A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.

Answers

Answer 1

The equation of motion for the mass attached to the spring

x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2

What is the equation of motion?

Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.

In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:

k = F/x = 400 N/2 m = 200 N/m

The equation of motion for a mass on a spring is given by:

F = ma = -kx

where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.

Substituting the values for the spring constant and the mass, we get:

-kx = -(200 N/m)(50 kg)(x'')

Solving for the acceleration, we get:

x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2

This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.

Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:

x = x_0 + v_0t + (1/2)at^2

where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.

Substituting the values for the acceleration and the initial velocity, we get:

x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2

This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.

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Related Questions

Jose earns a monthly salary of $3,257.22.What is his annual pay?

Answers

His annual pay is 12 months of earnings.

$3,257.22 per month for 12 months gives

\(\frac{3,257.22}{\text{month}}\times12months=39,086.64.\)

Hence, Jose's annual salary is $39,086.22.

Label the triangle sides, assuming the angle of interest is the 30-degree angle:

solve for
The side with x is the
blank side.
The side with y is the



NO SPAM I WILL REPORT YOU
blank side.
The side with 17 is the blank side

Label the triangle sides, assuming the angle of interest is the 30-degree angle:solve forThe side with

Answers

Check the picture below.

Label the triangle sides, assuming the angle of interest is the 30-degree angle:solve forThe side with

Please help!!! Thanks


Math problem

Please help!!! ThanksMath problem

Answers

Answer:

67

Step-by-step explanation:

(5-2)180

=540

540-131-105-153-84

=67

Do you think that students should be proficient in addition before learning multiplication? answer in 175 words! thank you so much :)

Answers

Answer:

Yes, Because if you can't add then you do not know how many times to add the number. For example, 5 x 5= 25

If you don't know what 5+5 equals then how are you supposed to figure out 5+5+5+5+5. That is just common knowledge that you should have learned in your early school years. You need to know how to subtract to divide so it is basically the same concept. I do not know anyone that does not know how to multiply but not add. To me, that does not even seem possible. I know that you have to be really good at adding to multiply too. Cause if you only know how to add up to 100 what happens when you get in high school and college and need to multiply in school over 100? Or thinking higher than that you need to know so that you can do taxes, pay bills, etc... So my answer to this question is yes, you should be proficient in addition to learn multiplication.

This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*

This may be hard to put together, but I need help with an angle equation. I'm looking for example equations

Answers

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

I tried -2, -1, 0, 1, -3, -4, but it did not work. Any ideas on what the correct answer actually is?

I tried -2, -1, 0, 1, -3, -4, but it did not work. Any ideas on what the correct answer actually is?

Answers

y = -4, -3, -2, -1, 0, 1

Step-by-step explanation:

-5 < y < 2

y = -4, -3, -2, -1, 0, 1

-5 < -4, -3, -2, -1, 0, 1 < 2 ☑

Which is the polynomial function of lowest degree with leading coefficient of 4 and roots 7 and 3?
O f(x)= x2 – 3x-+3-17
O f(x)= 4x² -1245x+3/7
O f(x)=x2 – 3x? – X+21
O x) = 4x° - 12x - 28x+84

Answers

Answer:

Step-by-step explanation:

If the roots are 7 and 3, then x = 7 and x = 3 are solutions. In factor form, x = 7 is (x - 7); in factor form, x = 3 is (x - 3). We FOIL these together to get

\(x^2-3x-7x+21\) which simplifies to

\(x^2-10x+21\) and we distribute in the 4:

\(4(x^2-10x+21)\) to get

\(4x^2-40x+84\) which is another way to write the last choice you're given.

8.1 Recognising and describing 2D shapes and solids Two pairs of opposite angles equal the name of each 2D shape that is described. rent lengths' One pair of opposite angles equal All angles 90° 8. TH It Two pairs of parallel sides ✓ One pair of parallel sides Two pairs of equal sides ✓ Four equal sides Quadrilateral Square Rectangle Parallelogram Rhombus Kite Trapezium Exercise 8.1 1 Copy and complete the table to show a description of the 2D quadrilaterals. The parallelogram has been done for you.​

Answers

Answer:

Hopefully this graph helps you!

8.1 Recognising and describing 2D shapes and solids Two pairs of opposite angles equal the name of each
Here is the completed table showing the description of 2D quadrilaterals:

Quadrilateral Two pairs of opposite angles equal One pair of opposite angles equal Two pairs of parallel sides One pair of parallel sides Two pairs of equal sides All angles 90°
Square ✓ ✓ ✓
Rectangle ✓ ✓ ✓
Parallelogram ✓ ✓
Rhombus ✓
Kite
Trapezium ✓ ✓
Note: "Trapezium" is the British English term for what is called a "trapezoid" in American English.

To isolate the variable on one side of the equal sign, divide both sides of the equation by .

Answers

To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.

the perimeter of a rectangle is 68 cm. The length is 4cm more than its width. Find the dimensions of the rectangle

Answers

Answer:

W=15cm

L=19cm

The dimensions are 15cm by 19cm

Step-by-step explanation:

P=2W+2L

L=4+W

68=2W + 2(4+W)

68=4W+8

60=4W

W=15cm

L=4+15

L=19cm

HELP ME NOWWWWWW PLZZZZZZ EXPLAIN UR ANSWER FOR BRAINLIEST

HELP ME NOWWWWWW PLZZZZZZ EXPLAIN UR ANSWER FOR BRAINLIEST

Answers

Answer:

The answer's A 1/52

Step-by-step explanation:

That's because there's only one ace of hearts in a deck of 52 cards.

Answer: A) 1/52

Step-by-step explanation:

There is 52 cards in a whole deck, and the probability of getting that ace card is 1/52 because there is only 1 ace card in an entire deck of cards.

Hence, the answer is 1/52

The formula for the volume
of a cone is V= 1/3 pi r^2h. Write the formula expressed as the radius, r.

Answers

Answer:

\(\sqrt{ \frac{{3V\pi } }{h}\) = r

Step-by-step explanation:

V = 1/3 pi r^(2) *h

Rewrite:

V = pi * r^(2) * h/3

Inverse operations:

V / h / 3 = pi * r^2

Simplify:

3V/h = pi * r^2

Inverse operations:

3V/h / pi = r^2

Simplify:

3Vpi/ h = r^2

Inverse operations:

sqrt( 3Vpi/h) = r

\(\sqrt{ \frac{{3V\pi } }{h}\) = r

How much interest would you have if you deposited $200 that if you deposited $150? ​

How much interest would you have if you deposited $200 that if you deposited $150?

Answers

Answer:

Difference = 206 - 154.5 = $51.5

In short, Your Answer would be: $51.5

Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box​

Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type

Answers

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

How to determine the key features?

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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ASAAHLcongremeror vingName thequadrilaName thethe crancyABCA'B'C'What is the surface area of the regularpyramid?3114 ftA=3f3 ftA 17 ft²B 24 ft²3 ftC 33 ft²D 36 ft²

ASAAHLcongremeror vingName thequadrilaName thethe crancyABCA'B'C'What is the surface area of the regularpyramid?3114

Answers

Surface area:

\(S=L+B\)

1. Find the Lateral area:

\(\begin{gathered} L=\frac{1}{2}Pl \\ \\ P=3ft+3ft+3ft+3ft=12ft \\ L=\frac{1}{2}(12ft)(4ft)=24ft^2 \end{gathered}\)

2. Find the area of the base:

\(\begin{gathered} B=3ft*3ft \\ B=9ft^2 \end{gathered}\)

3. Sum L and B to find the surface area:

\(\begin{gathered} S=L+B \\ S=24ft^2+9ft^2 \\ S=33ft^2 \end{gathered}\)Then, the surface area of the given pyramid is 33 square feetAnswer: C

Can someone help me with this math problem asap

Can someone help me with this math problem asap

Answers

The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

How to define the absolute value function?

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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What is the surface area of the rectangle pyramid below 13 13 13

Answers

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

I need help on this.

I need help on this.

Answers

Answer:

Step-by-step explanation:

Jose is right

Let (-3,-2) be a point on the terminal side of theta. Find the csc(theta)

Answers

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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g According to the U.S. department of Agriculture (USDA), 48.9% of males aged 20 to 39 years consume the recommended daily requirement of calcium. After an aggressive "Got Milk" advertising campaign, the USDA conducts a survey of 35 randomly selected males aged 20 to 39 and finds that 21 of them consume the recommended daily allowance (RDA) of calcium. At the ????=0.05level of significance, is there evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased?

Answers

Answer:

We can conclude that there is no sufficient evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased

Step-by-step explanation:

H0 : p = 0.489

H1 : p > 0.489

Phat = x/ n ; x = 21 ; n = 35

Phat = x/ n = 21 / 35 = 0.6

Test statistic :

(Phat - P0) ÷ sqrt[P0(1 - P0) /n]

1 - P0 = 1 - 0.489 = 0.511

Phat - P0 = 0.6 - 0.489 = 0.111

Test statistic = 0.111 ÷ sqrt[(0.489 * 0.511) / 35]

Test statistic = 0.111 ÷ sqrt(0.0071394)

Test statistic = 0.111 ÷ 0.0844949

Test statistic = 1.314

Pvalue from Tstatistic :

Pvalue = P(Z < 1.314) = 0.90558

α = 0.05

Pvalue > α ; Hence, we fail to reject the Null

We can conclude that there is no sufficient evidence to conclude that the percentage of males aged 20 to 39 who consume the RDA of calcium has increased

1.11111 as a fraction

Answers

Answer:

Answer:

1.11111=111111100000

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

1.11111=1.111111

Multiply to remove 5 decimal places. Here, you multiply top and bottom by 105 = 100000

1.111111×100000100000=111111100000

Simplify the improper fraction,

=111111100000

In conclusion,

1.11111=111111100000

Step-by-step explanation:

The fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

To express the decimal 1.11111 as a fraction, we can use algebraic manipulation. Let's denote the repeating decimal as x:

x = 1.11111...

To eliminate the repeating part, we can multiply x by 10:

10x = 11.11111...

Now, we can subtract the original equation from the multiplied equation to eliminate the repeating part:

10x - x = 11.11111... - 1.11111...

Simplifying the equation:

9x = 10

Dividing both sides by 9:

x = 10/9

Therefore, the fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

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find the values of a and b such that x^2-4x+9=(x+a)^2+b

Answers

Answer:

  a = -2; b = 5

Step-by-step explanation:

Expanding the right side of the given equation, we have ...

  x^2 -4x +9 = x^2 +2ax +a^2 +b

Comparing coefficients, we see ...

  -4 = 2a . . . . . coefficient of x term

  9 = a^2 +b . . . constant term

The first of these tells us ...

  -2 = a . . . . divide by 2

The second of these tells us ...

  9 = (-2)^2 +b . . . substitute for a

  5 = b . . . . subtract 4

The values of a and b are (a, b) = (-2, 5).

Answer:

a=-2

b=5

Step-by-step explanation:

type this on mathswatch and you will get it right

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 km/h slower than the other. If the two cyclists are 120 kilometers apart after 2 hours, what is the rate of each cyclist?

Answers

Cyclist 1 = 26km/h. Cyclist 2 = 34km/h. Explanation: One cyclist is 4km/h faster and we know that they are 120 km apart in 2 hours so 4 x 2 = 8 more km in 2 hours. 52 km + 68 km = 120 km. 52/2 = 26km/h. 68/2 = 34km/h

PLEASE HELP
Does anybody remember that game people used to play as kids on the computers. When I was in 1st grade there would be this game where I placed like a number or something and then a circle or stuff would be drawn. If you know that game pls tell me.

Answers

Answer:

ABC ya?

Step-by-step explanation:

I think its in a minigame

Pls help with math !!!

Pls help with math !!!

Answers

Kevin's kick can be considered the best among the four.

To determine the most impressive kick, we can compare the distances and heights achieved by each player.

Andre's kick reached a maximum height of 17 yards and landed 48 yards away from the goal.

Juana's kick followed the path y = -x + 14 - 24, where y represents the height of the ball in yards and x represents the horizontal distance from the goal line. From the graph, we can estimate that her kick landed about 38 yards from the goal and reached a maximum height of 14 yards.

Kevin's kick is shown in the graph, indicating that it landed approximately 19 yards from the goal and had a peak height of 20 yards.

Emiko's kick reached a maximum height of 18 yards and landed approximately 20 yards from the goal.

Considering these measurements, Kevin's kick stands out. It traveled the farthest, landing closest to the goal line, and it achieved the highest height, reaching 20 yards. Consequently, Kevin's kick can be considered the best among the four.

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Basic factoring. Please help!

Basic factoring. Please help!

Answers

Answer:

3rd Option: -1(x + 15)

Step-by-step explanation:

When we factor our a negative 1, we take the opposite signs of what is given:

-1(x + 15)

To check, we simply just redistribute to check if it matches the original expression:

-x - 15

So the 3rd option is the correct choice.

Answer:

It's the third option (it's correct with you)

Step-by-step explanation:

- X - 15

So here we should the common factor between - x and - 15, where it is - 1 because both of these have minus in common.

Then the answer is:

-X - 15

= - 1 ( x + 15)

Hope this helps you..

Good Luck!

The points L(0, 5), M (-7, 1), N(-9, -5), and O(-2, -1) form quadrilateral
LMNO. Plot the points then click the "Graph Quadrilateral" button

The points L(0, 5), M (-7, 1), N(-9, -5), and O(-2, -1) form quadrilateralLMNO. Plot the points then

Answers

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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Drag steps of the solution into order to solve for x in the equation 7(x-4)=84

Answers

7x + 7*-4 =84
7x + -28 =84
7x = 112
X = 16

Strawberries cost $1.19 per pound. What is the cost of 2.16 pounds of strawberries?

PLEASEEE HELPPPP

Answers

Answer:

$ 2.57

Step-by-step explanation:

1.19 $/pound  * 2.16 pound =

Question 2 of 15
A car travels along the highway to Austin at a steady speed. When it begins, it
is 500 miles from Austin. After 5 hours, it is 200 miles from Austin. Which
function describes the car's distance from Austin? Helpppp

Answers

Answer:

d(h) = 500 - 60h

----------------------------------

This relationship is linearInitial value is 500,The rate of change (speed) is (200 - 500)/5 = - 300/5 = - 60

The function to reflect this situation isd(h) = 500 - 60h, where d- distance from Austin, h - number of hours in travel

Answer:

\(\boxed{y=500-60x}\)

where:

x is the time (in hours).y is the car's distance from Austin (in miles).

Step-by-step explanation:

Define the variables:

Let x be the time (in hours).Let y be the car's distance from Austin (in miles).

Given:

When x = 0, y = 500.When x = 5, y = 200.

Find the rate of change:

\(\implies \textsf{Rate of change}=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{500-200}{0-5}=-60\)

Therefore, for every hour that passes, the car is 60 miles closer to Austin.

Therefore, the function that describes the car's distance from Austin is:

\(\boxed{y=500-60x}\)

where:

x is the time (in hours).y is the car's distance from Austin (in miles).
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