determine the fundamental period of the signal x(t) = 2cos(10t 1)-sin(4t -1)
1. 8
2. 48
3. 6
4. 24

By using the formula of perimeter of square and triangle, the following results are obtained.

Length of the side of square = 9

length of the side of triangle = 12

Area of square = 81

What is perimeter of square and triangle?

Perimeter of square and triangle is the total space taken by the square and triangle.

If the side of the square is a, then perimeter of square is 4a

If the side of the equilateral triangle is a, then perimeter of square is 3a

Length of the side of square = 4x - 3

Length of the side of triangle = 5x - 3

Perimeter of square = 4(4x - 3) = 16x - 12

Perimeter of triangle = 3(5x - 3) = 15x - 9

By the problem,

\(16x - 12 = 15x - 9\\16x - 15x = 12 - 9\\x = 3\)

Length of the side of square = \(4 \times 3 - 3 = 9\)

Length of the side of triangle =  \(5 \times 3 - 3=12\)

Area of square = \(9 \times 9 = 81\)

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Answer:

It is 30

Step-by-step explanation:

This is because u are finding the LCM so hence 3 x 10 = 30 u are finding the LCM of the two different denominators keep that in mind

To prevent moral hazard in the situation where the owner of a bagel shop visits it only once a day and employees are supposed to pay for the bagels they eat, the owner could implement monitoring mechanisms and establish clear accountability measures.

To address the moral hazard issue, the owner could introduce surveillance systems or assign dedicated supervisors to keep track of employee activities and ensure compliance with the policy. This monitoring can help deter employees from taking advantage of the owner's absence and indulging in free bagels. Additionally, the owner can establish a system where employees are required to document and pay for the bagels they consume, providing a transparent and accountable process. By implementing these measures, the owner creates a culture of responsibility and reduces the likelihood of moral hazard, fostering an environment where employees adhere to the company policy and pay for the bagels they consume.

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It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. The spring constant k will be 212.5 N/m.

The potential energy stored in a spring is given by the formula:

PE = (1/2) kx^2

where k is the spring constant, x is the displacement from the equilibrium position, and PE is the potential energy.

In this problem, the spring is stretched from its natural length of 2 m to a length of 6 m, so the displacement is x = 6 m - 2 m = 4 m.

The work done on the spring is equal to the change in potential energy, so:

Work = PE final - PE initial

1700 J = (1/2) k(4² - (1/2) k(0)²

1700 J = 8k

k = 212.5 N/m

Therefore, the spring constant is 212.5 N/m.

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Explanation:

Focus on the slanted side of the parallelogram, which is 26 units long. The opposite side to this is also 26 units long since opposite sides of any parallelogram are always congruent.

Now turn your attention to the triangle formed by that dashed line. Specifically this is a right triangle. It has a legs of x and 10, where x is the unknown height (also the height of the parallelogram). The hypotenuse of this right triangle is 26 units as mentioned in the previous paragraph.

Use the pythagorean theorem to find x

a^2+b^2 = c^2

10^2+x^2 = 26^2

100+x^2 = 676

x^2 = 676-100

x^2 = 576

x = sqrt(576)

x = 24

This is a 10,24,26 right triangle, which is based on the 5,12,13 right triangle (divide every part by 2)

-------------------

Now that we know the height of the parallelogram, the area is simply base times height

area of parallelogram = base*height = 32*24 = 768

Then we subtract off the area of the shaded gray rectangle, so we subtract off 7*16 = 112 to get 768 - 112 = 656 and this is the area of the unshaded region inside the parallelogram.

-------------------

Side note: The hypotenuse of 10*sqrt(2) you wrote down would only be correct if that dashed height line was 10 units.

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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The value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

The expression is given as:

(3x^5 + y^2)^2

Expand the expression

So, we have

(3x^5 + y^2)^2 = (3x^5 + y^2)(3x^5 + y^2)

Expand the bracket

(3x^5 + y^2)^2 = 9x^10 + 3x^5y^2 + 3x^5y^2 + y^4

Evaluate the sum

(3x^5 + y^2)^2 = 9x^10 + 6x^5y^2 + y^4

Hence, the value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

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Answer:

cosP = 4/5

Step-by-step explanation:

cosP= b/h = b/√(b²+p²) = 24(√(24²+18²)= 24/30= 4/5

The volumes of the solids generated by rotating the given region around the given axis of rotation are 200π, 120π, 120π, and 80π, respectively.

Pappus' Theorem states that the volume of a solid generated by rotating a planar region about an external axis is equal to the product of the area of the region and the distance traveled by the centroid of the region during the rotation.

We can apply this theorem to find the volume of the solids generated by rotating the given region around the given axis of rotation.

a. When the region R is rotated around the x-axis, the distance traveled by the centroid is 2π(5) = 10π. Therefore, the volume of the solid is 20 × 10π = 200π.

b. When the region R is rotated around the y-axis, the distance traveled by the centroid is 2π(3) = 6π. Therefore, the volume of the solid is 20 × 6π = 120π.

c. When the region R is rotated around x=2, the distance traveled by the centroid is 2π(5-2) = 6π. Therefore, the volume of the solid is 20 × 6π = 120π.

d. When the region R is rotated around y=1, the distance traveled by the centroid is 2π(3-1) = 4π. Therefore, the volume of the solid is 20 × 4π = 80π.

Therefore,the solids generated by rotating the specified region around the specified axis of rotation have volumes of 200π, 120π, 120π, and 80π,  respectively.

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Answer:

the area of triangle OAP is 12 square units.

Step-by-step explanation:

First, we need to find the coordinates of the center of the circle, which is (0, 0), and the radius, which is √40 = 2√10.

Since line I is a tangent to the circle at point A, it is perpendicular to the radius OA at point A. Therefore, OA is perpendicular to line I and forms a right angle with it.

We can find the equation of line I using the point-slope form:

slope of radius OA = (0 - 6) / (0 - 2) = -3

slope of line I = 1 / 3 (because it is perpendicular to OA)

equation of line I: y - 6 = (1/3)(x - 2)

simplifying, we get: y = (1/3)x + 4

To find the x-coordinate of point P, we need to solve for x when y = 0:

0 = (1/3)x + 4

x = -12

Therefore, point P has coordinates (-12, 0).

Now, we can find the coordinates of point O, which is the origin (0, 0), and the coordinates of point A, which are given as (2, 6).

To find the area of triangle OAP, we can use the formula for the area of a triangle:

Area = (1/2) x base x height

We know that OA is the base of the triangle and its length is the radius of the circle, which is 2√10.

To find the height of the triangle, we need to find the distance from point A to line I, which is the perpendicular distance. We can use the formula for the distance between a point and a line:

distance = |ax + by + c| / √(a² + b²)

where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point.

In this case, the equation of line I is y = (1/3)x + 4, so a = -1, b = 3, and c = -12.

Substituting the values, we get:

distance = |(-1)(2) + (3)(6) - 12| / √((-1)² + 3²)

distance = |6| / √10

distance = 3√10 / 5

Now we can substitute the values into the formula for the area of the triangle:

Area = (1/2) x base x height

Area = (1/2) x 2√10 x (3√10 / 5)

Area = 6/5 x 10

Area = 12

Therefore, the area of triangle OAP is 12 square units.

Answer

Vertical asymptote: x = π.

Vertical asymptote: x = 2π.

Explanation

Given the graph of the function

we can find the limit of the function when x approaches π from the left:

Thus:

indicating that it has a vertical asymptote at x = π.

Then, we can also find the limit of the function when x approaches 2π from the left:

indicating that it has a vertical asymptote at x = 2π.

Answer:

A decimal number is a number that has two parts, the whole and the fractional. These parts are divided by a decimal point. For example: 7.45 or 102.7 are decimal numbers.

Answer:

Bisecting an Angle.

Step-by-step explanation:

This image shows the Bisection of an Angle. The 'x' shaped mark between the angle is formed when a protractor is used to mark the place in which a ray must pass through the center of the 'x' to be an equal bisection of the angle. This shows that the process that is being undergone is finding the bisection of the angle.

Answer:

bisecting an angle

just took the test!

Step-by-step explanation:

Answer:

y=-5x+19

Step-by-step explanation:

The measure of <m> is less than 2, In the diagram, we see that <m> is the angle between two tangents to a circle. We also see that <m> is an exterior angle of the triangle formed by the two tangents and the radius connecting the point of tangency to the center of the circle.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, the two remote interior angles are <a> and <b>.

Since <a> and <b> are both acute angles, their sum is less than 180 degrees. Therefore, the measure of <m> must be less than 180 - (<a> + <b>).

We are given that <a> = 90 degrees and <b> = 60 degrees. Therefore, the measure of <m> must be less than 180 - (90 + 60) = 30 degrees.

Therefore, the measure of <m> is less than 2.

Here is a diagram of the triangle:

O

/

\

a <---- b

/

\

m

As you can see, the measure of <m> is less than the sum of the measures of <a> and <b>. This is because <m> is an exterior angle of the triangle.

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Answer:D

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the benchmarks between which 3/8 falls, we need to identify the nearest fractions with denominators that are multiples of 8.

The fraction 3/8 is halfway between 1/4 and 1/2, which can be written as 2/8 and 4/8 respectively. So, we know that 3/8 is greater than 2/8 and less than 4/8.

Therefore, the benchmarks between which 3/8 falls are 2/8 and 4/8. Alternatively, we can express these fractions as decimals and say that 3/8 falls between 0.25 and 0.5.

The conversion of the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates results in the equation (x - 8)^2 + (y - 3.5)^2 = 113. This equation represents a circle in the Cartesian coordinate system.

To convert the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates, we can use the following trigonometric identities:

cos(θ) = x/r

sin(θ) = y/r

where x and y represent the rectangular coordinates, and r represents the radial distance from the origin.

Substituting these identities into the given equation, we have:

r = 16(x/r) + 7(y/r)

To eliminate the fraction, we can multiply both sides of the equation by r:

r^2 = 16x + 7y

Now, we need to express r^2 in terms of x and y. In the rectangular coordinate system, r^2 can be written as:

r^2 = x^2 + y^2

Substituting this expression into the equation, we have:

x^2 + y^2 = 16x + 7y

This is the equation in rectangular coordinates that corresponds to the given polar equation.

To simplify this equation further, we can rearrange it:

x^2 - 16x + y^2 - 7y = 0

Completing the square for the x and y terms, we need to add half of the coefficient of x and y, squared, to both sides:

(x^2 - 16x + 64) + (y^2 - 7y + 49) = 64 + 49

(x - 8)^2 + (y - 3.5)^2 = 113

So, the equation in rectangular coordinates, after completing the square, is:

(x - 8)^2 + (y - 3.5)^2 = 113

This equation represents a circle in the Cartesian coordinate system, centered at the point (8, 3.5), with a radius of √113.

In summary, the conversion of the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates results in the equation (x - 8)^2 + (y - 3.5)^2 = 113. This equation represents a circle in the Cartesian coordinate system.

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Answer: What is The Value of X?

Step-by-step explanation:

We know that vertical angles are congruent, meaning that they have the same measure. Therefore, m/ZB = m/A = (2x - 26)°. We also know that m/LB = (x+25)°. Since ZA and B are vertical angles, we can set their measures equal to each other:

2x - 26 = x + 25

Solving for x:

x = 51

Therefore, the value of x is 51.

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The price of the cheaper vehicle is $34000. And the price of the other vehicle is $ 57000. The total becomes $91000.

The total price for two cars at a dealership is $91,000, where one car's price is $11,000 less than twice the other.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Let the price of one car be 'X' and other be 'Y' such that:

X+Y = $91000.

According to the question,

X = 2Y - $11000

Manipulating and calculating both the equations we get,

X = $57000 and Y = $34000.

So the cheaper car is of $34000.

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As per the given Ratio difference between the amount of money spent and the amount of money saved in a week is $2.

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.

The ratio formula can be used to represent a ratio as a fraction. For any two quantities, say a and b, the ratio formula is a:b = a/b. Because a and b are separate amounts for two portions, the total quantity is given as (a + b).

et 5x be the money he spends and 4x be the amount he saves

therefore, 5x+4x= 18

9x= 18

x= 18/9= 2

Tom spends, 5×2 = $10

and he saves, 4×2= $8

Difference, = $10-$8= $2

Therefore, as per the given ratio in the question difference between the amount of money spent and the amount of money saved in a week is $2.

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Tom receives $18 from his father in a week. The ratio of the amount of

the money he spends to the amount of money he saves in a week is 5:4

What is the difference between the amount of money spent and

amount of money saved in a week?

Answer:

graph 1  

Step-by-step explanation:

Graph using table of values

x           y

2       -2/3

1         -4/3

0          -2

they are all on that graph

The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

According to the question

Represents a line with a slope of -2/3  

i.e ,

m = -2/3  

y-intercept equal to that of the line

y = \(\frac{2}{3}x-2\)

i.e ,

at y-intercept , x = 0

y = -2

Now, Putting value in standard form of line

y = mx + c

-2 = 0 + c  

c = -2

now , substituting the values of m and c in standard form of line

y = mx + c  

y =  \(\frac{-2}{3}x-2\) --------- (equation of graph )

Now ,

x             y

0            -2

3/2         1

3             0

Only option 4 have these points

Hence, The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

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The probability that a particular serving contains fewer than 300 calories is 0.71, more than 250 calories is -2.86, between 275 and 310 calories is  0.7186.

To solve this problem, we need to use the normal distribution and the corresponding z-scores. We can find the z-score for a particular value of x (number of calories) using the following formula:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the specific value we are interested in.

Probability of serving containing fewer than 300 calories:

z = (300 - 290) / 14 = 0.71

Using a standard normal distribution table or calculator, we find that the probability of a z-score being less than 0.71 is 0.7611. Therefore, the probability of a serving containing fewer than 300 calories is 0.7611.

Probability of serving containing more than 250 calories:

z = (250 - 290) / 14 = -2.86

Using a standard normal distribution table or calculator, we find that the probability of a z-score being greater than -2.86 is 0.9977. Therefore, the probability of a serving containing more than 250 calories is 0.9977.

For 275 calories:

z = (275 - 290) / 14 = -1.07

For 310 calories:

z = (310 - 290) / 14 = 1.43

Next, we use a standard normal distribution table or calculator to find the probability of z falling between -1.07 and 1.43. For example, using a standard normal distribution table, we can find that the probability of z falling between -1.07 and 1.43 is approximately 0.7186.

Therefore, the probability that a particular serving of McDonald's Egg McMuffin contains between 275 and 310 calories is approximately 0.7186, or 71.86%.

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the greatest number of pigs Kevin can keep in the field is 4.

How to solve the question?

To determine the maximum number of pigs that Kevin can keep in his field, we need to divide the total area of the field by the area required by each pig.

If we let x represent the maximum number of pigs that can be kept in the field, then we can write the equation:

36x ≤ A

where A is the total area of the field in square meters.

To solve for x, we can divide both sides of the inequality by 36:

x ≤ A/36

This means that the maximum number of pigs that can be kept in the field is equal to the total area of the field divided by 36.

For example, if the field has an area of 144 square meters, then the maximum number of pigs that can be kept in the field is:

x ≤ 144/36 = 4

Therefore, the greatest number of pigs Kevin can keep in the field is 4.

It is important to note that the above calculation assumes that each pig will have exactly 36 square meters of space. In reality, the actual amount of space required per pig may vary depending on factors such as breed, age, and weight. Additionally, it is important to consider other factors such as food, water, and shelter when determining the number of pigs that can be kept in a field.

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Answer: Option D

Step-by-step explanation:

Step-by-step explanation:

As we know domain of a function is represented by x values on the graph and y values represents the range of the function.

From the given table domain will be the set of all real numbers.

Range of the same function will be y > 4

Option D is the answer. there you go o(*￣︶￣*)o it was hard to but now its easy

Answer:

Option A

Step-by-step explanation:

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The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data

The answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.

In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.

Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.

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