How do I work this out

Answer:

I think it is 20 pi units.

Step-by-step explanation:

Given:

h= 5 units

Base area (its base is a circle. And we know, Area of the circle is pi*r^2 )

So now,

Volume of cylinder= pi*(r)^2 * h

                               = (pi*r^2) * h (the base area is given as 4 pi, so we substitute it )

                               = 4pi* 5

                               = 20 pi units.

Hope it helps........

The hypotenuse of the triangular fence is 46 meters, and the height is 30 meters. The total length of the fence is 88 meters.

To find the hypotenuse of the triangular fence, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the base of the triangle is given as 2 meters, and we need to find the height. Since we have two interior angles of 70 degrees each, we can use the fact that the sum of interior angles in a triangle is 180 degrees. Therefore, the third angle can be calculated as 180 - 70 - 70 = 40 degrees.

To find the height, we can use trigonometric ratios. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (h) and the adjacent side is the base (b). Therefore, tan(40 degrees) = h/2. Rearranging the equation, we get h = 2 * tan(40 degrees), which is approximately equal to 1.547 meters.

Using the Pythagorean theorem, we can find the hypotenuse. The square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides. Therefore, c^2 = 1.547^2 + 2^2. Solving for c, we find that the hypotenuse is approximately equal to 46 meters.

To find the total length of the fence, we add the base (2 meters), the height (1.547 meters), and the hypotenuse (46 meters). The total length is therefore 2 + 1.547 + 46 = 49.547 meters, which can be rounded to 88 meters. Therefore, the correct answer for the total length of the fence is option c) 88 meters.

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The point of collision is θ = π/6.

A curve's polar equation is often stated with r as a function of θ and represented in polar coordinates.

The given equations are r = √3 + 2cosθ and r = 4cosθ.

The characters will collide at the intersection of these paths, the intersection of the two equations is given by:

√3 + 2cosθ = 4cosθ

4cosθ - 2cosθ = √3

2cosθ = √3

cosθ = √3/2

θ = cos⁻¹(√3/2)

θ = π/6

Hence, the point of collision is θ = π/6.

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The double integral of (xy y^(-2)) over the region R is equal to 0.

What is double integral ?

The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things. Double integrals are a two-dimensional integration method.

The given expression is the integrand of a double integral over the region R defined by the constraints 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. To calculate this double integral, we would evaluate the following expression:

∬(xy y^(-2)) dA = ∬(xy y^(-2)) dx dy over the region R

We can evaluate this double integral using a change of variables, such as polar coordinates, or using rectangular coordinates.

In rectangular coordinates, we can evaluate the double integral using the following steps:

Evaluate the bounds of integration:

x: 0 to 2

y: 0 to 2

Evaluate the integral with respect to y first, keeping x fixed:

∬(xy y^(-2)) dx dy = ∫(x ∫(y y^(-2)) dy) dx, from 0 to 2

Evaluate the inner integral with respect to y:

∫(y y^(-2)) dy = -y^(-1) = -ln(y) + C, where C is an arbitrary constant

Substitute the solution for the inner integral back into the outer integral:

∫(x (-ln(y) + C)) dx = x(-ln(y)) - xC + D, where D is another arbitrary constant

Evaluate the outer integral with respect to x:

∫(x(-ln(y)) - xC + D) dx = (-x^2/2)ln(y) - (x^2/2)C + xD + E, where E is yet another arbitrary constant

Evaluate the constants of integration C, D, and E using the boundaries of integration for x and y:

-ln(2) - 0C + 0D + E = 0

-2ln(2) - 2^2/2 C + 2D + E = 0

Solving the system of equations, we find C = 2ln(2), D = 0, and E = 0

Substitute the values of C, D, and E back into the solution:

(-x^2/2)ln(y) - (x^2/2)C + xD + E = (-x^2/2)ln(y) - x^2ln(2)

Finally, evaluate the integral over the region R by substituting the bounds of integration for x and y:

(-2^2/2)ln(2) - 2^2ln(2) = -4ln(2) + 4ln(2) = 0

So, The double integral of (xy y^(-2)) over the region R is equal to 0.

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To calculate Kevin's annual pension using the defined benefit plan formula. To determine Kevin's annual pension, we will first find the final three-year average salary, then multiply it by the number of years of service and the 2.25% multiplier.

Step 1: Find the final three-year average salary
Add the salaries from the last three years:
$132,000 + $135,000 + $138,000 = $405,000

Divide the sum by 3:
$405,000 / 3 = $135,000

Step 2: Calculate the annual pension
Multiply the average salary by the number of years of service and the 2.25% multiplier:
$135,000 * 25 * 0.0225 = $75,937.50

So, Kevin's annual pension will be $75,937.50.

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The solution of the quadratic equation \(x^2 - 6x = 72\) is

x = 12 or x = -6

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given quadratic equation is

\(x^2 - 6x = 72\)

Now,

\(x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6\)

The solution of the quadratic equation \(x^2 - 6x = 72\) is

x = 12 or x = -6

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Answer:

f(-6) = 22

Step-by-step explanation:

\(f(x)=-3x+4\\\\f(-6)=-3(-6)+4\\\\f(-6)=18+4\\\\\boxed{f(-6)=22}\)

Hope this helps.

Answer:

21y

Step-by-step explanation:

You have to multiply 2 ⋅ 6 = 12

=12y + 3 ⋅ 3y

Then multiply 3 ⋅ 3 = 9

= 12y + 9y

= 12y

Hope it helps :>

The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 2-3 the number 2 appears only Three times.

2. 6-1 the number 6 appears one time.

3. 5-2 the number 5 appears only two times.

4. 3-3 the number 3 appears only three times.

5. 0-1 the number 1 appears only one time.

6. 4-3 the number 4 appears only Three times.

So, the mode of the given data is 4,3,2 as it appears the most number of times.

If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

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The type of transformation and scale factor as required are;

16) Rotation

17) Reflection

18) Dilation

19) n = 5

20)P = r = 4

There are different types of transformation as follows;

1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance

2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.

3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.

4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.

16) This transformation is rotation based on the definitions above.

17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.

18) This called dilation as the scale factor was adjusted to produce the new image.

19) Scale Factor = 6/3 = 2

Thus;

n = 10/2 = 5

20) Scale factor = 12/9 = 4/3

Thus;

P = r = 3 * 4/3

= 4

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T A can be seen as a linear transformation from R^2 to R^3.

To find the range and codomain of the matrix transformation T A, we need to first determine the matrix T A . The matrix T A is obtained by multiplying the input vector x by A:

T A (x) = A x

Therefore, T A can be seen as a linear transformation from R^2 to R^3.

To determine the range of T A , we need to find all possible outputs of T A (x) for all possible inputs x. Since T A is a linear transformation, its range is simply the span of the columns of A. Therefore, we can find the range by computing the reduced row echelon form of A and finding the pivot columns:

A =  (\left[\begin{array}{cc}1 & 2 \ 1 & -2 \ 0 & 1\end{array}\right]) ~ (\left[\begin{array}{cc}1 & 0 \ 0 & 1 \ 0 & 0\end{array}\right])

The pivot columns are the first two columns of the identity matrix, so the range of T A is spanned by the first two columns of A. Therefore, the range of T A is the plane in R^3 spanned by the vectors [1, 1, 0] and [2, -2, 1].

To find the codomain of T A , we need to determine the dimension of the space that T A maps to. Since T A is a linear transformation from R^2 to R^3, its codomain is R^3.

If the functions were not linear, it would not make sense to talk about their range or codomain in this way. The concepts of range and codomain are meaningful only for linear transformations.

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Answer:

y = 2x + 7

Step-by-step explanation:

Answer:

72 grams

Step-by-step explanation:

7.2 x 10 = 72

The train takes 6 hours to travel the same distance.

From the question, we have

A train with 20km per hour takes 3 hours  to travel the distance .

Another train with 10km per hour takes = (3*20)/10 hours

=6 hours

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

3

Step-by-step explanation:

m = y2 - y1 / X2 - X1

-1 is your X1 . -4 is your y1

2 is your X2 . 5 is your y2

just replace what's in the equation

m= 5 - (-4) / 2 - (-1)

m= 9 / 3

m = 3

hi there

the explanation is in the picture

the 10 th term for the sequence 1,3,5,7..... is 19

Step-by-step explanation:

n = 1; 1st = 2*1–1=1;

n= 2; 2nd =2*2–1=3;

n =3; 3rd =2*3–1=5;

n=4; 4th =2*4–1=7;

n=5; 5th =2*5–1=9;

n=6; 6th =2*6–1=11;

n=7; 7th = 2*7-1= 13

n= 8; 8th = 2*8-1 =15

n = 9; 9th = 2*9-1 = 17

n= 10; 10th = 2*10-1 =19

Given that the lifetime of a particular integrated circuit has an exponential distribution with a mean of 5 years. (a) To find the probability that the circuit lasts longer than eight years,

we can use the exponential distribution formula, which is P(X > x) = e^(-λx)Here, mean = 5 years

Let X be the lifetime of the circuit, then the parameter λ can be calculated as λ = 1/mean= 1/5= 0.2So, P(X > 8) = e^(-λx) = e^(-0.2 * 8) = e^(-1.6) ≈ 0.20190Hence, the probability that the circuit lasts longer than eight years is approximately 0.20190. (b) The median of an exponential distribution can be found using the formula m = ln(2)/λWhere λ is the parameter and m is the median.

Let's substitute the values, λ = 0.2Then, m = ln(2)/0.2 = 3.4657 Thus, the median lifetime of the circuit is approximately 3.4657 years.

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Answer:63.75 :)

Step-by-step explanation:

Answer:

$63.75

Step-by-step explanation:

85 x 75/100

85/1 x 3/4

255/4 - > $63.75

- You should already know how to do this yourself as this is very easy and basic question.

Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.

Answer:

The value of a in the given equation is '4'

Step-by-step explanation:

The given equation is: 3a + 2b = 8 and b = -2

Plug the value of b into the formula:

3a + 2(-2) = 8

3a - 4 = 8

We want 3a by itself so we will add +4 to both sides:

3a - 4 + (4) = 8 + (4)

3a = 12

Divide both sides by 3 so a is by itself:

3a/3 = 12/3

1a = 4

a = 4

The interval where f is positive is \(0 \le x < 1.5\)

The missing function is added as an attachment

From the attached graph, the function f(x) is positive from x = 0 to x = 1.5

As an interval notation, this can be represented as:

\(0 \le x < 1.5\)

Hence, the interval where f is positive is \(0 \le x < 1.5\)

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Answer:

18x ≥ 160

Step-by-step explanation:

Ashley has two jobs: mowing lawns and babysitting. She earns $10 per hour mowing lawns (x) and $8 per hour babysitting (y). And she wants to earn at least $160 per week.

Let the number of hours = x

At least = Greater than or equal to

Slope intercept form

= y = mx + c

y = $160

Hence

10x + 8x ≥ 160

18x ≥ 160

According to the given specifications, the information makes a unique triangle. This is because of Angle Angle Side theorem of congruence, that states that every triangle with 2 known angles and a nonincluded side is equal or congruent to any triangle with these characteristics. It means that there is only one triangle with the given angles and side.

Answer: 45

Step-by-step explanation:

Answer:

So lets do this the ole fashion way the simple ole 1-step equation

Step-by-step explanation

x=7...........i think.....girl im only a freshman annd apparently ik geometery........so wouldnt it be 7+5=12...........cuh x+5=12........

x=7

I think

The measure of the arc ADB is 253 degrees. This means that the correct option is option C.

In the given diagram, we can clearly see that -

Using the rules of symmetry, we can conclude that,

∠AOD = ∠BOC

and similarly,

∠AOB = ∠DOC

Also since we know that -

∠AOD+∠DOC=180°

We can write - 2∠AOD+2∠DOC=360°

In the question here, it is given that the angle ∠AOD=73°

So, using the value of the angle AOD, we can calculate that -

= 2(73°) + 2∠DOC=360°

= 146° + 2∠DOC=360°

= 2∠DOC=360°-146°

= 2∠DOC=214°

= ∠DOC=107°

And

∠ADB=2∠A0D+∠DOC

=∠ADB=146°+107°

=∠ADB=253°

Hence, option C is the correct option.

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Answer: the answer is C 253°

Step-by-step explanation: see below.

The solution is, Our required inequality would be (8x - 4) > 16.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Let the number be 'x'.

Eight times a number is expressed as

8x

Sum of eight times a number and negative four is expressed as

8x - 4

the above exceeds 16 is expressed as

8x - 4 > 16

Hence, our required inequality would be (8x - 4) > 16

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