Please help I will mark brainiest ✅

Physical meaning of the given equation: The motion of a damped mass-spring system is described by the given equation. The equation includes different parameters such as mass, stiffness, damping coefficient, and time.

Here, mass is 1 kg, stiffness is 3 N/m, damping coefficient is 2, and time is represented by t. The equation describes the motion of a mass that is attached to a spring, where the mass can move in the horizontal direction.

The force required to move the mass is proportional to the spring constant and the distance of movement from the equilibrium position. The presence of damping in the system accounts for the dissipation of energy and decay of the amplitude of oscillation. b) Solution of the given equation:

The given differential equation is x"+2x+3x = sin(t) + 6(1-2)Given that x(0) = 0 and x'(0) = 0.

The characteristic equation of the given differential equation isr² + 2r + 3 = 0On solving the above quadratic equation we get, r = -1 ± √2 iThus, the homogeneous solution of the given differential equation is

xh(t) = e^(-t) [ c1 cos(√2t) + c2 sin(√2t) ].

Now, let us find the particular solution of the given differential equation.

Particular solution,xp(t) = sin(t) + 6(1-2) / 3Using the given initial conditions,

x(0) = xp(0) + xh(0) = 0⇒ c1 = -1xp'(t) = cos(t)x'(0) = xp'(0) + xh'(0) = 0⇒ c2 = -√2.

Substituting the values of c1 and c2 in xh(t),xh(t) = e^(-t) [ -cos(√2t) - √2 sin(√2t) ].

Therefore, the complete solution of the given differential equation

isx(t) = e^(-t) [ -cos(√2t) - √2 sin(√2t) ] + sin(t) - 2x(t) = e^(-t) [ -cos(√2t) - √2 sin(√2t) ] + sin(t) - 2

The physical meaning of the given equation is that it describes the motion of a mass that is attached to a spring. The mass can move in the horizontal direction, where the force required to move the mass is proportional to the spring constant and the distance of movement from the equilibrium position.

The presence of damping in the system accounts for the dissipation of energy and decay of the amplitude of oscillation.

The solution of the given differential equation is obtained by finding the characteristic equation of the differential equation, which gives the values of r.

On solving the quadratic equation we get the value of r, and by substituting this value in the homogeneous solution, we can find the complete solution. The particular solution of the differential equation is also obtained by using the given initial conditions.

The complete solution of the given differential equation isx(t) = e^(-t) [ -cos(√2t) - √2 sin(√2t) ] + sin(t) - 2.

The given equation describes the motion of a mass that is attached to a spring, where the mass can move in the horizontal direction.

The solution of the given differential equation is obtained by finding the characteristic equation of the differential equation, which gives the values of r. By substituting this value in the homogeneous solution, we can find the complete solution. The particular solution of the differential equation is also obtained by using the given initial conditions.

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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Baking cupcakes for the time suggested for baking a cake may result in overbaked and dry cupcakes.

This is because cupcakes are smaller and have less volume than cakes, so they require less baking time to cook through. Overbaking can also cause cupcakes to lose their moisture and become tough. It is important to follow the suggested baking time for cupcakes to achieve the desired texture and flavor.

To ensure that cupcakes are baked correctly, it is recommended to test them for doneness using a toothpick or cake tester. Insert the toothpick in the center of the cupcake, and if it comes out clean, the cupcakes are done.

If the toothpick has batter on it, the cupcakes need more time to bake. Adjust the baking time accordingly, and continue checking until the toothpick comes out clean.

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Answer:

x=8

Step-by-step explanation:

x-3=5

+3=+3(cancel 3)

_____________

x=8

the radius of the circle is 30 cm when the circumference is 188.4 . The length of the boundary is its circumference.

A boy has traveled a certain distance if, after sprinting around the park once, he arrives at point "A" from point "A" in the first place. The park's circumference, which has the shape of a circle, is the length or border that it encompasses. The length of the boundary is its circumference.

calculation

Circumference=2πr

188.4=2×3.14×r

188.4=6.28×r

r= 188.4/6.28

radius=30cm

the radius of circle is 30 cm when the circumference is 188.4 .

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Answer:

Yes it is correct answer

                                                        Answer

__________________________________________________________

__________________________________________________________

Least to Greatest

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Hope this helps! <3

__________________________________________________________

Answer:

inside

120

Step-by-step explanation:

E D G E N U I T Y

Stay safe and have a wonderful day/afternoon/night!!!!!

Brainliest?!?!

Answer:

1.) Inside

2.) 120

Step-by-step explanation:

Give Him/Her Brainliest!    ↑   ( ˙ ˘ ˙)

ʕ •ᴥ•ʔ  εїз

There are 5 ways that the sum of the dice be equal to 6 if a pair of distinct dice are rolled one time

It is the ordered arrangement of members belonging to a set with no repeats.

Analyzing the possibilities for the sum of the dice be equal to 6, assuming that each die has six sides:

Red die = 6 sides

Blue die = 6 sides

The possibilists are:

(Bleu, red)

(1,5)

(2,4)

(3,3)

(4,2)

(5,1)

There are 5 ways to get at sum of 6 if a pair of distinct dice are rolled one time

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The solution for x in the given expression (7 = 3x/9) is: C. 21.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to describe the steps that should be taken to rearrange and solve for x. Therefore, the appropriate and required steps are listed as follows:

Multiplying both sides by 9, we have:

9 × 7 = 3x/9 × 9

63 = 3x

Dividing both sides by 3, we have:

3x/3 = 63/3

x = 21.

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solución:

A=1450cm²

~~~~~~~~~~~~~

Answer:

1) C

2) C

Step-by-step explanation:

Question 1)

We want a parabola that has the vertex (-8, -7) and also passes through the point (-7, -4).

So, we can use the vertex form. Remember that the vertex form is:

\(y=a(x-h)^2+k\)

Where a is our leading co-efficient and (h, k) is our vertex.

We know that our vertex is (-8, -7). So, substitute this into the equation:

\(y=a(x-(-8))^2+(-7)\)

Simplify:

\(y=a(x+8)^2-7\)

Now, we need to determine the value of our a. To do so, we can use the point the problem had given us. We know that the graph passes through (-7, -4).

So, when x is -7, y is -4. Substitute -7 for x and -4 for y:

\((-4)=a((-7)+8)^2-7\)

Solve for a. Add within the parentheses:

\(-4=a(1)^2-7\)

Square:

\(-4=a-7\)

Add 7 to both sides. Therefore, the value of a is:

\(a=3\)

So, our entire equation in vertex form is:

\(y=3(x+8)^2-7\)

Our answer is C.

Question 2)

We are given a graph and are asked to find the equation of the graph.

Again, let's use the vertex form. From the graph, we can see that the vertex is at (-2, 2). Let's substitute this into our vertex equation:

\(y=a(x-(-2))^2+2\)

Simplify:

\(y=a(x+2)^2+2\)

Again, we need to find the value of a.

Notice that the graph crosses the point (-1, 5).

So, let's substitute -1 for x and 5 for y. This yields:

\(5=a((-1)+2)^2+2\)

Solve for a. Add within the parentheses.

\(5=a(1)^2+2\)

Square:

\(5=a+2\)

Subtract 2 from both sides. So, the value of a is:

\(a=3\)

Therefore, our entire equation is:

\(y=3(x+2)^2-2\)

Our answer is C.

And we're done!

Answer:

m∠B ≈ 28.05°

Step-by-step explanation:

Because we don't know whether this is a right triangle, we'll need to use the Law of Sines to find the measure of angle B (aka m∠B).  

The Law of Sines relates a triangle's side lengths and the sines of its angles and is given by the following:

\(\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}\).

Thus, we can plug in 36 for C, 15 for c, and 12 for b to find the measure of angle B:

Step 1:  Plug in values and simplify:

sin(36) / 15 = sin(B) / 12

0.0391856835 = sin(B) / 12

Step 2:  Multiply both sides by 12:

(0.0391856835) = sin(B) / 12) * 12

0.4702282018 = sin(B)

Step 3:  Take the inverse sine of 0.4702282018 to find the measure of angle B:

sin^-1 (0.4702282018) = B

28.04911063

28.05 = B

Thus, the measure of is approximately 28.05° (if you want or need to round more or less, feel free to).

Answer:

if you wanna go out than its a to number 3

B. the starting temperature of the water in each cup

Answer:

see explanation

Step-by-step explanation:

Given

\(\frac{x}{7}\) + 2y = 6

Multiply through by 7 to clear the fraction

x + 14y = 42 ( subtract 14y from both sides )

x = 42 - 14y

Answer: 16

Step-by-step explanation: The angles are equal so x+24 = 3x-8

The solution to the equation 2x + 9 = 15 is x = 3.

In the given linear equation, 2x + 9 = 15, we are tasked with finding the value of x that satisfies the equation. To solve it, we need to isolate the variable x on one side of the equation.

To begin, we subtract 9 from both sides of the equation, which gives us 2x = 15 - 9. Simplifying further, we have 2x = 6.

Next, to solve for x, we divide both sides of the equation by 2. This yields x = 6/2, which simplifies to x = 3.

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Answer:

Answer:

19 : 10 = 19 : 10

Solution:

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 19 and 10 is 1

Divide both terms by the GCF, 1:

19 ÷ 1 = 19

10 ÷ 1 = 10

The ratio 19 : 10 cannot be reduced further by dividing both terms by the GCF = 1 :

This ratio is already in lowest terms.

Therefore:

19 : 10 = 19 : 10

Step-by-step explanation:

To find the average quarterly loads for the rest of the years, you can use the formula below:

Average Quarterly Load = Total Annual Load  4 For example, let's say the total annual load for Year 1 is 800.

To find the average quarterly loads for Year 1, we would divide 800 by 4 to get an average quarterly load of 200. Then, you can use this average quarterly load to find the seasonal indices for each quarter of each year.To find the seasonal index for a given quarter and year, you would divide the actual quarterly load by the average quarterly load for that year.

For example, let's say the actual load for Quarter 1, Year 1 is 240. To find the seasonal index for this quarter and year, we would divide 240 by 200 to get a seasonal index of 1.2. You would repeat this process for each quarter and year to find the seasonal indices for all quarters and years.

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Answer:

she didnt go back from 15 she went back from 20and the arrows should be going backwords not forwards

The three errors that Emily makes are: The arrows should point in the negative direction. The arrows should end on negative 15. The arrows should start at zero.

The number line is a representation of numbers on the line which can be used for different arithmetic operations such as additions, subtractions, multiplication, and division of numbers and algebraic expressions. It usually starts from the origin 0 with the positive axis in the right direction and the negative axis in the left direction.

From the given information;

-15 ÷ 5 = -3

By representing the above information on the number line, the errors that Emily make with her diagram are:

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To determine fx when f(x, y) = 2x − y/2x y, we need to take the partial derivative of f with respect to x.

We use the product rule and the chain rule to differentiate f with respect to x. The first term, 2x, differentiates to 2. For the second term, we use the product rule to get 2y + x(dy/dx). We also need to use the chain rule to differentiate y with respect to x, which gives us dy/dx. Putting it all together, we get:

fx = 2 - y/2x - xy/(2x^2)

Simplifying this expression, we get:

fx = (4x^2 - y)/(4x^2)

Therefore, the expression for fx when f(x, y) = 2x − y/2x y is (4x^2 - y)/(4x^2).

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The total distance travelled covered by the Daren is greater than that of  Umberto.

Distance travelled is the product of speed of the body and the time for which it moved. Mathematically -

Distance = Speed x Time

Given is that Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. Now, Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours.

Total distance travelled by Daren is -

d₁ = 8.55 x 3.5

d₁ = 29.925 Km

Total distance travelled by Umberto is -

d₂ = 9.5 x 3

d₂ = 28.5 Km

It can be seen that -

d₁ > d₂

Therefore, the total distance travelled covered by the Daren is greater than that of  Umberto.

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Answer:

1. trapezoid

2. 360°

Step-by-step explanation:

plz mark me brainliest, :)

Answer: 1: D 2: 360

Step-by-step explanation:

the shapes have the top and bottom two that are parallel and then the sides aren’t parallel

Answer:

Step-by-step explanation:

To find the mean just add the scores and divide the answer by however many scores there are (in this question there are 5 scores):

                  \(\text{mean}=\frac{38+29+16+42+33}{5}=\frac{158}{5} =31.6\)

The mean number of points scored is 31.6

Answer:31.0

Step-by-step explanation:

82+2=84

Answer:

Step-by-step explanation:

Mean=((4+10+3+6+9+10+a)/7)=7

=>42+a=49

=>a=7Mean=((4+10+3+6+9+10+a)/7)=7

=>42+a=49

=>a=7

Answer:

a = 7

Step-by-step explanation:

Given:

7 is mean of 10,3,4,a,6,9,10

To Find:

Value of a

Solve:

Mean → \(\frac{(4+10+3+6+9+10+a)}{7}=7\)

⇒ 42+a=49

Subtract 42 from both sides

x + 42 - 42 = 49 - 42

Simplify

⇒ a=7  

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The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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