consider the area shown in (figure 1). suppose that a=h=b= 210 mm .
Locate the centroid x of the shaded area. Express your answer to three significant figures and include the appropriate units.
____

Answer:

Sqrt92

9.6 or rounded to the nearest whole #, 10

Step-by-step explanation:

The triple integral representing the volume is:

\(\[V = \int_{0}^{2\pi} \int_{0}^{3} \int_{1}^{12} \rho \, dz \, d\rho \, d\theta\]\)

To find the volume of the solid enclosed by the given cylinder and planes using a triple integral, we'll set up the integral based on the given conditions.

The cylinder equation \(\(x^2 + y^2 = 9\)\) describes a cylinder with a radius of 3 units centered at the origin. The planes y + z = 12 and z = 1 define the limits of the solid.

We'll integrate over the cylindrical coordinates \(\((\rho, \theta, z)\)\). The limits of integration are as follows:

- For \(\(\rho\)\), the radial coordinate, the limits are from 0 to 3 since the cylinder's radius is 3.

- For \(\(\theta\)\), the azimuthal angle, we integrate over the full circle, so the limits are from 0 to \(\(2\pi\)\).

- For z, the vertical coordinate, the limits are from 1 to 12, as determined by the planes.

The volume \(V\) can be calculated as the triple integral:

\(\[V = \iiint_R dV\]\)

where \(\(dV = \rho \, d\rho \, d\theta \, dz\)\) is the volume element in cylindrical coordinates.

Therefore, the triple integral representing the volume is:

\(\[V = \int_{0}^{2\pi} \int_{0}^{3} \int_{1}^{12} \rho \, dz \, d\rho \, d\theta\]\)

Evaluating this integral will give us the volume of the solid enclosed by the given cylinder and planes.

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can't see the Question.

Answer:

C

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

factors of 20 are 20, 10, 5, 4, 2, 1

factors of 35 are 35, 7, 5, 1

factors of 50 are 50, 25, 10, 5, 2, 1

looking from right to left, the largest number they all share is 5

Answer:

Richie should add the number 36 to both sides.

Step-by-step explanation:

To complete the square, you need to divide b by 2, square it, then add it to both sides. In this case, you'd do this:

12/2=6

6^2=36

Answer:

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Step-by-step explanation:

The ounce is a mass unit, as we notice that the metallurgist wants to make 12 ounces of an alloy containing 45 % copper by mixing two metal with different copper proportions. We can use the following two equations:

Alloys

\(m_{R} = m_{A}+m_{B}\) (Eq. 1)

Copper

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A}+r_{B}\cdot m_{B}\) (Eq. 2)

Where:

\(m_{A}\) - Mass of the 30 % copper alloy, measured in ounces.

\(m_{B}\) - Mass of the 50 % copper alloy, measured in ounces.

\(m_{R}\) - Mass of the 45 % copper alloy, measured in ounces.

\(r_{A}\) - Proportion of copper in the 30 % copper alloy, dimensionless.

\(r_{B}\) - Proportion of copper in the 50 % copper alloy, dimensionless.

\(r_{R}\) - Proportion of copper in the 45 % copper alloy, dimensionless.

Now, the mass of the 50 % copper alloy is cleared in Eq. 1 and eliminated in Eq. 2:

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A} + r_{B}\cdot (m_{R}-m_{A})\)

\((r_{R}-r_{B})\cdot m_{R} = (r_{A}-r_{B})\cdot m_{A}\)

And we clear and calculate the mass of the 30 % copper alloy:

\(m_{A} = m_{R}\cdot \left(\frac{r_{R}-r_{B}}{r_{R}-r_{A}} \right)\)

If we know that \(m_{R} = 12\,oz\), \(r_{R} = 0.45\), \(r_{A} = 0.30\) and \(r_{B} = 0.50\), the mass of the 30 % copper alloy:

\(m_{A} = (12\,oz)\cdot \left(\frac{0.45-0.50}{0.30-0.50} \right)\)

\(m_{A} = 3\,oz\)

And the mass of the 50 % copper alloy is:

\(m_{B} = m_{R}-m_{A}\)

\(m_{B} = 12\,oz-3\,oz\)

\(m_{B} = 9\,oz\)

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Answer:

36

Step-by-step explanation:

12 x 3 = 36 (inverse operation)

Answer:

36

Step-by-step explanation:

Since the figure is dilated by a factor of 4, the coordinates of point g of the pre-image is (-2, 1)

The coordinates of the image are given as:

The dilation rule is given as:

(x,y) -> 4(x,y)

So, we have:

(-8,4) = 4 * g

Divide both sides by 4

g = (-2,1)

Hence, the coordinates of point g of the pre-image is (-2, 1)

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Answer:

A

Step-by-step explanation:

edge

Answer:

10%

Step-by-step explanation:

original price = 9000

sold for 8100

price lost = 900

percentage of price lost = 900/9000 × 100

= 10 %

Hope this helps.

The correct answer to this question is Option B. 

A word that can function as a noun or a noun phrase is called a Pronoun. For Example, he, she, it, etc. Pronouns are of five types; Possessive pronouns, Reflexive pronouns, Reciprocal pronouns, Relative Pronouns, and Demonstrative pronouns. 

The error in this sentence occurs at (B), where there is an error in pronoun use. There is nothing in the sentence to which the possessive pronoun "your" can logically refer. There is no error at (A). The subordinating conjunction "As" appropriately introduces the dependent clause ("As we rely on. . . on the Internet").

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The required solutions are x = 15/8 and y = 1/2 which is determined by the elimination method.

Given the linear system of equations as

y = 2 - 4x +6  or

4x + y = 8 …(i)

y= - 5² + 20x - 12 or

20x - y = 37 …(ii)

Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.

So, we have to find out the value of 'x’ and 'y’.

Add equation (i) and equation (ii), we get

4x + y + 20x - y = 8 + 37

24x = 45

x = 45/24

x = 15/8

Substitute the value of 'x’ into equation (i) and we get

4(15/8) + y = 8

60/8 + y = 8

y = 8 - 15/2

y = 1/2

Hence, the required solutions are x = 15/8 and y = 1/2.

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Answer:

5 times the quantity of 30 is (5*30) = 150 robots are needed.

Step-by-step explanation:

....

nice pic dear :)Step-by-step explanation:

ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Set of such values is called solution set to the considered equation or inequality.

The shaded portion will be consider as the dashed line joining points

The portion affected by the two shadings would be the portion common to the right of the dashed line joining points

The ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

Hence, ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

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Answer:

24/3 hours

Step-by-step explanation:

assuming the work speed of these 3 people are

a, b, c, (per hour)

So ba=8b=4c=M

T= M/a+b+c = M/ m/b+ m/8+m/4= 24/13 hours

Answer:

\(\frac{24}{13} \ [hour].\)

Step-by-step explanation:

1) if all the work is 1, then the performance/efficiency/productivity for Abby is 1/6, for Brian is 1/8 and for Charles is 1/4;

2) if the performance/efficiency/productivity are 1/6; 1/8 and 1/4, then it is possible to make up for all work was done ('t' - required time):

\((\frac{1}{6} +\frac{1}{8} +\frac{1}{4} )*t=1;\)

3) if to solve the equation above, then t=24/13 [hour]≈111 [min].

P.S. the suggested solution is not the only, there are several ways to solve this task.

Significant zeros are zeros that contribute to the precision of a number, while nonsignificant zeros are placeholders or indicate the magnitude of a number.

Significant zeros are zeros that are considered significant and contribute to the precision of a number. They are located between nonzero digits or at the end of a number with a decimal point.

For example:

In the number 4,503, the zeros between 4 and 3 are significant.

In the number 0.00856, the zeros after the decimal point and before the 8 are significant.

Nonsignificant zeros, on the other hand, are zeros that do not contribute to the precision of a number and are used for placeholders or to indicate the magnitude of a number. They are typically located at the beginning or end of a number without a decimal point. Examples include:

In the number 0420, the zero at the beginning is nonsignificant.

In the number 0.003, the zeros before the decimal point is nonsignificant and serve as placeholders.

It's important to note that the significance of zeros can vary depending on the context and the rules of significant figures or decimal places being used in a specific calculation or measurement.

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Answer:

Step-by-step explanation:

475                                          

:)

Answer:

The question is unable to be answered without the out of money she had prior to the shared expenses.

Step-by-step explanation:

So what I think that you would do is add the variable expenses and that is your answer.

The first-order necessary conditions for the given NLP problem involve the KKT conditions, and a specific solution satisfying these conditions needs further analysis.

(a) The first-order necessary conditions for constrained optimization problems are defined by the KKT conditions. These conditions require that the gradient of the objective function be orthogonal to the feasible region, the constraints be satisfied, and the Lagrange multipliers be non-negative.

(b) Assuming the first Lagrangian multiplier constraint is active means that it holds with equality, while the second one is inactive implies that it does not affect the solution. By incorporating these assumptions into the KKT conditions and solving the resulting equations along with the given constraints, a solution can be obtained.

(c) To determine if the solution satisfies the first-order necessary conditions, one needs to verify if the obtained values satisfy the KKT conditions. This involves checking if the gradient of the objective function is orthogonal to the feasible region, if the constraints are satisfied, and if the Lagrange multipliers are non-negative. Only by performing this analysis can it be determined if the solution satisfies the first-order necessary conditions.

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Answer:We know that the area of a rectangle is represented by the product of its length and width, so the equation for the area of the rectangle is:

A = l * w

We also know that the area of the rectangle is given as 32X^3 and the length of the rectangle is 4X. Therefore, we can substitute these values into the equation:

32X^3 = (4X) * w

To find the width of the rectangle, we can divide both sides of the equation by 4X:

w = 32X^3 / 4X

Simplifying the equation, we can get the value of w:

w = 8X^2

So the width of the rectangle is 8X^2

Step-by-step explanation:

Both -5 and 1 are extraneous solution to the equation

A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

c²+2c-4-1-2c = 0

c²+2c-2c -4-1 = 0

c²-5 = 0

Therefore both -5 and 1 are extraneous solution in the equation.

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The execution of the code segment will result in statement2 being executed. The code segment contains a conditional statement that uses the logical OR operator (||) to combine two conditions.

The first condition checks whether the result of dividing num1 by num2 is less than 0, while the second condition checks whether the product of num1 and num2 is greater than 0.

Given that num1 is 0 and num2 is 10, the first condition will evaluate to false, because 0 divided by any positive number is 0. However, the second condition will evaluate to true, because the product of two non-zero numbers with the same sign is always positive.

Since the logical OR operator requires only one of the conditions to be true for the entire statement to be true, the overall result will be true. As a result, statement1 will not be executed, and statement2 will be executed instead.

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Answer:

Step-by-step explanation:

The probability of it landing heads up at least three times is 1/4.

According to the statement

We have a given that the coin is tossed 4 times And we have to find the probability of it landing heads up at least three times.

So, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

So, According to the statement

Coin is tossed 4 times and we have to probability of find heads three times it means n = 3.

To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin.

Thus there are only 4 outcomes which have three heads.

The probability is 4/16 = 1/4.

So, The probability of it landing heads up at least three times is 1/4.

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1000

Step-by-step explanation:

Find the height of the triangle using the Pythagoras theorem

Then, use it to calculate the area of the triangle

Answer: A circular prism is a 3-dimensional figure with circular cross-sections perpendicular to its height. The formula to calculate the volume of a circular prism is:

Volume = π * r^2 * h

Where:

π (pi) is a mathematical constant approximately equal to 3.14

"r" is the radius of the circular base

"h" is the height of the prism

So, to calculate the volume of a circular prism, you need to know the radius and height, then plug those values into the formula and perform the calculation.

For example, let's say you have a circular prism with a radius of 5 cm and a height of 10 cm. The calculation would be:

Volume = π * r^2 * h = π * 5^2 * 10 = 3.14 * 25 * 10 = 785 cm^3

So, the volume of the circular prism is 785 cubic centimeters.

Step-by-step explanation:

Point S represent the point which is opposite to the number -5 \(\frac{1}{2}\).

Number line is a straight line drawn horizontally where the integers are place in an equal intervals, usually 1 unit apart.

Number line includes negative integers, 0 and positive integers. 0 is located in the middle of the number line.

Midpoint of the number line is 0.

So the number opposite to a negative number must be at the positive side with the same magnitude.

-5 \(\frac{1}{2}\) is actually -5.5, which is located at the exact middle in between -5 and -6.

Then the opposite of the number -5 \(\frac{1}{2}\) is +5 \(\frac{1}{2}\).

+5 \(\frac{1}{2}\) lies in the positive side in between 5 and 6, which is represented by point S.

Hence point S represents the number opposite the number -5 \(\frac{1}{2}\).

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This set represents all possible values of \(y\) that result from substituting each value of  \(x\) in the given domain into the equation \(y=x-6.\)

The equation \(y=x-6\) is in slope-intercept form, where the slope is 1 and the y-intercept is \(-6\). This means that for any value of x, the corresponding value of y can be found by subtracting 6 from x.

Here are some values for y, given different values of x:

When \(x=0, y=(-6)\)

When \(x=1, y=(-5)\)

When  \(x=2, y=(-4)\)

When \(x=3, y=(-3)\)

When \(x=4, y=(-2)\)

When \(x=5, y=(-1)\)

When \(x=6, y=0\)

When \(x=7, y=1\)

Therefore, This set represents all possible values of y that result from substituting each value of x in the given domain into the equation \(y=x-6.\)

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