Determine the value, k, so that y=kcos(3x)+4sin(x) is a solution to the differential equation y’’+y=-9cos(2x)

1.

f'(x) = 8 · x^(8-1) = 8·x^7

2.

g'(x) = -4· 4·x^(4-1) = -16·x^3

3.

h(x) = 1/x^5 = x^(-5), so

h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6

Answer:

Step-by-step explanation:

Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).

The slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).

The line goes through the origin (0, 0), so the slope is the ratio of y to x.

  m = y/x = 4/1 = 4

This is the constant of proportionality.

The constant of proportionality is 4, choice A.

The equation of a proportional relationship is ...

  y = kx . . . . . . where k is the constant of proportionality

Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...

  m = 4c . . . . . choice D

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The number line is shown below:

The given inequality:

x -5 < 11

Add 5 on both sides

x -5 + 5 < 11 + 5

Add x < 16

Thus, this is represented in the number line below:

A graphical illustration of numbers in a line is known as a number line. It is utilized for indicating the relation between values, and also to do calculations such as subtraction, multiplication, division, etc. The figures get bigger from left to right and diminishes from right to left.

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The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.

To calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.

From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:

Contribution margin per unit = Selling price per unit - Variable cost per unit

= $900 - $600

= $300

Since the sales target is 35,000 units, the total contribution margin is:

Total contribution margin = Contribution margin per unit x Number of units sold

= $300 x 35,000

= $10,500,000

The total cost can be calculated as follows:

Total cost = Fixed cost + Variable cost

= $3,500,000 + ($600 x 35,000)

= $25,100,000

Adding the additional selling expense of $200,000, the new total cost becomes:

New total cost = $25,100,000 + $200,000

= $25,300,000

Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:

Operating profit = Total revenue - Total cost

= ($900 x 35,000) - $25,300,000

= $10,500,000 - $25,300,000

= -$14,800,000

This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

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Okay, here are the steps to solve this:

* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.

* We are making 12 cups of granola.

* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.

* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.

Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.

Answer:

a. The probability of getting an O on the first draw can be calculated by dividing the number of O tiles by the total number of tiles in the bag:

```

P(O on first draw) = 3/15 = 0.2

```

Therefore, the probability of getting an O on the first draw is 0.2 or 20%.

b. After removing one O tile, there are 14 tiles left in the bag, of which 2 are U tiles. Therefore, the probability of getting a U if you didn't replace the O is:

```

P(U without replacing O) = 2/14 = 1/7 ≈ 0.143

```

Therefore, the probability of getting a U if you didn't replace the O is approximately 0.143 or 14.3%.

c. The probability of getting O and then U if you don't replace the O can be calculated as follows:

```

P(O and then U) = P(O on first draw) * P(U without replacing O)

               = 3/15 * 2/14

               = 1/35

               ≈ 0.029

```

Therefore, the probability of getting O and then U if you don't replace the O is approximately 0.029 or 2.9%.

Step-by-step explanation:

If you want to transform rectangular coordinates (x, y) into its polar counterpart (r, θ), do the following:

Firstly, obtain r by computing the distance from the origin to point (x,y), making use of the Pythagorean theorem or simply put, by evaluating r = sqrt(x^2 + y^2).

Secondly, acquire θ which denotes the angle formed between the positive x-axis and a line correlating the origin and the coordinate (x,y). Calculate this via inverse tangent function: θ = atan2(y, x).

Thirdly, in case the measurement for θ is indicated in radians while you require degrees instead, multiply by 180/π to convert it.

Usually expressed as (r, θ), where r indicates proximity disentangled between the origin and the point (x,y), whilst θ identifies the aforementioned angle.

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Answer: $1.182

Step-by-step explanation: 3.546 divided by 3

Answer:

$1,182

Step-by-step explanation:

I just took the total of $3546 and divided the total by the three grade levels so 3 and I got the answer 3,546. But honestly i'm not sure if it's right lol, so if it's incorrect let me know and I'll work into it more.

The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces

A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.

Part of the question obtained from a similar question posted online can be presented as follows;

The amount of fudge the student has = 3 pounds

The amount of fudge the student eats = 1 pound of the fudge

Required; The amount of fudge the student has left

The amount of fudge the student has left = 3 - 1 = 2 pounds

The fraction of the remaining fudge the student gives to her sister = (1/2)

Therefore;

The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound

1 pound = 16 ounces

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Hence the correct option is D. 38inches long, to the nearest inch, should the strip of foil be.

The circumference of a circle  in mathematics is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. In according to broader  the perimeter is the length of any closed figure of  curve.

A  straight line and cuts through the middle of a body or figure. particularly  the length of a diameter is a line segment passing through the center of a circle with its ends on the circumference.

We determine the circumference of the pie pan in order to determine the length of the aluminium foil strip required.

Circumference =2[tex]\pi[/tex]r.

where, r = circle of radius and [tex]\pi[/tex] = mathematical constant =3.14.

The pie pan of  radius = half of its diameter=12 inches/2= 6 inches.

Now, the pie pan of circumference is:

Circumference: 2 [tex]\pi[/tex]r=2[tex]\pi[/tex] *6 inches= 37.7 inches

Therefore , the length of the aluminium foil strip = 38 inches,

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the coordinates of the point that represents the number of snowballs needed to make 2 snowmen should be option C. which is (2,6)

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2 and x=0 making it (0,2)

Thus, decimal word problem that involves subtraction and division-

The two empty water container weighs 0.64 kg and 1.728 kg when filled with water. Find the water weigh?

The decimal point, which distinguishes between a decimal number's whole number and fractional component, is a little dot. Decimal numbers include 4.14, 3.786, 5.453, and 123.5687 as examples.

decimal word problem : (subtraction and division)

The two empty water container weighs 0.64 kg and 1.728 kg when filled with water. Find the water weigh?

Division: Weight of one water container = 0.64 / 2 = 0.34 kg.

Subtraction: Weight of water : 0.728 - 0.34 = 0.385 kg.

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The number line where we plotted 1 1/4 and 5/2 is added as an attachment

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

-1 1/4 and 5/2

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-5/4 and 5/2

Rewrite the denominators of the fractions

So, we have

-5/4 and 10/4

This means that we can plot -5/4 at -5 and 10/4 at point 10 where the difference in each interval is 1/4

Using the above as a guide, we have the following:

The number line is attached

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Okay, let's analyze the r^2 values for the 4 options:

a. y=16.5839•1.0185^x

r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.

b. y=0.985515x-2.81333

This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.

In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.

Does this help explain the approach? Let me know if you have any other questions!

Answer:

this is the Pythagorean theorem this is the formula a^2 + b^2 = c^2

Step-by-step explanation:

please mark as brainliest have a great day :D

The equation of the plane passing through the lines of intersection of the planes 2x - 7y + 4z = 3 and 3x - 5y + 4z + 11 = 0 and the point (-2, 1, 3) is

-13x - 8y + z + 90 = 0

We have,

To find the equation of the plane passing through the intersection of two planes, we need to first find the direction vector of the line of intersection of the two planes.

Let's call the two planes P1 and P2, which are given by the equations:

P1: 2x - 7y + 4z = 3

P2: 3x - 5y + 4z + 11 = 0

To find the direction vector of the line of intersection of P1 and P2, we can take the cross product of the normal vectors of P1 and P2. The normal vectors are:

n1 = <2, -7, 4>

n2 = <3, -5, 4>

Taking the cross-product of n1 and n2.

n1 x n2 = <-13, -8, 1>

This vector is parallel to the line of intersection of P1 and P2. We can use this vector as the direction vector for the line.

Now, we need to find a point on the line.

We can use the point of intersection of P1 and P2 as a point on the line.

To find this point, we can solve the system of equations:

2x - 7y + 4z = 3

3x - 5y + 4z + 11 = 0

Subtracting the first equation from the second, we get:

x + 2y + 7 = 0

Solving for x in terms of y,.

x = -2y - 7

Substituting this expression for x into the first equation, we get:

-4y - 14 - 7y + 4z = 3

Simplifying.

-11y + 4z = 17

Choosing y = 1.

-11 + 4z = 17

Solving for z.

z = 7

Substituting y = 1 and z = 7 into the equation for x.

x = -2(1) - 7 = -9

So a point on the line is (-9, 1, 7).

Now, we can use the point (-9, 1, 7) and the direction vector <-13, -8, 1> to write the equation of the plane passing through the line of intersection of P1 and P2.

Let's call this plane P3.

Using the point-normal form of the equation of a plane.

-13(x + 9) - 8(y - 1) + (z - 7) = 0

Expanding and simplifying, we get:

-13x - 8y + z + 90 = 0

Thus,

The equation of the plane passing through the lines of intersection of the planes 2x - 7y + 4z = 3 and 3x - 5y + 4z + 11 = 0 and the point (-2, 1, 3) is:

-13x - 8y + z + 90 = 0

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Answer:

Profit when producing 70 items = $3,050

Profit when producing 80 items = $1,350

Step-by-step explanation:

To find the profit when producing a certain number of items, we need to subtract the cost from the revenue:

Profit = Revenue - Cost

Let's calculate the profit for producing 70 items:

Revenue when producing 70 items:

R(70) = -0.5(70-120)^2 + 7,200 = $6,800

Cost of producing 70 items:

C(70) = 50(70) + 250 = $3,750

Profit when producing 70 items:

Profit = Revenue - Cost = $6,800 - $3,750 = $3,050

Similarly, let's calculate the profit for producing 80 items:

Revenue when producing 80 items:

R(80) = -0.5(80-120)^2 + 7,200 = $5,600

Cost of producing 80 items:

C(80) = 50(80) + 250 = $4,250

Profit when producing 80 items:

Profit = Revenue - Cost = $5,600 - $4,250 = $1,350

We can see that the profit is less when producing 10 more units because the cost of producing those additional units exceeds the revenue generated from selling them. In other words, the marginal cost (the cost of producing one additional unit) is greater than the marginal revenue (the revenue generated from selling one additional unit) beyond a certain point.

This is an example of the law of diminishing returns, which states that as we increase the quantity of inputs while keeping other inputs constant, the marginal product (output per unit of input) eventually decreases.

Hope this helps!

Answer:

B represents a function.

Okay, let's evaluate each modeling equation candidate based on the r^2 value:

a. y=16.5839•1.0185^x

No r^2 value given, so cannot determine if this is the best fit.

b. y=0.985515x-2.81333

No r^2 value given for this linear model, so cannot determine if it is the best fit.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value, it would be the best fit.

Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.

Does this help explain the approach? Let me know if you have any other questions!

The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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A​ T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.

The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.

To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.

The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.

t = -b/2a = -78/(2*(-16)) = 2.4375

Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.

To find the maximum height, we substitute this value of t into the equation for h:

h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet

Therefore, the maximum height of the T-shirt is approximately 97.19 feet.

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Answer:

a line graph

Step-by-step explanation:

1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.

That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.

1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.

That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.

Answer:

x = 15

Step-by-step explanation:

Simplifying the expression:

Add the numbers:

Combine like terms:

Subtract 1 from both sides:

Subtract 4x from both sides:

Answer:

x = 15

Step-by-step explanation:

Simplifying the expression:

Add the numbers:

Combine like terms:

Subtract 1 from both sides:

Subtract 4x from both sides:

The radius of this circle with center (8, 2) is equal to 6.71 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;

Distance = √[(14 - 8)² + (-1 - 2)²]

Distance = √[(6)² + (-3)²]

Distance = √[36 + 9]

Distance = √45

Distance = 6.71 units.

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Complete Question:

What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places