Is the point (3, 4) a solution to the linear equation 5x - 9y = 32?

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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Weight that is 1.5 standard deviation below the mean: To find the weight that is 1.5 standard deviation below the mean, subtract 1.5 times the population standard deviation from the population mean.

The population mean, population standard deviation, and weight that is 1.5 standard deviation below the mean for the Houston Rockets can be calculated using the following steps:

1) Population mean: The population mean is the average of all the values in the population. To calculate the population mean, add up all the values in the population and divide by the total number of values. For example, if the weights of the Houston Rockets players are 200, 210, 220, 230, and 240 pounds, the population mean would be (200 + 210 + 220 + 230 + 240) / 5 = 220 pounds.

2) Population standard deviation: The population standard deviation is a measure of how spread out the values in the population are. To calculate the population standard deviation, first calculate the deviation of each value from the population mean, square each deviation, add up all the squared deviations, divide by the total number of values, and take the square root of the result. For example, if the weights of the Houston Rockets players are 200, 210, 220, 230, and 240 pounds, the population standard deviation would be √[((200 - 220)^2 + (210 - 220)^2 + (220 - 220)^2 + (230 - 220)^2 + (240 - 220)^2) / 5] = 14.14 pounds.

3) Weight that is 1.5 standard deviation below the mean: To find the weight that is 1.5 standard deviation below the mean, subtract 1.5 times the population standard deviation from the population mean. For example, if the population mean is 220 pounds and the population standard deviation is 14.14 pounds, the weight that is 1.5 standard deviation below the mean would be 220 - (1.5 * 14.14) = 199.79 pounds.

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There are 84,672 different meals that can be ordered by selecting one item from each category.

To determine the number of different meals that can be ordered by selecting one item from each category, we need to multiply the number of choices in each category together.

In this case, the number of choices for each category are as follows:

Drinks: 12 choices

Appetizers: 7 choices

Main Entrees: 8 choices

Side Dishes: 14 choices

Desserts: 9 choices

To calculate the total number of different meals, we multiply these numbers together:

Number of different meals = Number of choices in Drink category × Number of choices in Appetizer category × Number of choices in Main Entree category × Number of choices in Side Dishes category × Number of choices in Dessert category

Number of different meals = 12 × 7 × 8 × 14 × 9

Calculating this expression gives us:

Number of different meals = 84,672

Therefore, there are 84,672 different meals that can be ordered by selecting one item from each category.

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Answer:

1. x = 9°

angleA=36°

angleB=54°

2. x = 28°

angleA=28°

angleB=62°

Step-by-step explanation:

1. 6x + 4x = 90° (By ASP)

2. 2x + 6 + x = 90° (By ASP)

The ordered pair for each point using the grid is (4,3). An ordered pair is a set of two numbers that represent a point in the coordinate plane.

In general, the first number represents the horizontal or x-coordinate, and the second number represents the vertical or y-coordinate. These coordinates are usually represented in brackets and separated by a comma. For example, (2,3) is an ordered pair whose x-coordinate is 2, and whose y-coordinate is 3. What is a grid? A grid is a set of horizontal and vertical lines that are used to form boxes, creating a pattern of squares. In mathematics, we use grids to represent the coordinate plane. The x-axis, which runs horizontally, is marked with positive numbers to the right and negative numbers to the left of the origin. The y-axis, which runs vertically, is marked with positive numbers above and negative numbers below the origin. How to write the ordered pair for each point? To write the ordered pair for each point using the grid, we need to follow these steps: Step 1: Locate the point on the grid. Let's say we have a point that lies in the third row (y-coordinate) and the fourth column (x-coordinate). We would locate this point by counting three rows down and four columns to the right. This point is shown below. Step 2: Write the ordered pair for the point. In this case, the x-coordinate is 4, and the y-coordinate is 3. We write these coordinates in brackets, separated by a comma. Therefore, the ordered pair for this point is (4, 3). The ordered pair for each point using the grid is (4,3). The first number in the ordered pair is the x-coordinate, and the second number is the y-coordinate.

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To calculate the energy of the resulting explosion when a 10,000 kg UFO made of antimatter crashes with a 40,000 kg plane made of matter, we can use Einstein's famous equation, E=mc², which relates energy (E) to mass (m) and the speed of light (c).

In this case, we'll need to calculate the total mass of matter and antimatter involved in the collision and then use the equation to find the energy released. The equation E=mc² states that energy is equal to the mass multiplied by the square of the speed of light (c). In this scenario, we have a collision between a UFO made of antimatter and a plane made of matter. Antimatter and matter annihilate each other when they come into contact, resulting in a release of energy.

To calculate the energy of the resulting explosion, we need to determine the total mass involved in the collision. The total mass can be calculated by adding the masses of the UFO and the plane together. In this case, the UFO has a mass of 10,000 kg and the plane has a mass of 40,000 kg, so the total mass is 50,000 kg.

Next, we can use the equation E=mc² to calculate the energy. The speed of light (c) is a constant value, approximately 3 x 10^8 meters per second. Plugging in the values, we have E = (50,000 kg) x (3 x 10^8 m/s)². Simplifying the equation, we have E = 50,000 kg x 9 x 10^16 m²/s².Multiplying the numbers, we get E = 4.5 x 10^21 joules. Therefore, the energy of the resulting explosion when the UFO and plane collide is approximately 4.5 x 10^21 joules.

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Answer:

Step-by-step explanation:

Preimage (4, - 7) and image (7, 4).

Rule applied:

Correct choice is A

Answer:

Option A

Step-by-step explanation:

90° counterclockwise rotation about origin rule is

So here

Rotate it

Option A is correct

Answer:

the rate  of change is 5

Step-by-step explanation:

$90 / 18 cars = $5 per car

$45 / 9 cars = $5 per car

$60 / 12 cars = $5 per car

That means the rate of change is 5 (5/1)

See attachment for reply.

The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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Answer:

a = 16.71 b=19.92

Step-by-step explanation:

sin40 = a/26

a = 16.71

sin50 = b/26

b=19.92

The equation of the first graph is

y > 2x - 4

The equation of the first graph is

y ≥ -x + 4

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculating using the points on the graph (0, -4) and  (2, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-4 - 0) / (0 - 2)

m = (-4) / (-2)

m = 2

c = y intercept, from the graph

c = -4

The equation of the line is y = 2x - 4

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the second graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

c = y intercept, from the graph

c = 4

The equation of the line is y = -x + 4

shading above the line is greater than and solid lines means there is equal to in the inequality

hence y ≥ -x + 4

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Option second "-Even though for a majority of the race they accelerated at the same rate, Beverly won -because her initial acceleration was greater than Carl’s" is correct.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

We have:

A graph with horizontal axis time (seconds) and vertical axis velocity (meters per second).

An orange line labeled for Beverly

A blue line labeled for Carl

As we can see in the line graph Beverly and Carl accelerated at the same rate from point zero.

Beverly won the race because their initial acceleration of Beverly is greater than that of Carl.

Thus, option second "-Even though for a majority of the race they accelerated at the same rate, Beverly won -because her initial acceleration was greater than Carl’s" is correct.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Area of a circle = π x radius ^2 = π r^2

Replacing with the values given:

A C = π 12^2 = 452.39 cm^2

Area of a rectangle: Length x width

A R = 11 x 5 = 55 cm^2

To find the shaded region, subtract the area of the rectangle to the area of the circle:

452.39-55 = 397.39 cm^2

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

ight A on top since it's the cmallest followed by B,C,D,E

Step-by-step explanation:

If 4 less than a certain integer is multiplied by 5 more than the integer, the product is 3 less than the square of the integer. The integer is 8

To find the value of the integer, let's call it 'x.' According to the given information, when 4 less than 'x' is multiplied by 5 more than 'x,' the resulting product is 3 less than the square of 'x.' Mathematically, we can represent this as (x - 4) * (x + 5) = x^2 - 3.

Simplifying the equation, we expand the product on the left side: x^2 + 5x - 4x - 20 = x^2 - 3. By combining like terms, the equation becomes x^2 + x - 20 = x^2 - 3.

Next, we eliminate the x^2 terms by subtracting x^2 from both sides of the equation: x^2 - x^2 + x - 20 = x^2 - x^2 - 3. This simplifies to x - 20 = -3.

To isolate the 'x' term, we add 20 to both sides: x - 20 + 20 = -3 + 20. This yields x = 17.

Therefore, the value of the integer 'x' is 17.

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Step-by-step explanation:

Median= n+1/2 ( if n is even )

So,

10+1/2=11/2=5.5

Therefore,

135 is your second answer

Spread of the data = in the above mentioned picture the wave given to find the spread of the data

Hope it helps

The total price of the bicycle in Pierce county is $4136.24

An equation shows the relationship between two or more variables and numbers.

Let P represent the total price after taxes. The tax rate is 10.3% and the price of the bicycle is $3749.99. Hence:

Tax = 10.3% of $3749.99 = 0.103 * 3749.99 = $386.25

The total price (P) is:

P = $3749.99 + Tax = $3749.99 + $386.25

P = $4136.24

Therefore, the total price of the bicycle in Pierce county is $4136.24

The money left is $13.25.

Given data,

Your parents handed you $50 to spend on movie tickets for your sister and brother. You paid $8.25 for your ticket, while your siblings paid $4.25.

To know how much money you bring home after spending an extra $20 on soda and popcorn,

Your entry cost is $8.25

$4.25 for the brother's ticket

Sister's entry fee is $4.25.

$20 for soda and popcorn.

Total = 8.25 + 4.25 + 4.25 + 20.00 = $36.75

You received $50 from your parents.

You have spent $36.75.

Balance: 50.00 - 36.75 = $13.25

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Answer:

Kate is 13years and 4 months old,I suggest.

Answer:

y<−1

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−3y>3

Step 2: Divide both sides by -3.

−3y

−3

>

3

−3

=y<-1

Answer:

-1

Step-by-step explanation:

-1 is 11/12 at its simplest form

Answer:

2/3

Step-by-step explanation:

Simplify the numerator

(2x) ^3 = 8 x^3

8x^3 * 3x = 24 x^4

Simplify the denominator

(6x^2) ^2 = 36 x^4

Simplify the fraction

24x^4/ 36 x^4 =

24/36 = 2/3

x^4/x^4 =1

The fraction is 2/3  when x does not equal 0

a number that has a 6 in the thousandths place = 0.006

5 in the hundredths place,= 0.05

0 in the tenths place = 0.0

So, the number is = 6 in the thousandths place+ 5 in the hundredths place+0 in the tenths place

The number is = 0.006 + 0.05+ 0.0

Number = 0.056

Number less than your number : Number - 1

Number less than your number : 0.056 - 1 = 0.944

Number less then the your number is 0.944

Number greater than your number : Number + 1

Number greater than your number :0.056 + 1 = 1.056

Number greater than the your number is 1.056

Answer :

Number = 0.056

Number less then the your number is 0.944

Number greater than the your number is 1.056

Step-by-step explanation:

Hindi ko poh alam ✌️

Answer:

The answer would be team D as their range is 24.

Step-by-step explanation:

Team A: range of 27

Team B: Range of 32

Team C: Range of 27

Team D: Range of 24

Team D has the lowest range found by subtracting the larger number 46 by the smaller number 22.

Answer:

6/25

Step-by-step explanation:

Answer:

6/25

Step-by-step explanation:

100 divided by 25 is 4 and 4 multiplied by 6 is 24

Answer: 60 and 68/1000

Step-by-step explanation:

Not sure if you wanted it in fraction, decimal, or percentage form.

Answer:

60 and 68.000

Step-by-step explanation:

i not sure if that was what u were looking for