Raul is flying a kite with an angle of elevation equal to 60° if the height of the kite is 300 feet then now long is the kite string.

We have to solve this equation using the method of undetermined coefficients. Given differential equation:

\($d^2y/dx^2​+8dy/dx​+12y=5,y(0)=3,dy(0)​/dt=9$\)

Let's solve this equation part by part:

Solution:

a) The characteristic equation is $m^2+8m+12=0.$

To solve this equation, we use the quadratic formula. The roots are:

\($$\begin{aligned} m=\frac{-b±\sqrt{b^2-4ac}}{2a}\end{aligned}$$\)

\($$\begin{aligned}m=\frac{-8±\sqrt{8^2-4(1)(12)}}{2(1)}\end{aligned}$$\)

\($$\begin{aligned}m=-6,-2\end{aligned}$$\)

Therefore, the roots are \($-6$\) and\($-2$.\)

b) The roots are negative and distinct, so the type of solution is

\($$\begin{aligned}y(t)=C_1e^{-2t}+C_2e^{-6t}\end{aligned}$$\)

c) The complementary function solution is

\($$\begin{aligned}y_c(t)=C_1e^{-2t}+C_2e^{-6t}\end{aligned}$$\)

d) The particular integral solution is

\($$\begin{aligned}y_p(t)=A\end{aligned}$$\)

where \($A$\) is the particular constant.

e) The general solution is

\($$\begin{aligned}y(t)=y_c(t)+y_p(t)\end{aligned}$$\)

Substituting the given initial conditions in the general solution, we get

\($$\begin{aligned}3=C_1+C_2+A\\ 9=-2C_1-6C_2\end{aligned}$$\)

Solving these equations, we get

\($$\begin{aligned}C_1=0,C_2=-\frac{3}{4},A=\frac{15}{4}\end{aligned}$$\)

Therefore, the particular solution is

\($$\begin{aligned}y(t)=\frac{15}{4}-\frac{3}{4}e^{-6t}\end{aligned}$$\)

Hence, the solution of the given differential equation is

\($$\begin{aligned}y(t)=C_1e^{-2t}+C_2e^{-6t}+\frac{15}{4}-\frac{3}{4}e^{-6t}\end{aligned}$$\)

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a) Recursive definition: a1 = 2, an = an-1 + 4 for n > 1.

b) Recursive definition: a1 = 1, an = (-1)^(n+1) for n > 1.

c) Recursive definition: a1 = 0, a2 = 2, an = (n - 1) * n + a(n-2) for n > 2.

d) Recursive definition: a1 = 1, an = a(n-1) + (2n - 1) for n > 1.

In mathematics, a sequence is an ordered list of numbers or other elements. A recursive definition of a sequence is one that defines each term of the sequence in terms of one or more previous terms. To find the nth term of the sequence, we need to know the previous terms up to n-1.

a) For the sequence {an} given by an = 4n - 2, the first few terms are 2, 6, 10, 14, 18, ... To define this sequence recursively, we can say that a1 = 2 and for n > 1, an = an-1 + 4.

b) For the sequence {an} given by an = 1^(-1)n, the first few terms are 1, -1, 1, -1, 1, ... To define this sequence recursively, we can say that a1 = 1 and for n > 1, an = -an-1.

c) For the sequence {an} given by an = n(n-1), the first few terms are 0, 2, 6, 12, 20, ... To define this sequence recursively, we can say that a1 = 0 and for n > 1, an = (n-1)an-1.

d) For the sequence {an} given by an = n^2, the first few terms are 1, 4, 9, 16, 25, ... To define this sequence recursively, we can say that a1 = 1 and for n > 1, an = an-1 + 2n - 1.

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The expression 16w² + 24w + 9 can be written in form as (4w+3)².

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given as:

⇒ 16w² + 24w + 9

To factor this expression, we can use the following steps:

Find two numbers that multiply to 16w² and add to 24w. The two numbers are 4w and 6w.

Create two binomials with the two numbers found in step 1. The binomials are 4w+3 and  (4w+3).

Multiply the two binomials together to get the factored form of the expression. The factored form is  (4w+3)².

Therefore, the equivalent expression to 16w² + 24w + 9 is (4w+3)².

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To determine the number of plants needed for the large planter and garden, we'll calculate them separately :Large Planter: The gardener needs 6 plants for the large planter. No additional calculations are required for this part. Garden: For every 4 square feet in the garden, the gardener needs 5 plants. The total area of the garden is 7 square feet.

To calculate the number of plants needed for the garden, we'll divide the total area by 4 and then multiply it by 5:

Number of plants needed for the garden = (Total area / 4) * 5

Number of plants needed for the garden = (7 / 4) * 5

Number of plants needed for the garden = 1.75 * 5

Number of plants needed for the garden = 8.75

Since we cannot have a fraction of a plant, we round up to the nearest whole number.

Therefore, the gardener needs 9 plants for the garden.

The gardener needs 6 plants for the large planter and 9 plants for the garden, for a total of 15 plants.

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Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

The problem can be solved using the exponential growth model.

In the given problem, the formula for the growth model is given, that is:

f(x) = 45 (64)^(x)

Where:

f(x) = total number of bacteria present after x days

To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.

f(1) = 45 (64)¹ = 2,880

f(2) = 45 (64)² = 184,320

f(3) = 45 (64)³ = 11,796,480

Hence,

after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

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The greatest common divisor (GCD) of 24 and 16 is 8. (A)

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. One way to find the GCD of two numbers is to factor both numbers into their prime factors and then find the product of the common prime factors.

In this case, 24 can be factored as 2³ * 3 and 16 can be factored as 2⁴. The largest power of 2 that divides both 24 and 16 is 2³, so the GCD of 24 and 16 is 2³ = 8.

Another way to find the GCD is to use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number and taking the GCD of the smaller number and the remainder until the remainder is 0.

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Complete question:

what are the greatest common divisors of 24,16

A) 8

B) 4

C) 2

D) 1

Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a Visual representation of the field, allowing for easier analysis and planning.

To create a scale drawing of a football field using a scale of 1:1,000, Mia can follow these steps:

1. Determine the dimensions: The football field's dimensions are given as 120 yards by 53 1/3 yards. Convert the fractional measurement to a decimal for simplicity. In this case, 1/3 yard is approximately 0.333 yards.

2. Decide on the units: Since the scale is 1:1,000, Mia needs to determine the unit of measurement she will use in her scale drawing. For consistency, she can choose to use feet as the unit.

3. Calculate the scaled dimensions: To create the scale drawing, Mia needs to scale down the dimensions of the football field. Since the scale is 1:1,000, she can divide the actual dimensions by 1,000 to obtain the scaled dimensions. The scaled dimensions would be 120 yards / 1,000 = 0.12 yards (or 0.36 feet) for the length and 53.333 yards / 1,000 = 0.053333 yards (or 0.16 feet) for the width.

4. Draw the scaled football field: Using a ruler and a grid paper, Mia can draw a rectangle with dimensions of 0.12 feet by 0.053333 feet (or inches, depending on the size of the grid paper). She can label the sides of the rectangle with the corresponding measurements in feet.

5. Add additional markings: Mia can add other markings to the scale drawing, such as the goal posts, yard markers, and any other important features of the football field. She can refer to the actual measurements and proportions of these elements to ensure accuracy.

By following these steps, Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a visual representation of the field, allowing for easier analysis and planning.

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Answer:

W

Step-by-step explanation:

It is W because the y-intercept is always on the y line.

Answer:

y = (x-.5)^2 -12.25

Step-by-step explanation:

first, find the vertex

x from (x,y) = -b/2a

ax^2-bx - c

1x^2-1x -12

-1/2(-1) = -1/-2 - 1/2

(1/2,y) then use x value to find y value

y = 1/2^2 - 1/2 - 12

y = .25 -.5 - 12    = -12.25

(.5,-12.25) input values into this formula:

y = a(x-h)^2 + k where h = x-value and k = y-value. use same a value = 1

y = (x-.5)^2 -12.25

Answer:

the answer is

B. (0, 5) and (−2, 9)

C. (−1, 7) and (2, 1)

Step-by-step explanation:

hope that help...…..…..…

Answer:

A) 21.9 and D) 22.07

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

22.075

A=0.175 less

B=0.005 more

C=0.985 more

D=0.005 less

E=0.004 more

Answer:

(-5,-8.5)

Step-by-step explanation:

-3-7=-10

-9-8=-17

-10/2=-5

-17/2=8.5

I'm NGL dawg, your comments don't make sense but that's the mid point for (-3,-9) (-7,-8).

The probability of winning $3,899 is 0.0001, which is a very small probability, but still possible.

To write the probability distribution for a player's winnings in the Pick 4 game, we need to consider all the possible outcomes and their probabilities.

There are a total of 10,000 possible four-digit numbers that can be drawn in the game. Since the player has to match the numbers in the exact order, there is only one winning combination for each four-digit number. Therefore, the probability of winning is 1/10,000.

To calculate the player's winnings, we need to subtract the $1 cost of playing from the $3,900 prize. Thus, the player's net winnings can be calculated as follows:

Net Winnings = $3,900 - $1 = $3,899

The probability distribution for the player's winnings can be summarized in the following table:

| Winnings (x) | Probability (P) |
|--------------|-----------------|
| $0           | 0.9999          |
| $3,899       | 0.0001          |

Note that the table shows the possible winnings (x) in ascending order, as requested. The probability of winning $0 is 0.9999, which means that the player is most likely to lose their $1 bet.

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For path A, the total distance traveled is 480 meters. The magnitude of displacement from start to finish is 240 meters, and the direction of the displacement is southeast.

To determine the total distance traveled along path A, we add up the lengths of all the individual segments. Path A consists of two horizontal segments followed by two vertical segments, each of which is 120 meters long.  the total distance is 2 * 120 + 2 * 120 = 480 meters.

To calculate the magnitude of the displacement, we consider the straight-line distance from the starting point to the ending point. In this case, the displacement is equal to the length of the hypotenuse of a right triangle formed by the horizontal and vertical segments of path A. Using the Pythagorean theorem, we find the displacement to be sqrt((120)^2 + (120)^2) ≈ 169.7 meters.

The direction of the displacement can be determined by finding the angle between the displacement vector and the positive x-axis. In this case, the angle can be determined using trigonometry as arctan(120/120) ≈ 45 degrees. Since the displacement is in the southeast direction, the direction can be stated as 45 degrees southeast.

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Answer:

\(b = \frac{r}{3} - a\)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain a variable.

Hope this helps

It is possible to use a relational operator and math operators in the same expression.

In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.

For example, consider the following expression:

`if (2 * 3) > (4 + 1)`

In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:

`if (6) > (5)`

Then, the relational operator (>) is evaluated, and the expression becomes:

`if True`

The expression is true because 6 is greater than 5.

It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.

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Answer:

La altura inicial del cohete es de 20 yardas

Step-by-step explanation:

Los parámetros dados son;

La función que representa la altura en yardas del cohete es h (t) = -5 · t² + 10 · t + 20

Dónde;

t = El tiempo de duración después del cual se lanza el cohete

Por lo tanto, la altura inicial del cohete viene dada por la ecuación para la altura del cohete en el momento de inicio o de inicio cuando t = 0, que se da como sigue;

La altura inicial del cohete = h (0) = -5 × 0² + 10 × 0 + 20 = 20 yardas

La altura inicial del cohete = 20 yardas.

Answer:

x<-2

Solution:

x+4-4<2-4

Answer:

The surface area of the square pyramid with dimensions 17 ft x 9 ft x 17 ft is 595 square feet.

Step-by-step explanation:

To calculate the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.

For a square pyramid with side length s and slant height l, the surface area can be calculated as follows:

Surface area = s^2 + 2sl

where s is the length of one side of the square base, and l is the slant height of the pyramid, which is the height of each of the four triangular faces.

In your case, the dimensions given are 17 ft for the base and 9 ft for the height, which is also the slant height. Therefore, we can calculate the surface area as:

Surface area = 17^2 + 2(17)(9)

Surface area = 289 + 306

Surface area = 595

Math is considered to have a sequential learning pattern because concepts and skills are introduced in a specific order, building upon previously learned material.

In math, concepts and skills are typically organized in a sequential manner, where each new topic builds upon what has been previously learned. This sequential learning pattern allows students to develop a solid foundation and gradually progress to more advanced topics.

For example, in elementary school, students first learn basic arithmetic operations like addition and subtraction before moving on to multiplication and division. These foundational skills are essential for understanding more complex mathematical concepts later on, such as algebra, geometry, and calculus. By following a sequential learning pattern, students can gradually develop their mathematical understanding and problem-solving abilities. They are able to connect new concepts to what they have already learned, reinforcing their knowledge and enabling them to apply it in different contexts. This sequential approach also ensures that students have the necessary prerequisite knowledge and skills to comprehend more advanced mathematical concepts. It helps create a logical progression in mathematical education, allowing students to build upon their previous knowledge and continually expand their mathematical abilities.

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The polar coordinates of the point (6, 6) are approximately (8.49, 0.79) in radians.

To convert the point (6, 6) from Cartesian to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y/x)

Given that the point is (6, 6), we can substitute the values into the formulas to find the polar coordinates.

r = √(6² + 6²) = √(36 + 36) = √72 ≈ 8.49

θ = arctan(6/6) = arctan(1) = π/4 ≈ 0.79 (radians)

In polar coordinates, the value of r represents the distance from the origin (0, 0) to the point, and the value of θ represents the angle (measured in radians) between the positive x-axis and the line connecting the origin to the point. The angle θ is usually measured counterclockwise from the positive x-axis.

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Complete question is:

Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.

(6,6)

Answer:

i don get it

Step-by-step explanation:

i stil don get it

Answer: 92

Step-by-step explanation:

Observe that the probability is symmetric around \(45^{\circ}\).

If \(0^{\circ} < x < 45^{\circ}\), then \(\cos^2 x > \cos x > \sin x\). By the triangle inequality, it follows that \(\cos^2 x > \sin^2 x+\sin x \cos x\).

We can now rearrange as follows:

\(\cos^2 x > \sin^2 x+\sin x \cos x\\\\\cos^2 x -\sin^2 x > \sin x \cos x\\\\\cos 2x > \frac{1}{2}\sin 2x\)

Since \(\cos 2x\) and \(\sin 2x\) are both positive for the chosen interval,

\(2 > \tan x \implies x < \frac{1}{2}\arctan 2\).

Therefore, the probability is \(\frac{\frac{1}{2} \arctan 2}{45}=\frac{\arctan 2}{90}\).

This means, \(m=2, n=90 \implies m+n=92\).

Answer:

C) (1,0), and (-3,0)

Step-by-step explanation:

The parabola intercepts the x axis at points (1,0) and (-3,0).

your answer is

C) (1,0), and (-3,0)

have a good dayyy!

Let's split this up into two shapes: a half-circle and a triangle.

First, we'll find the area of the half-circle. The formula for the area of a circle is: A = 3.14 * r^2. Therefore, the area of a half circle will be: A = 1/2 * 3.14 * r^2. Using our new formula, let's plug in what we know and solve.

A = 1/2 * 3.14 * 8^2

A = 1/2 * 3.14 * 64

A = 3.14 * 32

A = 100.48 m^2

Next, let's find the area of the triangle. The formula for the area of a triangle is: A = 1/2 * base * height. Using our formula, let's plug in what we know and solve.

A = 1/2 * 12 * 8

A = 6 * 8

A = 48 m^2

Finally, we need to add the area of the half-circle and the area of the triangle to find the area of the shape.

100.48 + 48

148.48 m^2

Hope this helps!! :)

Step-by-step explanation:

area of the triangle

\( \frac{1}{2} (12)(8) \\ \frac{1}{2} (96) \\ 48\)

area of the half circle

\( \frac{1}{2} \pi {(8)}^{2} \\ \frac{1}{2} (3.14)(64) \\ \frac{1}{2} 200.96 \\ 100.48\)

area of entire shape

\(48 + 100.48 \\ 148.48 {m}^{2} \)

Therefore because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.

Speed is a tempo that is determined by the distance an entity travels in a predetermined period of time. Numerous methods exist for measuring speed, including miles per hour, laps per minute, and meters per second. The measurements of speed, distance, and time are related. The relationship can be expressed in three different ways:

D = RT, R = DT, & T = DR.

Here,

We are given that

Distance drives by a family=4\(\frac{1}{4}\) miles

Time = 1/10

We have to find the rate of speed in miles per hour.

The speed formula will be used to get the velocity in miles per hour.

Distance traveled in a given amount of time equals speed.

=> Speed = 17/4 * 10

=> Speed = 42.5

So, using the calculation, we arrive at 42.5 miles per hour.

The miles traveled in 3/4 miles are therefore:

Distance is calculated as speed times time,

therefore 42.5 * 3/4 would equal 31.875 miles in distance.

Because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.

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