A golfer hits a 50g golf ball with a golf club that weighs 200g. At the point of impact, the golf club has a velocity of 100mph. assume the coefficient of restitution is 0.80. How fast is the ball moving after impact? (Show all work)

The theory behind Euler's equation and the boundary conditions for a column with one fixed end and the other end free. Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2.

Euler's equation is derived from the Euler-Bernoulli beam theory, which states that a slender column under axial compression will buckle when the compressive stress exceeds a certain critical value. The buckling load is given by the equation P= xt^2π^2Et, where P is the buckling load, x is a dimensionless factor called the slenderness ratio (the ratio of the column length to its cross-sectional dimensions), t is the thickness of the column wall, E is the modulus of elasticity of the column material, and π is the mathematical constant pi.

For a column with both ends pinned, the value of x is given by x = nπ/L, where n is an integer and L is the length of the column. For a column with one end fixed and the other end free, the value of x is given by x = (2n - 1)π/2L, where n is an integer.  In this case, we have a column with one fixed end and the other end free, so we need to use the equation x = (2n - 1)π/2L to find the value of x. Since n can be any integer, we can choose n = 1 to simplify the equation and get x = π/2L.

Substituting this value of x into Euler's equation, we get P = (π/2L)²π²Et = π²Et/4L². This means that the buckling load for a column with one fixed end and the other end free is proportional to the modulus of elasticity and inversely proportional to the square of the length of the column.

Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2

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The amount of money Clint will plan to spend to replace the floors is $17404.09

The hardwood floor is rectangular.

Therefore,

area of hallway = 18 × 6 = 108 ft²

area of the kitchen = 20 × 30 = 600 ft²

area of the living room = 25 × 45 = 1125 ft²

area of each bedroom = 12 × 16 = 192 ft²

area of master bedroom = 14 × 20 = 280 ft²

Hence,

cost of flooring per square foot is $5.48

total cost for flooring = 108(5.48) + 600(5.48) + 1125(5.48) + 192(5.48) + 192(5.48) + 280(5.48) = $13683.56

Cost of installation is $1.49 per square.

total cost of installation = 108(1.49) + 600(1.49) + 1125(1.49) + 192(1.49) + 192(1.49) + 280(1.49) = $3720.53

Total  amount to replace the floor = 13683.56 + 3720.53 = $17404.09

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The amount it will cost to recarpet the the whole room is $891.12

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

For example, the area of a circle is given as: A = πr², where r is the radius and π is constant.

The room takes the shape of a rectangle, therefore,

Area of the room = l× w, where l is the length and w is the width.

Area = 3×8 = 24 m²

The cost of 1m² = $33.38

therefore the cost for 24m²

= 24× 33.8

= $801.12

therefore the cost to recarpet the room is $801.12

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Answer: omm

but I need this so

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation

x = 5pi/6 is not in the interval [0, pi/2]

Starting with the given equation:

4 cos x - 8 sin x cos x = 0

We can factor out 4 cos x:

4 cos x (1 - 2 sin x) = 0

So either cos x = 0 or (1 - 2 sin x) = 0.

If cos x = 0, then x = pi/2 since we're only considering the interval [0, pi/2].

If 1 - 2 sin x = 0, then sin x = 1/2, which means x = pi/6 or x = 5pi/6 in the interval [0, pi/2].

So the two solutions in the interval [0, pi/2] are x = pi/2 and x = pi/6.

That x = 5pi/6 is not in the interval [0, pi/2].

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The given equation is 4 cos x - 8 sin x cos x = 0. To find the solutions in the interval [0, pi/2], we need to solve for x.
Find the solutions within the given interval. Equation: 4 cos x - 8 sin x cos x = 0

First, let's factor out the common term, which is cos x:

cos x (4 - 8 sin x) = 0

Now, we have two cases to find the solutions:

Case 1: cos x = 0
In the interval [0, π/2], cos x is never equal to 0, so there is no solution for this case.

Case 2: 4 - 8 sin x = 0
Now, we'll solve for sin x:

8 sin x = 4
sin x = 4/8
sin x = 1/2

We know that in the interval [0, π/2], sin x = 1/2 has one solution, which is x = π/6.

So, in the given interval [0, π/2], the equation has only one solution: x = π/6.

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The correct answer is option A which is x = 3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The expression will be solved as:-

( 8x - 8 )\(^\dfrac{3}{2}\) = 64

We can write 64 as \(16^{\dfrac{3}{2}}\)

( 8x - 8 )\(^\dfrac{3}{2}\) =   \(16^{\dfrac{3}{2}}\)

8x - 8 = 16

8x = 24

x = 3

Therefore the correct answer is option A which is x = 3.

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Answer:

A. x=3.

Step-by-step explanation:

Edge 2022.

Answer:

Al evento entraron 82 adultos y 18 menores de edad.

Step-by-step explanation:

De acuerdo a la información proporcionada, puedes plantear las siguientes ecuaciones:

x+y=100 (1)

90x+45y=8190 (2), donde:

x es el número de adultos

y es el número de menores de edad

Puedes despejar x en (1):

x=100-y (3)

Después, puedes reemplazar (3) en (2):

90(100-y)+45y=8190

9000-90y+45y=8190

9000-8190=90y-45y

810=45y

y=810/45

y=18

Ahora, puedes reemplazar el valor de y en (3) para encontrar x:

x=100-y

x=100-18

x=82

De acuerdo a esto, la respuesta es que al evento entraron 82 adultos y 18 menores de edad.

The given differential equation is y' - y = e^(2x). Find the constant solutions, if any, that were lost in the solution of the differential equation.Solution:We are given a differential equation: y' - y = e^(2x)This is a linear, first order differential equation.

The general solution of this differential equation can be found by first solving the homogeneous differential equation:y' - y = 0The solution to the homogeneous differential equation is y = Ce^x, where C is the constant of integration.Now, we solve for the particular solution to the non-homogeneous differential equation. The method of variation of parameters can be used to solve this non-homogeneous differential equation.y' - y = e^(2x)

First, we find the complementary function, which is the solution to the homogeneous differential equation:y_c = Ce^xThe particular solution to the non-homogeneous differential equation is of the formThus, the constant solution that was lost in the solution of the differential equation is y = 0, which is the solution to the homogeneous differential equation.

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Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

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Answer:

Increases from points 0x,-6y to 2x,-3y.

Step-by-step explanation:

The total of five terms of the series we need to add in order to find the sum to the indicated accuracy.

A series called convergent  if the sequence of it's own partial sums tends to the a limit; that is, when addition one after the other with in order specified by the indices, partial sums become increasingly closer to a certain number.

Step1: The given series is a alternating series;

\(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{6}}\)

where \(a_{n}=\frac{1}{n^{6}}\) is decreasing monotonically with n>1.

Thus, the given alternating series is convergent series.

As a result, we determine the smallest n such that; \(a_{n}\) < 0.00005.

Thus, it is concluded that the total of the series' first n-1 terms approximates the sum within in the allowed error.

Step 2: We must discover the smallest n such that,

\(\begin{aligned}\frac{1}{n^{6}} & < 0.00005 \\\frac{1}{n^{6}} & < \frac{5}{100000}\end{aligned}\)

Taking reciprocal both side,

Because both side is positive, the inequality is reversed.

\(\begin{aligned}n^{6} & > \frac{100000}{5} \\n^{6} & > 20000\end{aligned}\)

Use hit and trial to get the result.

         \(\begin{gathered}a_{2}=2^{6}=64 \\a_{3}=3^{6}=729 \\a_{4}=4^{6}=4096\end{gathered}\)

\(\begin{gathered}a_{5}=5^{6}=15625 \\a_{6}=6^{6}=46656 \quad( > 20000)\end{gathered}\)

The smallest integer that fulfils this inequality gets satisfied is n=6.

As a result, n=6 is the lowest amount with an inaccuracy of less than 0.00005.

Therefore, to calculate the sum inside that allowed error, we simply have to add the very first five terms in the series.

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The complete question is-

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? \(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{6}}\)

Answer: 13/6

Step-by-step explanation:

Based upon the previous sequence.

1.there is a constant decrease of two in the numerator

2. There is a constant increase of one in the denominator

to find the fourth number in the sequence I used One of the numbers from the previous to determine the answer.

17/4 — —> then I followed the pattern and determine what fraction 3 was       .   .                 before it was converted into a whole number.

which would be 15/5 —> Now considering equations that are written like this also mean division, because in this case division is possible the answer would be 3, which would make the whole number 3 instead of 15/3. considering it was an improper fraction.

____________________________________________________________

Now If 15/5 wasn’t converted into 3, The answer to the  sequence would be 13/6. If you follow the pattern like I said before there is a certain amount of increase and decrease so 13/6 will be your answer. The only reason is not a whole number because 13 can’t be divided by six to get a whole number.

Answer:

The total number of hours the child spent in childcare after preschool was 96.5.

Step-by-step explanation:

The cost of the preschool, in function of the number of hours that the child spent there, is given by the following equation:

\(c(h) = 300 + 3.5h\)

If the one month charges for one child totaly $637.75, what was the total number of hours the child spent in childcare after preschool?

This is h when c(h) = 637.75. So

\(c(h) = 300 + 3.5h\)

\(637.75 = 300 + 3.5h\)

\(3.5h = 337.75\)

\(h = \frac{337.75}{3.5}\)

\(h = 96.5\)

The total number of hours the child spent in childcare after preschool was 96.5.

Answer:

the area of triangle formula is A = B*H  / 2 so it means 16 square = (x+4) x /2 so x²+4x -32=0, D' = 2²- (-32)= 36, sqrt of D' = 6 so x = -2 -6 = -8 or x= -2 +6 = 4 x must be positive so x = 4

Step-by-step explanation:

i really hoped this helped you.

The square of the hypotenuse is equal to the sum of the square of other two sides. The value of x from the given diagram to the nearest tenth is 11.2

According to the theorem, the square of the hypotenuse is equal to the sum of the square of other two sides.

From the diagram

hypotenuse = 5.6 + 8.4 = 14

Other sides are x and 8.4

According to the theorem:

14^2 = x^2 + 8.4^2

x^2 = 14^2 - 8.4^2

Simplify

x^2 = 196 - 70.56
x^2 = 125.44

x = 11.2

Hence the value of x from the given diagram to the nearest tenth is 11.2

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Answer:

11.2

Step-by-step explanation:

just did it

Answer:4x-y=8

Step-by-step explanation:

It is linear

move y to the left side

8=4x-y

4x-y=8

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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The interquartile range (IQR) is a measure of variability in a dataset that is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

Quartiles divide a dataset into four equal parts, with Q1 representing the 25th percentile and Q3 representing the 75th percentile.

To find the interquartile range, you first need to find the values of Q1 and Q3. Here's an example:

Example:

Consider the following dataset of 11 numbers: 1, 3, 4, 6, 7, 9, 10, 13, 14, 18, 20.

First, we need to order the data in ascending order,

1, 3, 4, 6, 7, 9, 10, 13, 14, 18, 20

Next, we find the median of the entire dataset. Since there are 11 numbers, the median is the 6th number, which is 7.

We divide the dataset into two halves, the first half consists of the numbers below the median, and the second half consists of the numbers above the median. In this case, the first half is 1, 3, 4, 6, and 7, and the second half is 9, 10, 13, 14, 18, and 20.

We find the median of each half of the dataset. For the first half, the median is the average of the two middle numbers, which are 4 and 6. So Q1 = 5. For the second half, the median is the average of the two middle numbers, which are 13 and 14. So Q3 = 13.5.

Finally, we calculate the interquartile range by subtracting Q1 from Q3: IQR = Q3 - Q1 = 13.5 - 5 = 8.5.

So the interquartile range for this dataset is 8.5. This means that the middle 50% of the data is contained within a range of 8.5 units.

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Answer:

The total is 105 miles ..........,....

Given:

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

\(P(x)=-12x^2+120x\)

To find:

The current that will produce the maximum power.

Solution:

We have,

\(P(x)=-12x^2+120x\)

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is \(f(x)=ax^2+bx+c\), then

\(Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)\)

In the given function, a=-12 and b=120. So,

\(-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}\)

\(-\dfrac{b}{2a}=-\dfrac{120}{-24}\)

\(-\dfrac{b}{2a}=5\)

Putting x=5 in the given function, we get

\(P(5)=-12(5)^2+120(5)\)

\(P(5)=-12(25)+600\)

\(P(5)=-300+600\)

\(P(5)=300\)

Therefore, 5 watt current will produce the maximum power of 300 amperes.

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer:

root 49= 7^2

root 100= 10^2

root 144= 12^2

root 324= 18^2

root 441= 21^2

Step-by-step explanation:

32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

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Here's ur perfect answer

The term "mean" or "average" refers to a statistical measure that describes the central value of a set of data.

It is found by adding all the numbers in a set and dividing the sum by the total number of items in the set. The mean is a valuable tool in interpreting and comparing sets of data. Given below are the solutions to the problems presented:

a. Mean (average) = (24 + 45 + 38 + 56 + 27)/5= 190/5= 38

b. Mean (average) = (24 + 31 + 17 + 39 + 9 + 17)/6= 137/6= 22.83

c. Mean (average) = (125 + 136 + 174 + 116 + 164)/5= 715/5= 143

d. Mean (average) = (3.8 + 9.2 + 6.7 + 11.5)/4= 31.2/4= 7.8e.

Mean (average) = (7.3 + 7.5 + 7.0 + 8.1 + 8.0)/5= 38.9/5= 7.78

Therefore, the mean (average) of the given sets of numbers is:

a. 38 b. 22.83 c. 143 d. 7.8 e. 7.78

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Answer:

16km

Step-by-step explanation:

Answer:

I REALLY hope I'm not wrong but I think it's 16

Step-by-step explanation:

I don't know I divided 224 by 14 to get 16.

To get an area you have to multiply length times width and the length is 14 so all you have to do if divide 224 by 14 to get your answer

Again, SO sorry if im wrong

Answer:

21

Step-by-step explanation:

Answer:

c = 16

Step-by-step explanation:

We have (a + b)² = a² + 2ab + b²

x² + 8x + c is of the form a² + 2ab + b²

where x² = a²

8x = 2ab

and c = b²

⇒ x² + 8x + c = (x + √c)² which is a perfect square

x² = a² ⇒ x = a

8x = 2ab

⇒ 8x = 2xb

⇒ b = 8x/(2x)

⇒ b = 4

c = b²

⇒ c = 4²

⇒ c = 16

(x + √c)² = (x + √16)²

= (x + 4)²

= x² + 2(x)(4) + 4²

= x² + 8x + 16

Therefore, c = 16 makes the expression a perfect square