step explanation:

I can provide general information about how to find the values, domain, range, x-intercepts, and y-intercepts of a function.

To answer these questions, we need to have a function f(x) to work with. Without knowing the specific function, it is impossible to accurately answer the questions. However, I can provide general information about how to find the values, domain, range, x-intercepts, and y-intercepts of a function.

a. To find the values of x for which f(x) > 0, we need to set f(x) > 0 and solve for x. The solution will give us the values of x that make the function greater than zero.

b. The domain of a function is the set of all possible x-values that can be plugged into the function. To find the domain of f, we need to look for any restrictions on the x-values, such as values that would make the denominator of a fraction equal to zero or values that would make the argument of a square root negative.

c. The range of a function is the set of all possible y-values that can be obtained from the function. To find the range of f, we need to look for any restrictions on the y-values, such as values that cannot be obtained from the function.

d. The x-intercepts of a function are the points where the function crosses the x-axis. To find the x-intercepts of f, we need to set f(x) = 0 and solve for x.

e. The y-intercepts of a function are the points where the function crosses the y-axis. To find the y-intercepts of f, we need to set x = 0 and solve for f(x).

f. The question "How often does the line" and cannot be answered without further information.

Learn more about domain

brainly.com/question/28135761

#SPJ11

Answer:

Length will be 46 ft and width will be 16 ft

Explanation:

Let the width be x.

then the length will be 3x - 2

using the rectangle perimeter formula:

2( length + width )

2(x + 3x-2) = 124

2(4x-2) = 124

8x - 4 = 124

8x = 128

x = 16 ft

Width will be 16 ft and

Length: 3x - 2

           : 3(16)-2

           : 46 ft

ATQ

\(\\ \tt\hookrightarrow 2(n+3n-2)=124\)

\(\\ \tt\hookrightarrow 2(4n-2)=124\)

\(\\ \tt\hookrightarrow 4n-2=62\)

\(\\ \tt\hookrightarrow 4n=64\)

\(\\ \tt\hookrightarrow n=16\)

Answer:

Step-by-step explanation:

a)     No of outcomes= 7

       total no of outcomes= 10

       probability = no of outcomes/total no of outcomes

       =7/10

b)     4/10 ( since the outcomes could be 1,2,3,4)

c)     no 1 to 10 has 5 odd numbers

       so, probability = 5/10 = 1/2

d)    multiples of 3 from 1 to 10 are :-

      3,6,9= 3 no's

      so probability = 3/10

Answer:

foreign stamps = 299

US stamps = 353

Step-by-step explanation:

Let number of foreign stamps be x.

Given she has 54 more U.S stamps than foreign , US stamps = x +54

Total stamps = US + Foreign

652 = x + 54 + x

652 - 54 = 2x

598 = 2x

x = 299