. if y1(x) and y2(x) are solutions of y″ p(x)y′ q(x)y = r1(x) and y″ p(x)y′ q(x)y = r2(x), show that y(x) = y1(x) y2(x) is a solution of y″ p(x)y′ q(x)y = r1(x) r2(x)

In this case, e area of the shaded region, r = 4 + 3 sin theta r = 4 and θ = 0, 2π, 4π, ...

The line created by the ends of phasors whose lengths represent the magnitude, or amplitude gain, of the system and which are drawn at angles according to their phase is known as the polar plot of the frequency response of a system.

In a polar plot, the area between the curve and the origin is shown as a shaded region. You can use the definite integral to calculate the area of this area. The following is the general formula for calculating the distance between a polar curve and the origin:

A = 1/2 * ∫r^2 dθ from θ1 to θ2

where r = 4 + 3 sin(θ) and θ1 and θ2 represent the bounds of the shaded region in terms of theta.

To find the exact bounds, you need to determine the values of θ for which the curve intersects the r-axis (i.e., when sin(θ) = 0). In this case, r = 4 and θ = 0, 2π, 4π, ...

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This statement suggests that people's honesty and integrity are influenced by situational factors such as the level of need they have for something, and the opportunity that presents itself.

People may be more likely to act with less honesty or integrity when they feel a strong need for something, and when they see an opportunity to fulfill that need. However, it's important to note that this statement is a generalization and not true for everyone, as honesty and integrity are personal traits that can vary greatly between individuals.

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Answer:

12 onces

Step-by-step explanation:

You're looking for the slope of the line that forms the triangle's hypotenuse (the diagonal). The slope formula's "rise" and "run" parameters are the two "legs" of the triangle. Slope is a climb or a run.

You may determine a line's slope using a slope triangle, which is a visual aid. Slope refers to how steep something is.

Consider ascending 1,000 feet in the air while piloting a plane. You have advanced (horizontally) 3,000 feet when you are 1,000 feet above the ground. You can calculate how steep your rise was using these two measurements.

The inclination is determined by the height at which the plane rises while moving a predetermined distance forward.

To put it another way, it aids in determining the slope of the line linking the plane's starting point and current location.

Triangle with an airplane slope

You may have seen the following slope formula:

Slope: climb / run

The rise is the triangle's vertical distance. Horizontal distance is measured as the run. For our aircraft, we receive:

Slope is equal to 1,000/3,000 feet, or one-third.

In other words, the plane rises one foot vertically for every three feet it moves across the ground.

The ascension of a plane is steeper if it is 2,000 feet above the earth after moving ahead 3,000 feet. It has advanced further vertically for the same horizontal distance. The triangle's slope is less flat in this instance.

Longer is the triangle's horizontal leg.

Slope is defined as: rise/run = 2,000 ft/3,000 ft = 2/3

1/3 is a smaller climb slope for the first airplane than 2/3 is for the second. More steeply ascending is the second aircraft.

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The function that represents the arithmetic sequence is an = 18 + (n - 1)(-3).  b. The seventh term is 0. c. No, the eight term won't apply as the water trains in 7 hours.

The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence.

The given sequence is 18, 15, 12, 9 ...

The common difference between the consecutive terms is:

d = 15 - 18 = -3

d = -3

The sequence is given by the equation:

an = a + (n-1)d

Substituting the value of d= -3 and a = 18 in the equation we have:

an = 18 + (n - 1)(-3)

The function that represents the arithmetic sequence is an = 18 + (n - 1)(-3).

b. The seventh term can be calculated by substituting the value of n = 7.

a(7) = 18 + (7 - 1)(-3).

a(7) = 18 - 18

a(7) = 0

c. No, the eight term won't apply as the water trains in 7 hours.

Hence, The function that represents the arithmetic sequence is an = 18 + (n - 1)(-3).  b. The seventh term can be calculated by substituting the value of n = 7is 0. c. No, the eight term won't apply as the water trains in 7 hours.

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The correct situation with relation is,

Situation                                                   Relation

1                                             Distance is not proportional to time.

2                                               Distance is proportional to time.        

3                                               Distance is proportional to time.

4                                                    Not much information.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Here, We are required to match the options to whether distance is proportional to time in the following situations.

1. A horse running around a race track.

Since, the horse is running around the race track. So, the speed of the horse can vary at different time

So, distance is not proportional to time.

2. A truck passing through 4 cities at a constant speed.

As, Distance = Speed × Time and we are given that the speed is constant.

So, distance is directly proportional to the time.

3. A dog jogging at a constant speed for 20 minutes.

As, Distance = Speed × Time and we are given that the speed is constant.

So, distance is directly proportional to the time.

4. A person running down a field to score a touchdown.

Since, there is no information about the speed of the person.

But, as the person is running to score a touchdown, he may run at a constant speed.

So, there is not much information.

Hence, we get,

Situation                                           Relation

1                                             Distance is not proportional to time.

2                                               Distance is proportional to time.        

3                                               Distance is proportional to time.

4                                                    Not much information.

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The complete question is this,

Drag each object to show whether distance is proportional to time in the situation represented. A horse running around a race track Distance Is Proportional to Time A truck passing through 4 cities at a constant speed A dog jogging at a constant speed for 20 minutes Distance Is NOT Proportional to Time A person running down a field to score a touchdown Draggable item Not Enough Information Draggable item.

The inequality 12x > 36 is used to describe the problem of how much dough Valentina used to make 12 cinnamon rolls of equal weight.

The algebraic idea of inequality is used in this query. A mathematical declaration that two expressions are not equal is known as an inequality.

In this question, the inequality 12x > 36 is used to describe the problem of how much dough Valentina used to make 12 cinnamon rolls of equal weight.

The steps for this process are as follows

The problem is asking how much dough Valentina used to make 12 cinnamon rolls of equal weight. We can set up an equation to solve this problem using the information we are given.

Let x represent the number of ounces of dough used for each cinnamon roll.

We are aware that the recipe typically yields 36 ounces of dough; therefore, 12x must be more than 36 as Valentina produced more dough.

Therefore, the inequality that describes the problem is 12x > 36.

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Answer:

Y=2x

Step-by-step explanation:

Answer:

B goes to 1

D goes to 2

C goes to 3

A goes to 4

Step-by-step explanation:

Supplementary angles is when two angles equal 180.

For #1, we have 49

Doing 180-49 gives us the first answer of 131

We do the same thing for the other 3

180-114 = 66

180-71 = 109

180-87 = 93

Set a is a subset of ω containing the elements 1,2,3. Set b is a subset of ω containing the elements 2,3,4,5,6,7. Finally, set c is a subset of ω containing the elements 7,8,9,10.

The universal set ω is defined as a set containing all elements that are being considered in a particular problem. In this case, ω is composed of the 10 elements 1,2,3,...,10. Set a is then defined as a subset of the universal set ω, meaning that it contains elements from ω. In this example, set a contains the elements 1,2,3. Set b is also defined as a subset of the universal set ω, meaning that it contains elements from ω. In this example, set b contains the elements 2,3,4,5,6,7, as it is composed of all elements of ω that are greater than or equal to 2 and less than or equal to 7. Finally, set c is defined as a subset of the universal set ω, meaning that it contains elements from ω. In this example, set c contains the elements 7,8,9,10, as it is composed of all elements of ω that are greater than or equal to 7.

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The cost of the materials for the cheapest rectangular storage container with an open top to have a volume of 24 cubic meters is $288.

Let the width of the base be x, then the length of the base is 2x. The height of the container is

[tex]24/(x2x) = 24/2x^2[/tex].

The total area of the base is[tex]x2x = 2x^2[/tex] and the total area of the sides is

[tex]2(x*24/2x^2) = 24x/x^2[/tex]= 24/x.

The cost of the base is

[tex]2x^2[/tex] * $12 = $24[tex]x^2[/tex] and the cost of the sides is

24/x * $6 = $144/x.

The total cost is $24[tex]x^2[/tex] + $144/x.

To find the cheapest container, we want to minimize the cost, which is equivalent to finding the minimum value of $24[tex]x^2[/tex] + $144/x.

We can use calculus to find the minimum, or we can use trial and error to find a reasonable value for x that minimizes the cost.

For x = 2, the cost is

$24 * [tex]2^2[/tex] + $144/2 = $96 + $72 = $168

which is less than $288.

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Correct Answer : C. Such data are not counts or measures of? anything, so it makes no sense to compute their average? (mean).

The average, also known as the mean, is a measure of central tendency in statistics. It is calculated by adding up a set of values and then dividing the sum by the total number of values in the set. The resulting number represents an estimate of the "typical" or "average" value in the set.

Clearly, the way in which data is collected, makes the collected data for variable "Favourite Food" strictly a categorical variable. It doesn't have any quantitative nature associated with it. So, it makes no sense to compute the mean.

Hence, option C is correct.

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B. The data given are categorical, not numerical or quantitative, which means the average (mean) cannot be found in the usual way. As such, it cannot be computed correctly with the given information.

The given calculation is wrong because the data given are categorical, not numerical or quantitative. This means that the average (mean) cannot be found in the usual way. To find the average (mean) in this case, the total number of respondents (698) must be divided by the number of categories (4) to get the average (mean) for each category. Then, each category can be assigned a numerical value (1 for Italian food, 2 for Mexican food, 3 for Chinese food, 4 for anything else). The numerical values for each category can then be multiplied by the number of respondents who chose that category and added together. Finally, the sum can be divided by the total number of respondents (698) to get the average (mean).

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Answer: Jacob

Step-by-step explanation:

Jacob = 39 sit-ups/30 seconds

Jordan = 59 sit-ups/50 seconds

2.5 minutes = 150 seconds

[tex]Jacob=\frac{39}{30} =\frac{195}{150}[/tex]

[tex]Jordan=\frac{59}{50}=\frac{177}{150}[/tex]

[tex]\frac{195}{150} > \frac{177}{150}[/tex]

To compare the number of sit-ups Jacob and Jordan can do in 2 1/2 minutes, we need to convert their current rates to the same unit of time. Since 2 1/2 minutes is the same as 150 seconds, we can use unit rates to find the number of sit-ups they can do per second.

Jacob's rate is 39 sit-ups in 30 seconds, so his unit rate is:

39/30 sit-ups per second

Simplifying the fraction, we get:

13/10 sit-ups per second

Jordan's rate is 59 sit-ups in 50 seconds, so his unit rate is:

59/50 sit-ups per second

Multiplying the numerator and denominator by 3, we get:

177/150 sit-ups per second

Now we can use these unit rates to estimate the number of sit-ups Jacob and Jordan can do in 2 1/2 minutes:

Jacob's estimated number of sit-ups = unit rate × time

= (13/10 sit-ups per second) × (150 seconds)

= 195 sit-ups

Jordan's estimated number of sit-ups = unit rate × time

= (177/150 sit-ups per second) × (150 seconds)

= 177 sit-ups

Based on these estimates, Jacob is likely to do more sit-ups in 2 1/2 minutes than Jordan, since he can do approximately 18 more sit-ups (195 - 177).

Therefore, Jacob is likely to do more sit-ups in 2 1/2 minutes than Jordan.

The human heartbeats 2,721,600,000 times in 70 years

Let's say that the human heart beats 1 time in 0.8 sec.

Noe, we need to know the number of seconds in 70 years

Number of months in 70 years = 70 x 12 = 840 months

Number of days in 70 years = 840 x 30 = 25,200 days

Number of hours in 70 years = 25,200 x 24 = 604,800 hours

Number of seconds in 70 years = 604,800 x 3600

                                                     = 2,177,280,000 seconds

Number of times a heartbeat in 0.8 sec = 1 time

Number of times a heartbeat in 2,177,280,000 seconds = (1/0.8) x 2,177,280,000

                                                  = 2,721,600,000 times

                                                  ≈ 2.7 billion times

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Answer:

The Lcm of Given Numbers.

1. 6,7 = 42 2. 4,5 = 20 3. 10, 11 = 110

4. 2,5 = 10 5. 6, 11 = 66 6. 8, 10 = 80

7. 3, 10 = 30 8. 5, 10 = 50 9. 7, 8 = 56

Step-by-step explanation:

Ok

best trick for Lcm you can multiply the given number and its answer is your Lcm of given numbers.

Thank you..

The combination of advanced military technology, numerical advantage, and the use of disease as a weapon were critical factors in enabling the Spanish conquistadors to seize control of Tenochtitlán and establish their colonial rule over the Aztec empire.

The Spanish conquest of the Aztec empire in 1521 was a turning point in world history, marking the beginning of Spanish colonial rule in the Americas.

One major factor was the advanced military technology and weaponry of the Spanish. The conquistadors were equipped with steel swords, guns, and armor, while the Aztecs relied on obsidian-tipped weapons and wooden shields.

Another factor was the advantage of numbers. The Spanish arrived in Mexico with a relatively small force of around 500 soldiers, but they were able to recruit indigenous allies and build up their army to around 8,000 soldiers.

A third factor was the use of disease as a weapon. The Spanish brought diseases such as smallpox, which devastated the indigenous populations and weakened the Aztecs, making them more vulnerable to attack.

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The volume of a solid generated by rotating a region about the x-axis is an important mathematical concept that can be applied in many real-world situations.

The volume of a solid is a measure of the amount of space that the solid takes up in three-dimensional space.

To find the volume of the solid generated when a region is bounded by an equation and revolved around the x-axis, we use a mathematical formula known as the "method of cylindrical shells."

This method involves slicing the solid into thin cylindrical shells, and then finding the volume of each individual shell. The sum of the volumes of the shells will equal the total volume of the solid.

The formula for the volume of a cylindrical shell is given by

=> V = 2πrh,

where r is the radius of the shell, h is the height of the shell, and π is the mathematical constant pi.

To use the method of cylindrical shells, we need to first determine the top and bottom boundaries of the region, and then graph the region.

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The function f(x) is defined as f(x) = 4x/8x-6.

This can be simplified to f(x) = 1/2x-3. The horizontal asymptote for this function is y = 0, as its denominator approaches 0 as x approaches infinity or negative infinity.The function f(x) is defined as f(x) = 4x/8x-6.  To find the vertical asymptote, we need to set the denominator to 0. We can solve this equation to find that the vertical asymptote of f(x) is x = 6. This means that as x approaches the value of 6, the function approaches infinity. Therefore, the horizontal asymptote of this function is y = 0 and the vertical asymptote is x = 6.

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The evaluated expression is 9x^13y√x

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

[tex]x\2sqrt{x}9xx^{7}yx^{5}[/tex]

Express properly

So, we have

x√x * 9x^7 * yx^5

Evaluate the products by applying the law of indices

So, we have the following representation

√x * 9* yx^13

This can be rewritten as

9x^13y√x

Hence, the solution is 9x^13y√x

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The set of all vectors in r4 satisfying the equation is,

( x, R , y ) = ( 1 , R , 1/2 ) ( 2 , R , 1 ) ( 3 , R , 3/2 ) ( 4 , R , 2 ) ( 5 , R , 5/2 ) ( 6 , R , 3 ) ( 7 , R , 7/2 ) ( 8 , R , 4 )

A basis for R4 always consists of 4 vectors. (TRUE: Vectors in a basis must be linearly independent AND span.) 4. The union of two subspaces is a subspace.

If S is a subspace of R4, then the zero vector 0=[0000] in R4 must lie in S. 2x+4y+3z+7w+1=0. So 0∉S, and we conclude that S is not subspace of R4.

The space R4 is four-dimensional, and so is the space M of 2 by 2 matrices. Vectors in those spaces are determined by four numbers. The solution space Y is two-dimensional, because second order differential equations have two independent solutions.

The interval of x is known and the relation of x , y is known.

So,

x = 2y  ;   x = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

Then,

1 = 2y , 2 = 2y , 3 = 2y , 4 = 2y , 5 = 2y , 6 = 2y , 7 = 2y , 8 = 2y ,

We can write,

y = { 1/2 , 1 , 3/2 , 2 , 5/2 , 3 , 7/2 , 4 }

Therefore,

The set of all vectors in r4 satisfying the equation is,

( x, R , y ) = ( 1 , R , 1/2 ) ( 2 , R , 1 ) ( 3 , R , 3/2 ) ( 4 , R , 2 ) ( 5 , R , 5/2 ) ( 6 , R , 3 ) ( 7 , R , 7/2 ) ( 8 , R , 4 )

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A. Equation: x + 48 +  52 = 180

B. x = 80°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

Two parallel line a and b are cut by a traversal line.

By the alternate exterior angles and angle addition postulates,

x + 48 +  52 = 180

This is the equation for Part A.

And x = 80°.

Therefore, the value of x is 80°.

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The pricing for each pizza is given as follows:

The pricing for each pizza is obtained applying the proportions in the context of this problem.

A pizza shop sells a medium pizza with a diameter of 12 inches for 15 dollars, hence the price per inch of the diameter is given as follows:

15/12 = $1.25.

The small pizza has a diameter of 4 inches, hence the price is given as follows:

4 x 1.25 = $5.

The large pizza has a diameter of 16 inches, hence the price is given as follows:

16 x 1.25 = $20.

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A right triangle consists of a right angle, another angle that is three less than negative one-fourth of a number, and an angle that is six less than negative two times a number. x = -44 and the angles are 90°, -2x - 6, and -1/x - 3. In the provided triangle, the necessary angles' measurements are 90°, 82°, and 8°.

The hypotenuse's square is equal to the sum of the squares of the other two sides of a right triangle, according to the Pythagorean rule.

A triangle is said to be right-angled if any one of its internal angles measures 90 degrees.

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Answer:

3.815g

Step-by-step explanation:

[tex]84.810 - 80.995 = 3.815[/tex]

Speed of a car traveling 5 miles in 20 minutes is 0.25 miles/ min.

To calculate the speed of a car, we can divide the total distance it has traveled by the time it took to travel that distance. In this case, the car traveled 5 miles in 20 minutes.

Speed = Distance ÷ Time

Speed = 5 miles ÷ 20 minutes = 0.25 miles/minute

So, the car was traveling at a speed of 0.25 miles per minute, or 15 miles per hour.

It's important to note that this speed only tells us how fast the car was moving at a specific moment in time, and it might have changed throughout its journey. Additionally, this calculation assumes that the car was traveling at a constant speed, which might not always be the case. To get a more accurate representation of the car's speed, we would need to take into account its speed at various points along its route and average those speeds over the entire journey.

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The value of Sn for the arithmetic series is, 1,600.

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

We have to given that;

For the arithmetic series,

⇒ a₁ = - 20

⇒ n = 25

⇒ an = 148

Now, We know that;

The nth partial sum of an arithmetic sequence can be calculated using the first and last terms as follows:

⇒ Sn = n(a₁ + an) / 2

Hence, Substitute all the given values, we get;

⇒ Sn = n(a₁ + an) / 2

⇒ Sn = 25(- 20 + 148) / 2

⇒ Sn = 25 × 128 / 2

⇒ Sn = 1600

Thus, The value of Sn for the arithmetic series = 1,600.

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The number of months that the tree has been growing is; 8.375 months

The general form for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, we are told that the tree grows 8 centimeters each month. This means the slope is 8 cm.

Now, since she trimmed 6 cm in the first month, it means that the y-intercept will be -6. Thus;

Equation is;

y = 8x - 6

Since the current height is 61 centimeters, then;

61 = 8x - 6

8x = 61 + 6

8x = 67

x = 67/8

x = 8.375 months

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if  RS=x+4, ST=8 and RT=3x then value of RS is 10 units.

Two or more expressions with an Equal sign is called as Equation.

Given that RS=x+4, ST=8 and RT=3x

We have to find RS

RS=RT-ST

x+4=3x-8

Take the variable terms on one side and constants on other side

12=2x

Divide both sides by 2

x=6

So RS is 6+4=10 units

Hence, if  RS=x+4, ST=8 and RT=3x then value of RS is 10 units.

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Answer:

by using the formula hypotension(h) is ? base(b) is 8 and perpendicular(p) is15

h=rootunder( p²+b²)

h=(8)²+(15)²

h=289