Consider the initial value problem my′'+ c y′+ k y=F(t),y(0)=0,y,(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t),where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k= 80 Newtons per meter, and F(t)=20sin(6t)Newtons.a. Solve the initial value problem.b. Determine the long-term behavior of the system.c. Is limt→[infinity]y(t)=0?If no, enter a function that approximates y(t)for very large positive values of t.

Answer:

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.

Step-by-step explanation:

The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:

[tex]P(t) = 9t^{2} + 34[/tex]

Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.

This is P(10).

[tex]P(t) = 9t^{2} + 34[/tex]

[tex]P(10) = 9*(10)^{2} + 34 = 934[/tex]

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.

Answer:

The answer is

Step-by-step explanation:

Usng the formula

[tex]A(n) = 3(2) ^{n - 1} [/tex]

Where n is the number of terms

For the first term

[tex]A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3[/tex]

For the fourth term

[tex]A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24[/tex]

For the eighth term

[tex]A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384[/tex]

Hope this helps you

Answer: –3; –24; –384

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

The Volume of the Rectangular prism on the left is 60

The Volume of the Rectangular prism on the right is 40

Answer:

Your correct answer is 40

Step-by-step explanation:

Multiply 8 x 5.

8 x 5 = 40

MUltiply 40 x 1.

40 x 1 = 40

So, it stays the same. Anything multiplied by 1 stays the same.

Therefore, your correct answer is 40.

Answer:

1) Radius of the cone = 9.5 cm

2) BA = 90.25 π cm²

3) SA = 384.7 π cm²

Step-by-step explanation:

1) Radius of the cone = 9.5 cm

2) Base Area of the cone = [tex]\pi r^2[/tex]

BA = (π)(9.5)²

BA = 90.25 π cm²

3) Surface Area of Cone = [tex]\pi r(r+\sqrt{h^2+r^2)}[/tex]

SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)

SA = 9.5π(9.5 + 31)

SA = 9.5π(40.5)

SA = 384.7 π cm²

Answer:

Volume of a cylinder is πr²h

Where

r is the radius

h is the height

Volume = 154cm³

radius = 3cm

height = ? cm

154 = π × 3² × h

154 = π × 9 × h

154 = 9πh

divide both sides by 9π

h = 154/9π

h = 5.4cm

Height is 5.4cm

Hope this helps

Answer:

[tex] \angle B[/tex]

Step-by-step explanation:

[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,

Answer:

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]\sigma = 1.27, n = 85[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 2.575*\frac{1.27}{\sqrt{85}}[/tex]

[tex]M = 0.3547[/tex]

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates:

[tex]m = \frac{10-(-4)}{6-2}[/tex]

Simplify:

[tex]m= \frac{14}{4}[/tex]

[tex]m = \frac{7}{2}[/tex]

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

Answer:

Option (3)

Step-by-step explanation:

Glide reflection of a figure is defined by the translation and reflection across a line.

To understand the glide rule in the figure attached we will take a point A.

Coordinates of the points A and A' are (2, -1) and (-2, 4).

Translation of pint A by 5 units upwards,

Rule to be followed,

A(x, y) → A"[x, (y + 5)]

A(2, -1) → A"(2, 4)

Followed by the reflection across y-axis,

Rule to be followed,

A"(x, y) → A'(-x, y)

A"(2, 4) → A'(-2, 4)

Therefore, by combining these rules in this glide reflections of point A we get the coordinates of the point point A'.

Option (3) will be the answer.

Answer:Reflection along the line y= -1

Step-by-step explanation:

took test

Answer:

Given,

CB=X

CD=3

CA=3+7=10

HERE,

[tex] {(cb)}^{2} = cd \times ca \\ {x}^{2} = 3 \times 10 \\ {x}^{2} = 30 \\ x = \sqrt{30} [/tex]

Hope this helps...

Good luck on your assignment..

The value of x is: x= √30.

Here, we have,

from the given figure, we get,

let, angle C = Ф

then, from triangle BCD,

cos Ф = 3/x

and, from triangle ABC,

cos Ф = x/10

so, we have,

3/x = x/10

=> x² = 10×3

=> x² = 30

=> x= √30

Hence, The value of x is: x= √30.

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Answer:

Option (2)

Step-by-step explanation:

In the figure attached,

ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.

Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.

Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]

                    = [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]

                    = [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]

                    = [tex]\frac{(6+12)}{6}[/tex]

                    = 3

Therefore, scale factor is 3 when center of dilation is B.

Option (2) will be the answer.

Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

Answer:

$25.00 + $10x = $115.00

Step-by-step explanation:

We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.

Answer:

0.006772

If the last dropping digit is less than 5 then it will be ignored

0.00677

if the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.0068

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.007

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.01

if the last digit is less than 5 so it will be ignored

0.0 is significant figure because zero to the right of decimal point are significant

Step-by-step explanation:

i hope this will help you :)

Answer:

0.007

Step-by-step explanation:

Rounding off 0.006772 to 1 significant figures:

=> 0.007

There is only 1 significant figure in this , since the zeroes on the left are not counted as significant figures.

Answer:

1/4

Step-by-step explanation:

There are 36 possible combinations.  Of those 36, the ones that add up to either 6 or 9 are:

1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3

There are 9 combinations that add up to either 6 or 9.  So the probability is 9/36, or 1/4.

The probability that the sum of the numbers rolled is either 6 or 9 is   [tex]\frac{1}{4}[/tex] . In rounded to the nearest millionth, the probability is 0.25.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Possible outcomes are

1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3.

The number of possible outcomes is 9.

Each dice has 6 possible outcomes.

Total number of outcomes = 6 × 6 =36

The probability is the ratio of total number of outcomes to possible outcomes.

The probability is 9/ 36 = 1/4 = 0.25

Hence, required probability is 1/4 or 0.25.

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Answereippcb.jrc.ec.europa.eu

Step-by-step explanation:

this I the wed go on it and you will get your answer

Answer:

W

Step-by-step explanation:

W is the vertex, you can see the letter above the angle

Answer:

W

Step-by-step explanation:

The vertex is where the 2 rays meet, or the corner of the angle

The vertex is W

[tex]

6+5\sqrt{249}-2x=7 \\

-2x=7-6-5\sqrt{249} \\

-2x\approx-77.9 \\

x\approx\frac{-77.9}{2}\approx38.95

[/tex]

Hope this helps.

Answer:

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Step-by-step explanation:

From the given information:

we are to find the first four nonzero terms of the Maclaurin series of the given function.

Sec x.

If we recall ; we will realize that the derivative of sec x = [tex]\dfrac{1 }{cos \ x}[/tex]

Also; for cos x ; the first four terms of its Maclaurin Series can be expressed as ;

=[tex]1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}+...[/tex]

However, using the long division method: we have;

[tex]\dfrac{1}{1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}}[/tex]

the rule of the long division method is to first use the 1 from the denominator to divide the 1 from the numerator. the multiply it with the answer we get which is (1) before subtracting it from  that answer (1).

i.e

1/1 = 1

1 × 1 = 1

1 - 1 = 0

Afterwards; we will subtract the remaining integers from this numerator.

So, we have:

[tex]\dfrac{-(1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!} )}{0+ \dfrac{x^2}{2!}-\dfrac{x^4}{4!}+ \dfrac{x^6}{6!}}[/tex]

We are going to apply the same process to the remainder [tex]\dfrac{x^2}{2!}[/tex];

which is to divide the second integer with 1

[tex]\dfrac{\dfrac{x^2}{2!}}{1}= \dfrac{x^2}{2!}[/tex]

Then we will multiply the numerator with [tex]\dfrac{x^2}{2!}[/tex] ; the result will then be subtracted from the polynomial.

[tex]= \dfrac{-( \dfrac{x^2}{2!} - \dfrac{x^4}{2! 2!} + \dfrac{x^6}{2! 4!}- \dfrac{x^8}{2! 6!}) }{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }[/tex]

Repeating the same process for remainder  [tex]\dfrac{5}{24}x^4[/tex]; we have:

[tex]\dfrac{ \dfrac{5}{24}x^4 }{1}= \dfrac{5}{24}x^4[/tex]

so; we will need to multiply 1 with [tex]\dfrac{5}{24}x^4[/tex] and subtract it from the rest of the polynomial

[tex]=\dfrac{{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }}{ 1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac {- ( \dfrac{5}{24}x^4 -\dfrac{5}{2!4!}x^6 - \dfrac{5x^8}{4!4!} - \dfrac{5x^{10}}{6!4!} } {0+ \dfrac{61}{720}x^6}[/tex]

Here ; the final remainder is [tex]\dfrac{61}{720}x^6}[/tex]; repeating the usual process for long division method; we have:

[tex]\dfrac{\dfrac{61}{720}x^6}{1}= \dfrac{61}{720}x^6}[/tex]

So;

[tex]= \dfrac{0+ \dfrac{61}{720}x^6}{1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac{-( \dfrac{61}{720}x^6)}{0 }[/tex]

Now the  first four nonzero terms of the Maclaurin series is the addition of all the integers used as remainders ; i.e

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Hey there! :)

Answer:

Has one solution.

(Graphed below)

Step-by-step explanation:

***The equations are graphed below, but this can also be solved algebraically.***

Set each equation equal to each other:

-6x + 6 = -3x - 3

Add 6x to both sides:

6 = 3x - 3

Add 3 to both sides:

9 = 3x

x = 3.

Plug in the value of x into an equation to solve for y:

y = -6(3) + 6

y = -18 + 6

y = -12.

The system of equations only has ONE solution at (3, -12).

On the graph, as well, the point of intersection is at (3, -12). This is the solution.

Answer:

x + (4x-85) = 90

Step-by-step explanation:

The two angles are complementary which means they add to 90 degrees

x + (4x-85) = 90

Answer: A

Step-by-step explanation:

Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × b × h

69.3 = 8.4 × h

h = 69.3 / 8.4

h = 8.25 mm

hope this helps

plz mark as brainliest!!!!!!

Answer:

16.5mm

Step-by-step explanation:

1. 69.3 x 2

2. 138.6 divided by 8.4

3. solve which equals 16.5mm

Hope this helps you:)

Volume before the gold:

3 x 2 x 4 = 24 cubic cm.

Volume after gold:

3 x 2 x 4.25 = 25.5 cubic cm

Volume of gold is the difference:

25.5 - 24 = 1.5 cubic cm.

Answer:

$10452958

Step-by-step explanation:

Initial profit = $11900848

Fall rate= $48263 per year

Equation:

where P(x)= profit at year of x, and 1990<x<2020

Answer:

D. BDCA

Step-by-step explanation:

B Start with the segment with point P. Center the compass at P and, with the same radius, strike two marks on the line on both sides of point P. Call these point A and D.

D Center the compass at D open the compass to a radius greater than the length DP.

C Draw an arc above segment CD. Center the compass at C, and using the same radius, draw another arc above segment CD that intersects the previous arc.

A Draw a line from the point of intersection of the arcs to point P. The is the perpendicular to line AB through point P.

Answer: BDCA

Answer: BDCA

Step-by-step explanation:

Start from point B.

Measure the distance BD.

Draw intersecting arcs of this distance from points C and point D above the line. Name this point E.

Join B and E to draw the perpendicular segment

Answer:

Step-by-step explanation:

Hello!

(a) Which genre has the highest mean audience score? The lowest mean audience score?

1) Action [tex]\frac{}{X}_1[/tex]= 58.63

2) Comedy [tex]\frac{}{X}_2[/tex]= 59.11

3) Drama [tex]\frac{}{X} _3[/tex] = 72.10

4) Horror [tex]\frac{}{X}_4[/tex]= 48.65

The lowest mean score is  [tex]\frac{}{X}_4[/tex]= 48.65

The highest mean score is  [tex]\frac{}{X} _3[/tex] = 72.10

(b) Which genre has the highest median score? The lowest median score?

1) Action Me₁= 51.00

2) Comedy Me₂= 58.00

3) Drama Me₃= 72.00

4) Horror Me₄= 52.00

The Lowest median is Me₁= 51.00

The Highest median is Me₃= 72.00

(c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score?

Lowest or minimum scores:

1) Action 32.00

2) Comedy 31.00

3) Drama 46.00

4) Horror 25.00

The genre with the lowest score is "Comedy"

Highest or maximum scores:

1) Action 93.00

2) Comedy 93.00

3) Drama 91.00

4) Horror 78.00

There are two genres with the highest score "Action" and "Comedy"

(d) Which genre has the largest number of movies in that category?

The number of movies for each category corresponds to the sample sizes:

1) Action n₁= 32

2) Comedy n₂= 27

3) Drama n₃= 21

4) Horror n₄= 17

The largest number of movies sampled was for the genre "Action"

(e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and, for the mean horror score.

Comedy [tex]\frac{}{X}_C[/tex]= 59.11

Horror [tex]\frac{}{X}_H[/tex]= 48.65

[tex]\frac{}{X}_C[/tex] -  [tex]\frac{}{X}_H[/tex]= 59.11 - 48.65= 10.46

I hope this helps!

Answer:

6/5

Step-by-step explanation:

you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.

The reciprocal fraction that is required will be 31/26.

A fraction is a numerical number that is represented in the numerator and denominator form.

We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction =  5(1/6).

Now,First, convert mixed fractions into simple fractions,i.e.First fraction  = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6

Now, According to the question,

Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)

Now, We get,= 26/31

So, the reciprocal fraction = 31/26.

Hence we can say that the reciprocal fraction that is required will be 31/26.

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Answer:

See below.

Step-by-step explanation:

Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]

We know that the diameter is 14, so the radius is 7.

Plug it into the equation:

[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]

Answer:

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Step-by-step explanation:

Let the hotel charge in the first city be x and in the second city be y.

Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:

[tex]y - x = \$1500[/tex] ...[1]

The tax in the first city was 5 %, and the tax in the second city was 8.5 %.

The total hotel tax paid for the two cities was $ 836.25

5% of x + 8.5% of y = $836.25

[tex]0.05x+0.085y=\$836.25[/tex]...[2]

Now putting value of y from [1] in to [2]:

[tex]y = \$1500+x[/tex]

[tex]0.05x+0.085\times (\$1500+x)=\$836.25[/tex]

On solving we get :

x = $5,250

Using vakue of x in [1] to find y:

[tex]y=\$1500+\$5,250=\$ 6,750[/tex]

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Answer:

πd or 2πr

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle by pi or multiply 2 times the radius times pi.

Hope that helps.

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Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.

                                            ` OR `

Plug the given value of the diameter into the formula and solve.[2]

Example problem: You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:

C = πd

C = π x 20

C = 62.8 feet

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀