Finding the work done in stretching or compressing a spring.

Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.

In this problem we assume that the force applied doesn't distort the metal in the spring.

A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.

Answer:

0,8,5

Step-by-step explanation:

x+22 <32

Subtract 22 from each side

x+22-22 <32-22

x <10

The choices that fit

0,8,5

Answer:

Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.

Step-by-step explanation:

x + 22 < 32

This problem is fairly simple! All we need to do is substitute each number given for x and compute to find out if the equation will be true! First what we need to do is plug in each number given into our variable x. Our numbers are: 0, 10, 8, 71, 15, and 5

x = 0

0 + 22 < 32

22 < 32

Is 22 less than 32? It is! So it belongs to the solution set.

x = 10

10 + 22 < 32

32 < 32

32 is equal to 32, not less than 32. A number cannot be itself and less than itself, thus x = 10 does not belong to the solution set.

x = 8

8 + 22 < 32

30 < 32

Is 30 less than 32? Yes! Since the inequality is true (that's what these kinds of equations are called) it  belongs to the solution set.

x = 71

71 + 22 < 32

94 < 32

Is 94 less than 32? No. 71 does not belong to this solution set.

x = 15

15 + 22 < 32

37 < 32

37 is not less than 32. Therefore it doesn't belong to the solution set.

x = 5

5 + 22 < 32

27 < 32

Is 27 less than 32? Yes. Therefore, it belongs to the solution set.

Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.

Answer:

13p

Step-by-step explanation:

12p+p

Factor out the p

p(12+1)

p (13)

13p

Answer:A

Step-by-step explanation:

h=85 f=36

Since it is a right angled triangle we can apply Pythagoras principle to get g

g=√(h^2 - f^2)

g=√(85^2 - 36^2)

g=√(85x85 - 36x36)

g=√(7225 - 1296)

g=√(5929)

g=77

Answer:

P represents the population in year 0

Step-by-step explanation:

The exponential growth function is f(x) = a (1 + r)^t, where a is the initial

amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth

in decimal ant is the time of growth

the function C(t) = P(1 + r)^t represents the population of

centerville at year t, where P is the initial population and r is the

rate of increase

If your investment is increased 10% annually, then that means

each year, your total has multiplied itself by 110% (the growth factor

is 1 + 10/100 = 1.1)

(1 + r) is the factor grows each year

C(t) = P(1 + r)^t

C depends on P(starting population) , r(the increasing rate and

t(the time in year)

r is the rate of increase means the percentage of increasing , then

0 < r < 1

r is not less than 0

P is the initial amount when t = 0

P represents the population in year 0

Answer:

P represents the population in year 0

Step-by-step explanation:

Answer:

  [tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]

Step-by-step explanation:

  [tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]

Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.

For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.

_____

Many calculators, spreadsheets, and web sites can do this tedious math for you.

Answer:

4x - 5y = 10

Step-by-step explanation:

Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.

Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:

4(-5) - 5(-6) = C, or

-20 + 30 = C.  Thus, C = 10, and the equation of the new line is

4x - 5y = 10

The equation of line is 4x - 5y = 10

A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.

Given the points (-5,-6)

and parallel to line 4x - 5y = 35...…..(1)

the equation of line is (y - y₁) = m( x - x₁)

for parallel line condition the value of m is equal to both equations

converting eq. 1 in the form of y = mx + c

4x - 5y = 35

we get y = 4/5x -7

here m = 4/5 and c = -7

substitute the value of m in  equation of line

where y₁ = -6; x₁ = -5

(y - (-6)) = 4/5(x - (-5))

y +6 = 4/5(x+5)

simplify above eq. we get

4x - 5y = 20

Hence the equation of  the line that passes through the point (- 5, - 6) is  4x - 5y = 20

Learn more about equation of line

https://brainly.com/question/29774095

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Answer:

15[tex]\pi[/tex]

Step-by-step explanation:

with diameter

A=[tex]\pi[/tex]d

A=[tex]\pi[/tex](15)

A=15[tex]\pi[/tex]

Answer:

The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.

Step-by-step explanation:

The slope of the model,

m = 15.345

c = 24

After comparing with the equation,

⇒  [tex]y=mx+c[/tex]

we get,

⇒     [tex]=15.345x + 24[/tex]

The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.

So that the above is the right answer.

Answer:

  x = 3

Step-by-step explanation:

2(x)+2=8

2*x+2-(8)=0

Pull out like factors :

2x - 6  =   2 • (x - 3)

2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

 x-3 = 0

X=3

Answer:

x= 3

Step-by-step explanation:

2x+2=8

substact 2 from both sides of the eqation,

then you get 2x=6

then you divide each side by 2 and get x= 3

hope this helped, good luck !!

brainliest ?? :))

Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:40

Step-by-step explanation:

21+8=29

29+11=40

Answer A

Step-by-step explanation:14+23-5

Answer:

im so sorry

Step-by-step explanation:

Answer:

(1/3)*(5 1/2) = 1.83333333333 or 1.8

Step-by-step explanation:

Answer:

15847

Step-by-step explanation:

I did the math

Answer:

15,847

Step-by-step explanation:

Answer:

A D E

Step-by-step explanation:

Answer:e

Step-by-step explanation:

Answer: 92 and 94

Step-by-step explanation:

x = first number

x + 2 = second number

x + x + 2 = 186

simplify

2x + 2 = 186

subtract 2 from both sides

2x = 184

divide both sides by 2

x = 92

92 + 2 = 94

The numbers are 92 and 94.

Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even integers here.

Any 2 consecutive even integers can be represented as x + x + 2.

So we can represent our integers as follows.

X ⇒ first integer

X + 2 ⇒ second integer

Since their sum is 168, our equation reads x + x + 2 = 186.

Simplifying on the left side gives us 2x + 2 = 186.

Now subtract 2 from both sides to get 2x = 184.

Now divide both sides by 2 and we find that x = 92.

If x = 92, then x + 2 will be 92 + 2 or 94.

So our two consecutive integers are 92 and 94.

Answer:

No more lonely time

Step-by-step explanation:

I have shriek to keep me company in bed;)

Answer:

- Something unpredictable -

Step-by-step explanation:

I would just scream all day about my appearance

Answer:

$2.1 per pound

Step-by-step explanation:

price/pounds

52.92 / 25 = 2.1

Answer:

15x-8=0

x=8/15

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

least common multiple

10 = 2*5

3 = 3

2*3*5 = 30

The least common multiple is 30

Answer:

20

Step-by-step explanation:

Since the truck goes 1040 miles and costs 52 gallons of gas every tiime it goes 1040 miles, we can divide 1040 by 52 to see how far 1 gallon of gas will get you.  1040/52=20 so every 20 miles cost 1 gallon of gas

Answer:

DUEDY A. 32 degrees

Step-by-step explanation:

PATROLLING WEE WOOO

Xd

Answer:

55  125

Step-by-step explanation:

Let the smaller angle = x

Let the larger angle = x + 70

They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.

x + x + 70 = 180

2x + 70 = 180

2x + 70 - 70 = 180 - 70

2x = 110

2x/2 = 110/2

x = 55

the smaller angle = 55 degrees

The larger angle = 55 + 70 = 125

Answer:

B. Dependent, 1/70

Step-by-step explanation:

The probability that the first pencil is yellow is 10/50.

There are now 49 pencils, so the probability that the second pencil is blue is 7/49.

There are now 48 pencils, so the probability that the third pencil is red is 24/48.

The total probability is (10/50) (7/49) (24/48) = 1/70.

Since the pencils aren't replaced after selection, each event changes the probability of the next, so the events are dependent.

Answer:

Step-by-step explanation:

Adding any multiple of 2π radians to the angle will result in the same point. So, one set of coordinates of the same point can be ...

  (7, π/3 +2kπ) . . . . for any integer k

The value of the radius can be negated, and an odd multiple of π can be added to the angle to get the same point. Another set of coordinates of the same point can be ...

  (-7, 4π/3 +2kπ) . . . . for any integer k

Answer:

( 2, 4 )

Step-by-step explanation:

Look at the attachment

Answer:

D. 290 square cm

Step-by-step explanation:

Surface area of polyhedron

[tex]= 2 \times 65 + 7 \times 8 + 4 \times 8 + 3 \times 8 + 3(2 \times 8) \\ = 130 + 56 + 32 + 24 + 48 \\ = 290 \: {cm}^{2} [/tex]

Step-by-step explanation:

She needs to baby sit for 5 hours = 5 x 110 = 550

Answer:

-> a + c = 1250 ____________ (1)

-> 8a + 5c = 7300 __________(2)

There were 900 children and 350 adults.

Step-by-step explanation:

Let the number of children at the carnival be c.

Let the number of adults at the carnival be a.

The admission fee at a carnival is $5 for children and $8 for adults on Friday.

1250 people attended the carnival and $7300 was collected. This means two things:

-> a + c = 1250 ____________ (1)

-> 8a + 5c = 7300 __________(2)

We now have a system of equations representing the problem.

To solve, make a subject of formula in (1):

a = 1250 - c _______(3)

Put (3) in (2):

8(1250 - c) + 5c = 7300

10000 - 8c + 5c = 7300

10000 - 7300 = 3c

3c = 2700

c = 2700 / 3 = 900

Put the value of c back in (3):

a = 1250 - 900 = 350

Therefore, there were 900 children and 350 adults at the carnival.

Answer:350000

Step-by-step explanation:

The number is 350000

350000 rounded to the nearest hundred thousand is 400000

350000 rounded to the nearest ten thousand is 350000