A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in metres) is

Answer:

The answer is number /Alphabetical:D

The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The experimental probability of the computer generating a 1 is D. 40 %.

First, add up the outcomes to see the total number of times the integers were generated ;

= 36 + 11 + 13 + 12 + 18

= 90

The number of times 1 was generated was 36.

The experimental probability is therefore;

= number of times 1 was generated / total number of outcomes

= 36 / 90

= 0. 4

= 40 %

Therefore, the experimental probability of the computer generating a 1 is 40 %.

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(a) Sam needs to sell 5,000 sets of plates to break even.

(b) The break-even revenue is $125,000.

(c) The break-even revenue, considering the additional cost, is $303,025.

a) To calculate the number of sets of plates that need to be sold to break even, we need to consider the fixed cost, variable cost, and selling price per set.

Each set of plates includes 8 plates, and the cost of each plate is $2. Therefore, the variable cost per set of plates is 8 * $2 = $16.

To break even, the total revenue from selling sets of plates should cover the fixed cost and variable cost. We can calculate the break-even point by dividing the fixed cost by the contribution margin per set.

Contribution margin per set = Selling price per set - Variable cost per set

Contribution margin per set = $25 - $16 = $9

Break-even point = Fixed cost / Contribution margin per set

Break-even point = $45,000 / $9

Break-even point = 5,000 sets of plates

Therefore, Sam needs to sell 5,000 sets of plates to break even.

b) To obtain the break-even revenue, we multiply the break-even point (number of sets) by the selling price per set.

Break-even revenue = Break-even point * Selling price per set

Break-even revenue = 5,000 * $25

Break-even revenue = $125,000

The break-even revenue is $125,000.

c) With the addition of the assistant, the fixed cost increases by $35,000, resulting in a new fixed cost of $45,000 + $35,000 = $80,000.

The variable cost per plate increases by 15%, which means it becomes $2 + ($2 * 0.15) = $2.30.

The new variable cost per set of plates is 8 * $2.30 = $18.40.

Contribution margin per set = Selling price per set - Variable cost per set

Contribution margin per set = $25 - $18.40 = $6.60

Break-even point = Fixed cost / Contribution margin per set

Break-even point = $80,000 / $6.60

Break-even point ≈ 12,121.21 sets of plates

Therefore, Sam needs to sell approximately 12,121 sets of plates to break even with the additional cost.

Break-even revenue = Break-even point * Selling price per set

Break-even revenue = 12,121 * $25

Break-even revenue = $303,025

The break-even revenue, considering the additional cost, is $303,025.

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Step-by-step explanation:

we multiply both sides by the denominator on the right to eliminate fraction, so we have..

p*(n+a)= (n²+a/n+a)*n+a

so we have

p(n+a)= n²+a

so opening the bracket on the left hand side we have,

p*n+p*a

pn+pa

so,

pn+pa= n²+a

so collecting like terms we have,

pn-n²= a-pa

so removing a from the equation on the right hand side we have,

pn-n²=a(1-p)

dividing both sides by the equation in the bracket on the right hand side, we have..

pn-n²/(1-p)= a

a = pn-n²/1-p

or

a = n(p-n)/1-p

The perimeter of triangle XYZ is equal to √192 or 8√3units.

In triangle XYZ, the base and the height are neither vertical nor horizontal and as such the calculations will be different.

In Mathematics and Geometry, the perimeter of a triangle can be calculated by using this mathematical equation:

P = a + b + c

Where:

P represents the perimeter of a triangle.

a, b, and c represents the side lengths of a triangle.

Next, we would determine the distance between each of the coordinates of triangle XYZ;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance XY = √[(10 - 2)² + (9 - 5)²]

Distance XY = √(64 + 16)

Distance XY = √80 units.

Distance XZ = √[(6 - 2)² + (1 - 5)²]

Distance XZ = √(16 + 16)

Distance XZ = √32 units.

Distance YZ = √[(6 - 10)² + (1 - 9)²]

Distance YZ = √(16 + 64)

Distance YZ = √80 units.

Perimeter of triangle XYZ = XY + XZ + YZ

Perimeter of triangle XYZ = √80 units + √32 units + √80 units

Perimeter of triangle XYZ = √192 or 8√3units.

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Answer: I think it’s 3

Step-by-step explanation: I took a look at 13 and 12 subtracted 6-3=3

so I believe this is the answer sorry if I’m wrong

Answer:

3?

Step-by-step explanation:

Answer:

6/8,

Step-by-step explanation:

Answer:

You tried and that’s what matters, better luck next time. I‘lol ray to help you next time. Good Job

The formula for the real portion of a complex function can be used to write re(e(1/z)) in terms of x and y: f(z) + f(z*) = re(f(z)) / 2

where z* denotes z's complex conjugate.

By applying this formula to the provided function, we obtain:

re(e(1/z)) = (e(1/z) + e(1/z*)) / 2

re(e(1/z)) = (e(x-iy) + e(x+iy)) / 2

re(e(1/z)) = (ex (cos y + I sin y) + ex (cos y - I sin y)) /2

As a result, re(e(1/z)) can be represented as ex cos y in terms of x and y.

Because it fulfills Laplace's equation, which asserts that the total of a function's second-order partial derivatives is equal to zero, this function is harmonic in every domain excluding the origin.

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The relationship between x and y is a strong negative relationship.

For this question, we need to determine the correlation coefficient,

Thus,

The correlation coefficient

= (21 - 5*6)/ \(\sqrt{9 * 10}\)

= -0.948

The above answer is too close to -1. Therefore correlation coefficient is a strong negative.

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The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.

A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.

Height of building = 54 m

Height of ground from base = 32 m Calculates the initial speed of the ball.

Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,

d = 1/2×g×t²

where g --> acceleration due to gravity

t --> time

d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².

So, 54 m = (1/2) × 9,81 m/s² × t²

=> t² = 54/4.90

=> t² = 540/49

=> t² = 11.02 sec²

=> t = 3.31963 ~ 3.32 sec

So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,

=> 32 m = 0 + v₀ₓ × 3.32 sec

=> v₀ₓ = 32/3.32

=> v₀ₓ = 9.6385 ≈ 9.64 m/sec

Hence, required value is 9.64 m/sec.

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Complete question:

A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?

Answer: C. g

Step-by-step explanation:

The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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The amount of seismic energy released increases by around 32 times for every whole-number increase in magnitude. In other words, a magnitude 7 earthquake is 32 times stronger than a magnitude 6 earthquake and produces 32 times more energy.

According to Jones, a magnitude 8 earthquake is 1,000 times more energetic than a magnitude 6, but it also spreads out and lasts longer.

In 1906 initially, it was estimated that the accident had claimed the lives of 700 individuals, but the actual death toll is now understood to have topped 3,000. Additionally, about 250,000 people were left homeless; those who survived tented in Golden Gate Park and the dunes west of the city or ran away to nearby cities. Within a short period of time, food and clothing relief shipments arrived in the city, while overseas donors from the Americas, Europe, Japan, and China sent numerous tens of millions of dollars in financial assistance. Despite receiving insurance money in the neighborhood of $300 million, the arduous job of rehabilitation was kept going by the bravery and perseverance of the locals.

A magnitude 6.9 earthquake that struck the San Francisco Bay Area on October 17, 1989, claimed 67 lives and left more than $5 billion in damages. The number of fatalities was very low despite the catastrophe being one of the most damaging and strong earthquakes to ever strike a populous area in the United States. Due to its location close to Loma Prieta Peak in the Santa Cruz Mountains, the event is also referred to as the San Francisco-Oakland earthquake and the Loma Prieta earthquake.

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False. If two lines are perpendicular, they do not have the same slope. When two lines are perpendicular, they intersect at a right angle, and their slopes are negative reciprocals of each other.

This implies that when one slope is a, the other slope is -1/a. We can define perpendicular lines using the following theorem.

The two lines in a plane are perpendicular if and only if the product of their slopes is -1. If line 1 has slope m1 and line 2 has slope m2, then the product of their slopes is m1*m2 = -1, which means m2 = -1/m1 and vice versa. The converse is also true, which means if m1*m2 = -1, then line 1 and line 2 are perpendicular.

Hence, the statement, "If two lines are perpendicular, they have the same slope" is false because the slopes of perpendicular lines are negative reciprocals of each other, not equal. Therefore, the answer is False.

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Correct answer is B. Total cost = $42000

Alistar’s 6-year investment plan consists of two periods :

Period 1 : From year 1  to year 3

Period 2 : From year 4 to year 6

In the first period, from  year 1 to 3,

Alistar make investment on his education.

In the second period, from year  4 to 6,

Amount which he starts earning = $32000

And the annual income of him = $25000

⇒ Alistar receives additional $7000 every year

Now, time taken to recover his investments = 6 years

Hence, Total cost = 7000 × 6

                              = $42000

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The probability of getting a flush when selecting 5 cards from a standard 52-card deck is about 0.198%.

Hi! To calculate the probability of getting a flush (all 5 cards from the same suit) when selecting 5 cards from a standard 52-card deck, follow these steps:

1. Calculate the total number of ways to choose 5 cards from a 52-card deck. This can be computed using combinations: C(52, 5) = 52! / (5! * (52-5)!), where ! denotes a factorial. C(52, 5) = 2,598,960.

2. Calculate the total number of ways to get a flush. There are 4 suits in a deck, and you need all 5 cards to be from the same suit. For each suit, you can choose 5 cards from the 13 available in that suit: C(13, 5) = 1,287. Since there are 4 suits, the total number of flushes is 4 * C(13, 5) = 4 * 1,287 = 5,148.

3. Compute the probability of getting a flush by dividing the total number of flushes by the total number of ways to choose 5 cards: probability = 5,148 / 2,598,960 = 0.00198, or approximately 0.198%.

So, the probability of getting a flush when selecting 5 cards from a standard 52-card deck is about 0.198%.

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The probability of getting a flush is quite low, but it is still possible.

The probability of getting a flush (all 5 cards from the same suit) if you select 5 cards from a standard 52 card deck can be calculated as follows:

There are 4 suits (clubs, diamonds, hearts, and spades) in a standard deck of cards, each with 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

The number of ways to select 5 cards from a deck of 52 cards is given by the combination formula:

\(C(52,5) = 52! / (5! \times (52-5)!) = 2,598,960\)

The number of ways to get a flush.

We can choose any one of the 4 suits for our flush, and then we need to select 5 cards from that suit.

C(13,5) ways to select 5 cards from a suit with 13 cards.

So, the total number of ways to get a flush is:

\(4 \times C(13,5) = 4 \times (13! / (5! \times (13-5)!)) = 4 \times 1,287 = 5,148\)

The probability of getting a flush when selecting 5 cards from a standard 52 card deck is:

\(P = number of ways to get a flush / total number of ways to select 5 cards\)

\(P = 5,148 / 2,598,960\)

\(P = 0.00198 or approximately 0.2\%\)

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Given that the volume of a rectangular prism is 240 cubic inches. We need to find the value of x.Let the length of the rectangular prism be l, the width of the rectangular prism be w and the height of the rectangular prism be x.

Therefore, Volume of rectangular prism = Length × Width × HeightV = l × w × xVolume of the rectangular prism is given as 240 cubic inches.240 = l × w × xThis is the required equation that will help us to determine the value of x in terms of l and w.

Now we can rearrange the equation to get the value of x in terms of l and w as:240 / lw = xThus, the value of x = 240 / lw Hence, the value of x is 240/lw.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{3}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)\(~\dotfill\\\\ \stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}\)

so we're really looking for the equation of a line whose slope is -1/3 and it passes through (2 , -6)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{1}{3} (x -2) \\\\\\ y+6=-\cfrac{1}{3}x+\cfrac{2}{3}\implies y=-\cfrac{1}{3}x+\cfrac{2}{3}-6\implies y=-\cfrac{1}{3}x-\cfrac{16}{3}\)

Once you have the probability and payout odds, you can use the above steps to determine the casino's expected gain/lose when 1000 people play the same bet throughout the day.

To accurately answer this question, more information is needed about the specific bet and the casino's odds for that bet.

However, I can help you determine the expected gain/lose once you provide the necessary information.
Step 1: Determine the probability of the bet outcome (win/lose) and the payout odds for each outcome.
Step 2: Calculate the expected gain/lose for a single bet by multiplying the probability of each outcome by its respective payout.
Step 3: Multiply the expected gain/lose per bet by the number of people (1000) to find the total expected gain/lose for the casino.

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Answer:

900.1

Step-by-step explanation:

hope this helps!

Answer:

9/50

Step-by-step explanation:

In total there are 50 people

There are 9 that are female and that didn't go to a university in England

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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The scale factor from the map to the actual hiking trails can be found to be 50, 000.

To find the scale factor, we first need to look at the scale which is :

3 cm : 1. 5 km

This scale needs to have the same units of measurement so we can convert the  1.5 km to centimeters.

This becomes :

= 1. 5 x 100, 000 cm per km

= 150, 000 cm

The scale factor for the map to the actual hiking trails is :

= 150, 000  / 3

= 50, 000

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Answer:

x=-10

x=7

Step-by-step explanation:

2x+6=x-4

2x-x=-6-4

x=-10

20x-8=18x+6

20x-18x=6+8

2x=14

x=7

Answer:

\(2(x + 3) = x - 4 \\ 2x + 6 = x - 4 \\ 2x - x = - 4 - 6 \\ x = - 10\)

___o___o___

\(4(5x - 2) = 2(9x + 3) \\ 20x - 8 = 18x + 6 \\ 20x - 18x = 6 + 8 \\ 2x = 14 \\ \\ x = \frac{14}{2} \\ \\ x = 7\)

I hope I helped you^_^

Answer:

C.

Step-by-step explanation:

This is because the absolute value of -12 is 12 and the absolute value of -2 is 2. So then the equation would look like this: 12 + 2 = 10, which is a false equation.

Hope this helps!

Answer:  b= x²-8

Step-by-step explanation:

Given:

A= 1/2 b h

A= 1/2 ( x³ + 8x² -8x -64)

h= x+8

Solution:

A= 1/2 b h                                                     >substitute what you know

1/2 ( x³ + 8x² -8x -64) = 1/2 b (x+8)              >simplify

b= \(\frac{x^{3} + 8x^{2} -8x -64}{x+8}\)

There are 2 ways to solve this. You can solve by factoring the polynomial or dividing.

Solution by Division:

Synthetic Division is easiest:

-8   |      1         8         -8         -64

      |                -8          0          64

              1        0           -8          0       =>       x²-8 = b

OR

Solution by Factoring:

b= \(\frac{x^{3} + 8x^{2} -8x -64}{x+8}\)            > group first 2 terms on top and 2nd 2 terms on top

b= \(\frac{(x^{3} + 8x^{2} )( -8x -64)}{x+8}\)       >take out gcf of both groupings

b=\(\frac{x^{2} (x + 8 )-8( x +8)}{x+8}\)           > take out x+8 on top as gcf

b=\(\frac{ (x + 8 )( x^{2} -8)}{x+8}\)                 > cancel x+8 from top and bottom

b= x²-8