Find the volume of a cylinder with a diameter of 20 km and a height of 5 km in terms of pie.

what is the volume of the cylinder?

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:

x^2 - y^2 = 2y

And the rotation angle is θ = arccos(3/5), we can proceed as follows:

1. Rewrite the given equation in matrix form:

[x, y] * [1  0] * [x]  = [2y]

        [-1 0]   [y]      [0]

2. Define the rotation matrix using the given angle θ:

R(θ) = [cos(θ)  -sin(θ)]

          [sin(θ)   cos(θ)]

3. Apply the rotation matrix to the equation:

[x, y] * R(θ)^T * R(θ) * [x] = [2y]

        [1  0]     [-1 0]   [y]     [0]

[x, y] * R(θ)^T * [1  0] * R(θ) * [x] = [2y]

                              [-1 0]   [y]     [0]

[x, y] * [cos(θ) sin(θ)] * [1  0] * [cos(θ)  -sin(θ)] * [x] = [2y]

        [-sin(θ) cos(θ)]   [-1 0]     [sin(θ)   cos(θ)]   [y]     [0]

Simplifying the expression:

[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y

Expanding and rearranging terms:

x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y

Combining like terms:

x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y

Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

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The partial fraction of the given rational expression is [tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

Given the following equation below:

[tex]\frac{25}{(x+1(x+2)}[/tex]

We are expression as the sum of partial fractions

Let the numerator of both partial expressions be A and B to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{A}{x-1} +\frac{B}{x+2}[/tex]

Simplifying the expression, we will have;

[tex]\frac{25}{(x+1(x+2)} =\frac{A(x+2)+B(x-1)}{x-1(x+2)}[/tex]

Cancelling the denominator:

25 = A(x+2) + B(x-1)


If x - 1 = 0, then x = 1. Substitute to have:

25 = A(1+2)

3A = 25
A = 25/3

If x + 2 = 0, x = -2

25 = B(-3)
B = -25/3

Substitute into the function to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

This gives the partial fraction of the given rational expression.

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Answer:

Step-by-step explanation:

General formula

(x-h)^2 + (y-k)^2 = r^2

where (h,k) center of circle whose radius r

applying the formula to our Q

(x – 5)² + y² = 81

(x – 5)² + (y-0)² = 9^2

---> center of circle (5,0)

---> radius is 9

The simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

From the question, we have the following parameters that can be used in our computation:

2|5k-3/5+1/10k

Express properly

So, we have

2|5k - 3/5 + 1/10k|

Collect the like terms in the expression

So, we have the following representation

2|5k - 3/5 + 1/10k| = 2|5k  + 1/10k - 3/5|

Evaluate the like terms

This gives

2|5k - 3/5 + 1/10k| = 2|51/10k - 3/5|

Expand the brackets

2|5k - 3/5 + 1/10k| = |51/5k - 6/5|

Hence, the simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

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The number of jerseys that the senior class at Legion Academy can purchase for $430, using quadratic equation, is 190.

Quadratic equation is an algebraic equation of the second degree in x, represented in the form of ax²+bx+c=0.

In the quadratic equation, a, b, and c are known values but a ≠ 0 and x is unknown.

x = [-b ± √b² - 4ac]/2a

when ax^2 + bx + c = 0

C = 0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x jerseys.

Simplifying the equation, we get:

x = 0.2 − 2.4 ± 40.4​

The two possible values of x are:

1) x = 0.2 − 2.4 + 40.4​ = 190

or

2) x = 0.2 − 2.4 − 40.4 ​= −214

The value of x cannot be negative, therefore, the class bought 190 jerseys for $430.

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Answer:

1,000 - 50x > 600

-50x > -400

$0.00 < x < $8.00

The amount that Za Kingdom charges for each pizza is $8.

To determine the amount charged by Za Kingdom, we first note that the cost of each pizza plus the delivery fee is $21.

Assuming the basic price to be $8 and the delivery fee of $13, we have the sum of $21. So, for 3 pizzas, we will have 8 times 3 = 24 + 13 = 37

Also, the amount for 10 pizzas will be 8 times 10 = 80 + 13 = 93. So, the price of each pizza is $8.

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Part A: After 15 days will have 32,768 magical beans.

Part B: As the value of the magical beans is less than the value of the car the trade does not make sense at least not from a financial perspective. B NO.

Part C: We would need at least 17 days for the number of magical beans to exceed the value of the car. C MAYBE?.

Based on the given information can observe that the number of beans doubles every day.

So, after 15 days will have 2¹⁵ = 32,768 magical beans.

The value of the 32,768 magical beans would be:

32,768 beans × $0.50/bean

= $16,384

Part C:

Let us assume that after 'n' days, the number of beans would be equal to or greater than the value of the car.

Value of the car in terms of magical beans = $65,000/$0.5 per bean

= 130,000 beans

Now, we can set up an equation based on the doubling of beans:

2ⁿ >= 130,000

Taking the logarithm base 2 on both sides, we get:

n × log2(2) >= log2(130,000)

n >= log2(130,000)

n >= 16.98

We would need at least 17 days for the number of magical beans to exceed the value of the car.

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Answer:

Step-by-step explanation:

B

There is a problem with the input -16 in the function f(x) = √x

From the question, we have the following parameters that can be used in our computation:

f(x) = √x

g(x) = (x - 2)²

h(x) = 2x - 7

k(x) = -x -1

Also, we understand that

He puts the functions in the machine in order

So, we have

f(x) = √x

The input is -16

So, we have

f(-16) = √-16

The square root of -16 is not a real number

Hence, there is a problem with the input

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If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.

option C.

When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.

If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.

In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.

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Answer: 3 quarts is equivalent to 5 pints

To achieve a 1 in row 1, column 1, divide row 1 by 4 in the given matrix, resulting in the updated matrix. This row operation preserves the system of linear equations represented by the matrix.

To get a 1 in row 1, column 1 of the given matrix, you can perform the following valid row operation:

R1 = (1/4) * R1

This operation scales row 1 by a factor of 1/4, resulting in the new matrix:

1 , -3/4 , -43/4

3 , -2 , -30

By dividing each element in row 1 by 4, the value in row 1, column 1 becomes 1. This row operation maintains the equivalence of the system of linear equations represented by the matrix.

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Answer:

90Y + 36

Step-by-step explanation:

just multiply the length by the width.

9 X (8y + 4 + 2y)

= 9 X (10y + 4)

= 90Y + 36

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:

Calculating the absolute change:

Absolute change = Final value - Initial value

= 57.7 pounds - 67.8 pounds

= -10.1 pounds

Step 2: Calculate the relative change:

Relative change = (Absolute change / Initial value) * 100

= (-10.1 pounds / 67.8 pounds) * 100

≈ -14.9%

The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

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Answer:

96π

Step-by-step explanation:

the shape is made up of a cylinder and a cone.

Volume of cylinder = π r ² h

= π (3)² (9)

= 81π.

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) (5) π (3)²

= 15π

volume of composite solid = 81π + 15π = 96π

The complete solution to the system is 25/17, 61/17, 2/17 respectively.

Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:

Starting matrix:

[1 -2/3 -1/3 | 1]

[1 -2 6 | -17]

[-3 -7 3 | -43]

Add Row 1 to Row 2 and Row 3:

[1 -2/3 -1/3 | 1]

[0 -4/3 17/3 | -18]

[0 -1 0 | -40]

Multiply Row 2 by -3/4:

[1 -2/3 -1/3 | 1]

[0 1 -17/4 | 27/2]

[0 -1 0 | -40]

Add Row 1 to Row 2 and Row 3:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 -17/4 | -13/2]

Multiply row 3 by -4/17:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 1 | 2/17]

Add Row 3 to Row 1 and Row 2:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Therefore, the solution of the system of linear equations is:

x = 25/17

y = 61/17

z = 2/17

So the solution is [25/17, 61/17, 2/17].

Thus the completed augmented matrix is:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

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Answer:

The distance from first base to third base is 127.3 ft,

Answer:

3:55

Step-by-step explanation:

3:55

The value of the variable is equal to 0

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

4x+4=4x-4

To determine the value of x, take the steps;

collect the like terms, we have;

4x - 4x = -4 - 4

subtract the values, we have;

0 = -8

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Answer: 350000

Step-by-step explanation: Let the total sale of noodles by the wholesaler be x.

Given: Commission for the wholesaler is 10%

After receiving a 10% commission the company got rupees 315000.

x-10% of x =315000

x - 10\100 = 315000

x-x\10 = 315000

10x - 10\10 =315000

9x = 3150000

x= 3150000\9

x= 350000

Realized income is NOT part of your budget.

Income that has really been received or generated within a certain period is referred to as realized income. It stands for the money that has been made or acquired through a variety of sources, including work, investments, or commercial ventures.

Realized income is a crucial part of a budget since it shows the actual cash that a person or organization has available for budgeting and financial planning.

The income is what may be used for a variety of costs, savings, investments, or other financial objectives.

In order to appropriately reflect the financial resources available for controlling spending and making financial decisions, realized income is often included as part of a budget.

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The measures are given as follows:

On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:

2x = 4

x = 2.

Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:

m < A = m < C = 110º.

Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:

m<B = 180º - 110º = 70º.

Considering the angle addition postulate, the measure of angle ABD is given as follows:

m < ABD = 70 - 36

m < ABD = 34º.

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To approximate the area under the curve y=x^3 from x=3 to x=6, we can use the midpoint rule with four subintervals.First, we need to find the width of each subinterval:delta x = (6 - 3) / 4 = 0.75Next, we can find the midpoint of each subinterval:x1 = 3 + 0.5 * delta x = 3.375

x2 = x1 + delta x = 4.125

x3 = x2 + delta x = 4.875

x4 = x3 + delta x = 5.625Now, we can evaluate the function at each midpoint:y1 = x1^3 = 40.39

y2 = x2^3 = 71.25

y3 = x3^3 = 106.29

y4 = x4^3 = 146.48Finally, we can use the midpoint rule formula to approximate the area:A ≈ delta x * (y1 + y2 + y3 + y4)

= 0.75 * (40.39 + 71.25 + 106.29 + 146.48)

= 267.98Therefore, the approximate area under the curve y=x^3 from x=3 to x=6 is 267.98 square units.

Jazmine has 80 quarts of lemonade, which is 5 times the amount Maliha has (16 quarts).

We are given that Maliha has 4 gallons of lemonade. To find out how much lemonade Jazmine has, we need to calculate 5 times the amount Maliha has.

To convert the gallons to quarts, we know that 1 gallon is equal to 4 quarts.

Therefore, Maliha has 4 x 4 = 16 quarts of lemonade.

Now, since Jazmine has 5 times as much lemonade as Maliha, we can calculate Jazmine's amount by multiplying Maliha's amount (16 quarts) by 5.

Jazmine's lemonade = 16 quarts x 5 = 80 quarts.

Hence, Jazmine has 80 quarts of lemonade.

This can be understood as follows:

Maliha's 4 gallons of lemonade can be converted to 16 quarts (4 gallons x 4 quarts/gallon). Jazmine, on the other hand, has 5 times as much lemonade as Maliha.

Therefore, we multiply Maliha's amount (16 quarts) by 5 to find Jazmine's amount, which equals 80 quarts.

It's important to note that 1 gallon is equal to 4 quarts, which is a conversion factor used to convert between the two units of measurement.

By applying this conversion factor, we can determine the amount of lemonade in quarts for both Maliha and Jazmine.

In conclusion, Jazmine has 80 quarts of lemonade, which is 5 times the amount of lemonade Maliha has (16 quarts).

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The experimental probability did not match the theoretical probability.

The experimental probability is the chance that is determined from the real results of an experiment or event. It is based on practical observations or information, rather than a mathematical expression.

The theoretical probability is the chance that is worked out using a mathematical equation founded on the assumptions and situations of the event or experiment.

The experimental probability of landing on heads :

= 40 / 100

= 40 %

The theoretical probability is 50 % which means the experimental and theoretical did not match.

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The calculated value of the period of the function is 6

From the question, we have the following parameters that can be used in our computation:

The equation, f(x) = 2cos(2π/6(x + 4)) +3

A sinusoidal function is represented as

f(x) = acos(2π/b(x + c)) + d

Where the period is B

When the equations are compared, we have

2π/b = 2π/6

This gives

b = 6

Hence, the period of the function is 6

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Complete question

Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?

The equivalent monthly interest rate is 1.91%

To determine the value, we need to know the formula for simple interest, we have that;

I = PRT/100

Such that the parameters of the formula are;

From the information given , we have that;

The annual interest rate R = 23%

Then, to determine its equivalent monthly, we get;

If 12 months = 23%

Then 1 month = x%

cross multiply the values, we have;

12x = 23

Divide by the coefficient

x = 23/12 = 1. 91%

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