A spring has a natural length of 30.0 cm. If a 20.0-N force is required to keep it stretched to a length of 42.0 cm, how much work W is required to stretch it from 30.0 cm to 36.0 cm? (Round your answer to three decimal places.) W = ______ J

The worth at the end of the third​ year is 15,400.

Depreciation:

The purchase value of an asset is the amount that it is purchased for. The value of the asset after a certain number of years is the difference between the purchase value and the accumulated depreciation.

There is a general formula to calculate Depreciation:

Depreciation Method = (Cost of an Asset – Residual Value)/Useful life of an Asset.

Given that Cost of an Asset=25000

Residual Value=2600

The useful life of an Asset=7

Now plug the given values in the above formula:

(25,000-2,600)/7=22,400/7=3,200

DM=3,200 which is calculated annually.

For the 3 years worth:

25,000-3,200*3

25,000-9,600=15,400.

At the end of the third year, the worth is 15,400.

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Answer:

2x² + 14x + 6

Step-by-step explanation:

A match box is in the shape of a right rectangular prism so we can use the formula for the surface area of such a solid

A=2(wl+hl+hw)

where l = length, w=width and h = height

Substituting l = x, w = x+1 and height = 3 we get

wl = x(x + 1) = x² + x

hl = 3x

hw = 3(x + 1) = 3x + 3

So A = 2( x² + x + 3x + 3x + 3)

A = 2(x² + 7x + 3)

A = 2x² + 14x + 6

Answer:

The second choices is the answer

{(-6,6), (8, 2), (8, -1), (3,3)} as you can see there's a repeating value of x or the Domain which is the 8.

Answer:

infinite many solutions

Step-by-step explanation:

Can be a useful tool for exploring the behavior of the solution to the ODE and understanding the accuracy of the approximation. The given statement is true.

True. It is possible to set up a spreadsheet to compute the iterations of Euler's method for approximating solutions to first-order ordinary differential equations (ODEs).

Euler's method is a numerical method used to approximate solutions to first-order ODEs. It involves approximating the solution to the ODE at discrete time steps using a simple iterative formula.

To set up a spreadsheet to compute the iterations of Euler's method, we can use the following steps:

Set up the time step, h. This is the distance between the discrete time points at which we will approximate the solution. We can choose a small value for h to get more accurate approximations, but this will increase the number of iterations needed.

Set up the initial condition. This is the value of the solution at the initial time point, t_0.

Define the ODE. This is the equation that describes how the solution changes with time. For example, if we are approximating the solution to the ODE dy/dt = f(t,y), we would enter the function f(t,y) in a cell.

Set up the iterative formula. Euler's method uses the formula y_(n+1) = y_n + hf(t_n,y_n), where y_n is the approximate solution at time t_n, and y_(n+1) is the approximate solution at time t_(n+1) = t_n + h.

Fill in the spreadsheet with the initial condition and the iterative formula. We can use the copy and paste functions to quickly fill in the formula for each time step.

Finally, we can graph the approximate solution to the ODE using the spreadsheet's graphing capabilities.

In summary, it is indeed possible to set up a spreadsheet to compute the iterations of Euler's method for approximating solutions to first-order ODEs. This can be a useful tool for exploring the behavior of the solution to the ODE and understanding the accuracy of the approximation.

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Answer:

$39.77

Step-by-step explanation:

Answer:

x + y =2

-x         -x

y = -1x + 2

Perpendicular is y= 1x + 2

Step-by-step explanation:

Answer:

2 * x = 12

Step-by-step explanation:

Answer:

2x = 12

Step-by-step explanation:

let the number be x then 2 times the number is 2x. so

2x = 12 ← in equation form

The reasonable estimate for the length of side DE is 3 units

Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.

Using the similarity theorem of a triangle, this is expressed as:

AC = DE

Using the pythagoras theorem to get the length of AC:

AB^2 = AC^2 + BC^2

5^2 + AC^2 + 4^2

AC^2 = 25 - 16

AC^2 = 9

AC= 3

Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units

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Answer:

5/3

Step-by-step explanation:

Answer:

the answer is -1 this is correct because a calculator is alwayd your frie d

Answer: -1

Step-by-step explanation:

6 times 5 is 30, then you add negative 36, which is really subtraction, so you get -6 divided by a positive 6 (negative divided by a positive is negative) which gives you -1

The probability that 3 < X < 6 is 0.0106. To find P(3 < X < 6 | Y), we need to integrate the joint pdf f(x,y) over the given range of X, which is 3 < X < 6. We can express this probability as follows:

P(3 < X < 6 | Y) = ∫3 to 6 10e^(-2x-5y) dx
Integrating this expression, we get:
P(3 < X < 6 | Y) = (-5/2)e^(-15y) [e^(-6) - e^(-3)]
To find the overall probability P(3 < X < 6), we need to integrate this expression over the range of Y, which is Y > 0. This can be expressed as follows:
P(3 < X < 6) = ∫0 to ∞ P(3 < X < 6 | Y) * f_Y(y) dy
where f_Y(y) is the marginal pdf of Y, which we can find by integrating the joint pdf f(x,y) with respect to X:
f_Y(y) = ∫0 to ∞ 10e^(-2x-5y) dx = 5e^(-5y)
Substituting this expression for f_Y(y), we get:
P(3 < X < 6) = ∫0 to ∞ (-5/2)e^(-15y) [e^(-6) - e^(-3)] * 5e^(-5y) dy
Simplifying this expression and evaluating the integral, we get:
P(3 < X < 6) = 0.0106 (rounded to 4 decimal places)
Therefore, the probability that 3 < X < 6 is 0.0106.

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i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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a) If the magnitude of force F is 78 N, and α=68° and γ=40° the magnitude of the Fx component is 26.76 N.

b) The magnitude of the Fy component is 72.79 N.

c) The magnitude of the Fz component is 59.51 N.

To find the x, y, and z components of the force F, we use trigonometry. We first identify the angles α, β, and γ, which represent the angles that the force makes with the x, y, and z axes, respectively.

We can use trigonometry to find the x, y, and z components of the force F, as follows and then, we use the formulas for finding the x, y, and z components of a force vector in terms of its magnitude and the angles it makes with the axes. Specifically, we use the cosine function to find the x and z components, and the sine function to find the y component.

Finally, we substitute the given values for the magnitude of the force and the angles α and γ to calculate the x and z components, and the angle β to calculate the y component.

a) Fx = F cos(α) = 78 N × cos(68°) = 26.76 N

b) Fy = F cos(β) = 78 N × sin(68°) = 72.79 N

c) Fz = F cos(γ) = 78 N × cos(40°) = 59.51 N

Therefore, the x component of the force is 26.76 N, the y component is 72.79 N, and the z component is 59.51 N.

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The question is -

The bolt is subjected to the force F, which has components acting along the x,y, and z axes as shown.

a) If the magnitude of F is 78 N, and α=68° and γ=40°, determine the magnitude of the Fx component,

b) determine the magnitude of the Fy component,

c) determine the magnitude of the Fz component.

Answer:

64

Step-by-step explanation:

Answer:

64...i think

Step-by-step explanation:

125 - 88=37

88-64=24

PLS MARK BRAINLIEST

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The given exponential function represents the growth in function with a percentage increase as 57.3%.

Given we have the exponential function as :

y=8800(1.573)ˣ

it is in the form of: y=k.aˣ

therefore, if a>2 then the function represents growth.

and if a<1 then the function represents decay.

now, x=1.573

1.573 > 1

so, the function represents change in growth.

therefore, 1.573 - 1

= 0.573

= 57.3%

hence the change in growth of the function is increased by 57.3%.

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The geometric series is convergent and its sum is \(1/\sqrt{10}\)

A geometric series is a series of numbers where each term is found by multiplying the preceding term by a constant ratio. It can be represented by the formula\(a + ar + ar^2 + ar^3 + ...\) where a is the first term, r is the common ratio, and the series continues to infinity. The sum of a geometric series can be calculated using the formula \(S = a(1 - r^n) / (1 - r)\), where S is the sum of the first n terms.

The given series is a geometric series with a common ratio of \(1/\sqrt{10}\)
For a geometric series to be convergent, the absolute value of the common ratio must be less than 1. In this case,\(|1/√10|\)is less than 1, so the series is convergent.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

sum = a / (1 - r),

where a is the first term and r is the common ratio.

Plugging in the values, we get:

\(sum = 1 / (\sqrt{10}  - 1)\)

Therefore, the geometric series is convergent and its sum is 1 / (\(\sqrt{10}\) - 1).

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The critical value for a left-tailed test of a population standard deviation for a sample of size n=15 is 6.571, 23.685. Therefore, the correct answer is option B.

Critical value is an essential cut-off value that defines the region where the test statistic is unlikely to lie.

Given,

Sample size = n = 15

Level of significance = α=0.05

Here we use Chi-square test. Because the sample size is given for population standard deviation,

For the chi-square test the degrees of freedom = n-1= 15-1=14

The critical values are (6.571, 23.685)...... From the chi-square critical table.

Therefore, the correct answer is option B.

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"Your question is incomplete, probably the complete question/missing part is:"

Determine the critical value for a left-tailed test of a population standard deviation for a sample of size n=15 at the α=0.05 level of significance. Round to three decimal places.

a) 5.629, 26.119

b) 6.571, 23.685

c) 7.261, 24.996

d) 6.262, 27.488

Answer:

y = 7x

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (100, 700 ) ← 2 points on the line

m = \(\frac{700-0}{100-0}\) = \(\frac{700}{100}\) = 7

y = 7 x ← equation of line

The points that must lie on the same quadrant are given as follows:

(p, q) and (2p, 2q).

When an integer is multiplied by 2, it's signal remains the same, hence the points that must lie on the same quadrant are given as follows:

(p, q) and (2p, 2q).

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Answer:

B. (p, q) and (2p, 2q) (correct)

Step-by-step explanation:

Question being asked: If p and q are nonzero integers, which pair of points must lie in the same quadrant?

(p, q) and (q, p) (incorrect)

(p, q) and (2p, 2q) (correct)

(p, q) and (–p, –q)(incorrect)

(p, q) and (p – 2, q – 2)(incorrect)

Hope this helps you :)

A) The third fundamental form of a differentiable surface is a mathematical concept that characterizes the intrinsic geometry of the surface. It is defined in terms of the second derivatives of the surface's parameterization. Geometrically, the third fundamental form measures the rate of change of the surface's unit normal vector as one moves in the direction of the surface.

Proof:

The third fundamental form, denoted as III, is given by the equation:

III = -N · (d²r/du²) · (d²r/dv²) / |dr/du × dr/dv|,

where N is the unit normal vector to the surface, r(u, v) is the parameterization of the surface, and d²r/du² and d²r/dv² are the second derivatives of r with respect to u and v, respectively. |dr/du × dr/dv| represents the magnitude of the cross product of the partial derivatives of r.

B) The properties of the third fundamental form include:

1. Invariance under reparameterization: The third fundamental form is invariant under changes in the parameterization of the surface. This property ensures that the geometric information encoded by the third fundamental form remains consistent regardless of how the surface is parameterized.

2. Symmetry: The third fundamental form is symmetric with respect to the two variables u and v. In other words, swapping the roles of u and v does not change the value of the third fundamental form.

3. Relationship with the second fundamental form: The third fundamental form is related to the second fundamental form, which characterizes the extrinsic curvature of the surface. More specifically, the third fundamental form is expressed in terms of the second fundamental form as:

III = -N · L,

where L is the linear operator defined as:

L = (d²r/dv²) · S · (d²r/du²) - (d²r/dv²) · S · (d²r/dv²),

and S is the shape operator associated with the surface.

The proofs for these properties involve calculations using the definition and properties of the second fundamental form, as well as manipulation of the differential operators. These proofs require a more detailed understanding of differential geometry and are beyond the scope of this brief explanation.

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The length of the side of the square lawn is 18 meters, and the cost of putting grass in the lawn is ₹3888 at ₹12 per square metre.

Let the side of the square lawn be x meters.

Then, the area of the lawn is x² square meters.

Given that the cost of putting grass in the lawn is ₹3888 at ₹12 per square metre.

So, the cost of putting grass in x² square meters is ₹3888.

Therefore, we can write:

12 x² = 3888

Dividing both sides by 12, we get:

x² = 324

Taking square root on both sides, we get:

x = ±18

Since x is the length of the side of the square lawn, it must be positive. Therefore, the length of the side of the lawn is 18 meters.

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Answer: x = 30

Step-by-step explanation:

Since AB and CD are straight lines, vertical angles formed by them are congruent. Angle DOB is equal to angle AOC which is equal to 2x. Since you know that a straight angle is equal to 180 degrees, you can say :

2x + 90 + x = 180

3x + 90 = 180

3x = 90

x=30

Hope this helped :)

Answer:

x=4

Step-by-step explanation:

5x-7=13

5x=13+7

5x=20

x=20/5

x=4

Answer:

x = 4

Step-by-step explanation:

5x - 7 = 13

add 7 to both sides:

5x - 7 + 7 = 13 + 7

5x = 20

divide both sides by 5

\(\frac{5x}{5} = \frac{20}{5}\)

x = 4

Answer:

4/15

Step-by-step explanation:

what's the answer? 4/5×1/3?

Answer:

8 inches

Step-by-step explanation:

L x 6 x4=192

192/24

L=8

\(\frac{1}{2} x+6(x+15)=12\\\\\frac{1}{2} x+6x+90=12\\\\6\frac{1}{2} x+90=12\\6\frac{1}{2} x=-78\\x=-12\)

\(y=x+15\\y=-12+15\\y=3\)