SMP 7 Describe how the graph ofg(x) = -(x-1)² + 4 is related to the graph off(x)=x².

Answer:

a) 90 boxes

b) 27 boxes

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

a-90

b-27

Step-by-step explanation:

Answer:

He will spend 282,000$ for rent of the apartment in 20 years.

He will spend 288,000$ on mortgage for the house in 20 years.

Step-by-step explanation:

Apartment:

1,175$ x 12 months= 14,100$

14,100$ x 20 years= 282,000$

House:

1,200$ x 12 months= 14,400$

14,400$ x 20 years = 288,000$

:))

Answer:

f(5) = 22; f(9) = 34

Step-by-step explanation:

f(5) = 3(5) +7

f(5) = 22

f(9) = 3(9) +7

f(9) = 34

Answer:

125

Step-by-step explanation:

C : F

10: 25

×5: ×5

50: ?

No. of fish in the tank = 25 × 5

                                    = 125

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

$65m + 125 = 1165

Step-by-step explanation:

Answer:

i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.

ii. t distribution with df = 96

iii. t = -2.38

iv. p-value = 0.0190

v. Alpha = 0.05

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.

iii. The calculated test statistic is -2.1095.

iv. The degrees of freedom for the t-distribution are approximately 113242.

v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).

iii. The test statistic for this hypothesis test is calculated as:

\(t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}\)

Where:

X = sample mean for mechanical engineering

Xe = sample mean for electrical engineering

Sm = standard deviation for mechanical engineering

Se= standard deviation for electrical engineering

nm = sample size for mechanical engineering

ne = sample size for electrical engineering

t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))

= -800 / √(3450² / 46) + (4230² / 52))

= -800 / 379.4303

= -2.1095

iv.

Calculating the degrees of freedom:

df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))

= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)

= 113242.1436

The degrees of freedom are approximately 113242.

Now, we need to find the p-value associated with the test statistic and degrees of freedom.

We can use a t-distribution table to look up the p-value.

Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.

Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.

v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

So, the significance level (alpha) is given as 5%.

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A)  the limit exists for all x, the radius of convergence is R = 6.

B)  The radius of convergence can again be found using the ratio test, which gives R = 6.

C) The radius of convergence can again be found using the ratio test, which gives R = 6.

(a) To find a power series representation for f(x), we can start by using the formula for the geometric series:

1 / (1 - t) = sum from n=0 to infinity of t^n

where |t| < 1.

We can rewrite f(x) as:

f(x) = 1 / [(6 + x)^2] = [1 / 36] * 1 / (1 - (-x/6))^2

Using the formula above, we get:

f(x) = [1 / 36] * sum from n=0 to infinity of (-x/6)^n * (n+1) choose 1

Simplifying this expression and changing the index of summation, we obtain:

f(x) = sum from n=0 to infinity of (-1)^n * (n+1) * x^n / 6^(n+2)

The radius of convergence can be found using the ratio test:

lim as n approaches infinity of |(-1)^(n+1) * (n+2) * x^(n+1) / 6^(n+3) * 6^(n+2) / ((-1)^n * (n+1) * x^n)|

= lim as n approaches infinity of |x/6| * (n+2)/(n+1)

= |x/6|

Since the limit exists for all x, the radius of convergence is R = 6.

(b) We can use the result from part (a) to find a power series for f(x) by differentiating both sides with respect to x:

f(x) = d/dx [sum from n=0 to infinity of (-1)^n * (n+1) * x^n / 6^(n+2)]

= sum from n=0 to infinity of (-1)^n * (n+1)^2 * x^(n-1) / 6^(n+2)

= sum from n=-1 to infinity of (-1)^(n+1) * (n+2)^2 * x^n / 6^(n+3)

The radius of convergence can again be found using the ratio test, which gives R = 6.

(c) We can find a power series for x^2 / (6 + x)^3 by multiplying the result from part (b) by x^2:

x^2 * f(x) = sum from n=-1 to infinity of (-1)^(n+1) * (n+2)^2 * x^(n+2) / 6^(n+3)

Shifting the index of summation and simplifying the expression, we obtain:

f(x) = sum from n=2 to infinity of (-1)^(n+1) * (n+2)*(n+1) * x^(n-2) / 6^(n+3)

Thus, the power series representation for f(x) is:

f(x) = [infinity] Σ[(-1)^(n+1) * (n+2)*(n+1) * x^(n-2) / 6^(n+3)] (n = 2)

The radius of convergence can again be found using the ratio test, which gives R = 6.

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With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

The distributive prοperty οf multiplicatiοn is a mathematical rule that states that the prοduct οf a number and a sum can be οbtained by adding the prοducts οf the number and each term in the sum. In οther wοrds, a(b+c) = ab + ac. This prοperty can be used tο simplify expressiοns by breaking them dοwn intο smaller parts.

It is an impοrtant cοncept in algebra and is οften used tο sοlve equatiοns and simplify expressiοns. The distributive prοperty can alsο be applied tο variables and expοnents, and is a fundamental principle in the study οf algebraic structures such as rings and fields.

With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

further simplified will give 3x + 6 + 5 = 3x + 11

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The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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Answer:

70 inches

Step-by-step explanation:

From the diagram attached,

Assuming the width, lenght and diagonal of the rectangle forms a right angle triangle.

Applying pythagoras theorem,

a² = b²+c²................... Equation 1

Where a = diagonal =  25 inches, b = width = 3x inches, c = length = 4x inches

Substitute these values into equation 1 and solve for x

25² = (4x)²+(3x)²

625 = 14x²+9x²

625 = 25x²

25x² = 625

x² = 625/25

x² = 25

x = √25

x = 5 inches.

Therefore,

Width(w) = 3×5 = 15 inches

Length(l) = 4×5 = 20 inches

Perimeter (P) = 2(l+b)

P = 2(15+20)

P = 2(35)

P = 70 inches

Hence the perimeter of the frame is 70 inches

The quotient of the equation 9−x² /3x and x² + 6x + 9/3x is x = 3

In arithmetic, a quotient is the quantity obtained by dividing two numbers. The quotient is widely used in mathematics, often called the integer part of division (in the case of Euclidean division), or as a fraction or ratio (in the case of proper division) .

According to the Question:

Given equation:

9-x²/3x and x²+6x+9/3x

     9-x²/3x =  x²+6x+9/3x

⇒ 3x(9-x²) = 3x(x²+6x+9)

⇒ 27x - 3x³ = 3x³+ 18x² +27x

⇒ -3x³ - 3x³ -18x² = 0

⇒ -6x³-18x² = 0

⇒ -6x² (x-3) =0

⇒ x =3

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The sum of t+4/t+5 and 9/t-1 with a common denominator is (t²+12t+41)/[(t+5)(t-1)].

To find a common denominator for the given expressions t+4/t+5 and 9/t-1, we need to determine the least common multiple (LCM) of the denominators (t+5) and (t-1):

The prime factorization of t+5 is (t+5).

The prime factorization of t-1 is (t-1).

Therefore, the LCM is (t+5)(t-1).

To convert t+4/t+5 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t-1):

t+4/t+5 = (t+4)(t-1)/[(t+5)(t-1)] = (t²+3t-4)/[(t+5)(t-1)]

To convert 9/t-1 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t+5):

9/t-1 = 9(t+5)/[(t+5)(t-1)] = (9t+45)/[(t+5)(t-1)]

Now both fractions have the same denominator, so we can add them:

(t²+3t-4)/[(t+5)(t-1)] + (9t+45)/[(t+5)(t-1)] = (t²+3t-4+9t+45)/[(t+5)(t-1)]

Simplifying the numerator gives:

t²+12t+41

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\(37 \frac 12 \%\)The overhead cost is $27 if the total cost is $72. This means that \(37 \frac 12 \%\) of the total cost is allocated to overhead expenses.

To calculate the overhead cost, we need to find \(37 \frac 12 \%\) of the total cost, which is $72.

To find \(37 \frac 12 \%\) of a value, we can multiply that value by 0.375 (which is the decimal representation of \(37 \frac 12 \%\)).

In this case, \(37 \frac 12 \%\) of $72 is calculated as:

$72 * 0.375 = $27.

Therefore, the overhead cost is $27 when the total cost is $72.

This means that out of the total cost of $72, \(37 \frac 12 \%\) ($27) is allocated to overhead expenses, while the remaining portion covers other costs such as direct expenses or materials. The overhead cost represents a significant proportion of the total cost in this scenario.

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Answer:

We can do this with u substitution

\(f(x) = ln(x^4+e^2^x)\\u = x^4+e^2^x\\f(x) = ln(u)\\f'(x) = \frac{u'}{u} \\u' = 4x^3 + 2e^2^x \\f'(x) = \frac{4x^3 + 2e^2^x}{x^4+e^2^x}\)

we can't simplify further

Answer:

A.Subtract 7.4−3.6

Step-by-step explanation:

Full Question:

12÷(7.4−3.6)+8−2

A.Subtract 7.4−3.6

B.Divide 12÷7.4

C. Add 3.6+8

D. Subtract 8 −2

Note:

Using PEMDAS

Parenthesis ( )

Exponents ²

Multiplication ×

Division ÷

Addition +

Subtraction -

Solve:

Thus, we have to start from the parenthesis which is (7.4-3.6)

Also known as :

A.Subtract 7.4−3.6

Kavinsky

Try: using the PEMDAS method. Stands out for Please Excuse My Dear Aunt Sally/Sue or parenthesis, exponents, multiplication, division, addition, and subtraction.

Answer: Choose Answer A

Why does PEMDAS help in these equations? As you can see, PEMDAS stands out as a method of solving these specific equations. It shows you a step-by-step guide to solving. This might sound difficult but in fact, it is the easiest way to solve a big equation, so indeed PEMDAS are awesome.

Hope this helps! Don't forget to hit the Thanks button! <3

Written by: RiBu

Answer:

Answer:

x = 2

Step-by-step explanation:

The vertex form of the parabola is given by  

Comparing this equation with vertex form of a parabola , where (h,k) is the vertex

h = 2

k = 3

Hence, vertex is (2,3)

Now, axis of symmetry of a parabola passes through the vertex and divide the parabola in two equal halves.

Hence, axis of symmetry of the parabola is given by

x = h

x = 2

Third option is correct.

Answer:

c

Step-by-step explanation:

Answer:

             \(\underline{\,\underline{\bold{(x+2)^2-13}}\,}\)

Step-by-step explanation:

You can do it by completing the square:

\(x^2+4x-9\\\\\underbrace{x^2+4x+4}-4-9\)

We add 4 to complete the square but we also subtract 4 because we don't  want to change the equation (+4-4=0 so it doesn't change anything in equation)

\(x^2+4x+4=x^2+2\cdot x\cdot2+2^2\)

so we get:

\(\underbrace{x^2+4x+4}-4-9\\\\{}\quad (x+2)^2-13\)

The vertex is:  (-2, -13)

(because x+2=x-h  ⇒h=-2 and  +q=-13 ⇒ q=-13)

We can also use that:

\(ax^2+bx+c=a(x-h)^2+k\)   for   \(h=\frac{-b}{2a}\,,\quad k=ah^2+bh+c\)

\(x^2+4x-9\quad\implies\quad a=1\,,\ b=4\\\\h=\frac{-4}{2\cdot1}=-\frac42=-2\\\\k=(-2)^2+4(-2)-9=4-8-9=-13\\\\a(x-h)^2+k\\\\1(x-(-2))^2+(-13)\\\\(x+2)^2-13\)

Answer:

m=80

Step-by-step explanation:

Let's solve your equation step-by-step.

181.2=5(0.05m+24.8+(0.3)(24.8))

Step 1: Simplify both sides of the equation.

181.2=5(0.05m+24.8+(0.3)(24.8))

181.2=(5)(0.05m)+(5)(24.8)+(5)((0.3)(24.8))(Distribute)

181.2=0.25m+124+37.2

181.2=(0.25m)+(124+37.2)(Combine Like Terms)

181.2=0.25m+161.2

181.2=0.25m+161.2

Step 2: Flip the equation.

0.25m+161.2=181.2

Step 3: Subtract 161.2 from both sides.

0.25m+161.2−161.2=181.2−161.2

0.25m=20

Step 4: Divide both sides by 0.25.

0.25m0.25=200.25

m=80

The function z = 3x² + 2y² – 24x + 16y + 8 has a local maximum at the point (4/3, -2/3) and a local minimum at the point (4, -2). There are no saddle points for this function.

To find the local maxima, local minima, and saddle points of a function, we need to determine its critical points and analyze their nature. To begin, we find the partial derivatives of z with respect to x and y:

∂z/∂x = 6x - 24

∂z/∂y = 4y + 16

Next, we set these partial derivatives equal to zero to find the critical points:

6x - 24 = 0  =>  x = 4

4y + 16 = 0  =>  y = -4/3

The critical point is (4, -4/3). To determine its nature, we calculate the second partial derivatives:

∂²z/∂x² = 6

∂²z/∂y² = 4

The discriminant of the Hessian matrix (∂²z/∂x² * ∂²z/∂y² - (∂²z/∂x∂y)²) is positive, which implies that the critical point (4, -4/3) is an extremum. The second derivative test can then be used to determine if it's a local maximum or minimum.

∂²z/∂x² = 6 > 0 (positive)

∂²z/∂y² = 4 > 0 (positive)

Since both second partial derivatives are positive, the critical point (4, -4/3) is a local minimum. To obtain the corresponding y-coordinate, we substitute x = 4 into ∂z/∂y:

4y + 16 = 0  =>  y = -4

Therefore, the local minimum occurs at the point (4, -4). Additionally, we can evaluate the function at the critical point (4, -4/3) to find the value of z:

z = 3(4)² + 2(-4/3)² - 24(4) + 16(-4/3) + 8 = -16/3

Now, we need to check if there are any saddle points. To do so, we examine the nature of the critical points that remain. However, we have already identified the only critical point, (4, -4/3), as a local minimum.

Therefore, there are no saddle points for this function.

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The reference triangles always have a leg perpendicular to the hypotenuse.

In a right triangle, the reference triangle is formed by dropping a perpendicular from one of the acute angles to the hypotenuse. This perpendicular leg, also known as the altitude, divides the hypotenuse into two segments. The reference triangle is created to establish a relationship between the angles and sides of the original right triangle. By considering the ratios of the sides in the reference triangle, we can apply trigonometric functions to solve various problems involving right triangles. The perpendicular leg of the reference triangle is crucial in determining the values of sine, cosine, and tangent for the given angle in the original triangle.

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The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10

A quadratic polynomial is a polynomial of the form ax² + bx + c

For any given quadratic polynomial we have

x² - (sum of zeros)x + (products of zeros) = 0

Given that the sum and product of its zeroes respectively 3/2 and 5,

We have that

Substituting the values of the variables into the equation, we have

x² - (sum of zeros)x + (products of zeros) = 0

x² - (3/2)x + (5) = 0

x² - (3/2)x + (5) = 0

Multiplying through by 2, we have

2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2

2x² - 3x + 10 = 0

So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10

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The sequence that models the amount of the radioactive substance left after each year is a geometric sequence with a recursive formula of An+1 = (2/3) * An.

The recursive formula for the sequence that models the amount of the radioactive substance left after each year can be derived from the given information that the substance decreases by one third each year. Let's denote the amount of substance after n years as An.

The recursive formula can be written as:

A1 = g (the starting amount)

An+1 = (2/3) * An (each year, the amount decreases by one third)

To determine whether the sequence is arithmetic or geometric, we need to check if the common difference or common ratio between consecutive terms is constant.

In this case, the sequence is geometric because the ratio between consecutive terms, An+1/An, is constant. It is equal to 2/3, indicating that each term is obtained by multiplying the previous term by the same ratio.

Therefore, the sequence that models the amount of the radioactive substance left after each year is a geometric sequence with a recursive formula of An+1 = (2/3) * An.

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Answer:

True

Step-by-step explanation:

Answer:

Dealership 2 has the higher loan cost.

Step-by-step explanation:

see attached answer.

The parametric form can be written as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

A matrix equation of the form \($A\overrightarrow x=0\) is called homogeneous matrix equation.

A matrix equation of the form  \($A\overrightarrow x=\overrightarrow b\) is called non - homogeneous matrix equation.

Given is to find the solution in parametric vector form.

If there are {m} free variables in the homogeneous equation, the solution set can be expressed as the span of {m} vectors :

\($\overrightarrow x=s_{1} \overrightarrow v_{1} + s_{2} \overrightarrow v_{2}+......+s_{m} \overrightarrow v_{m}\)

We have a matrix where {A} is the row equivalent to that matrix -

\(\begin{bmatrix} 1&3&0&-4 \\ 2&6&0&-8 \end{bmatrix}\)

Given matrix can be written in Augmented form as -

\(\left[ \begin{array}{cccc|c} 1&3&0&-4 & 0\\2&6&0&-8&0\\ \end{array} \right]\)

Row Reduced Echelon Form can be obtained using the following steps -

{ 1 } - Interchanging the rows R{1} and R{2}.

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0 \\ 1&3&0 &-4 & 0 \\ \end{array} \right]\)

{ 2 } - Applying the operation R{2} -> 2R{2} - R{1}, to make the second 0.

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0\\1&3&0&-4&0 \\ \end{array} \right] \;\;\;\;\;\;R_2 \rightarrow 2R_2 - R_1\)

\(\left[ \begin{array}{cccc|c} 2 & 6 & 0 & -8 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ \end{array} \right]\)

{ 3 } - Using R{1} -> R{1}/2

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0\\0&0&0&0&0\\ \end{array} \right]  \;\;R_1 \rightarrow \dfrac{1}{2} R_1\)

{ 4 } - Following equation can be deducted as

\(x_1 + 3x_2 - 4x_4 =0\)

{ 5 } - We can write the parametric form as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

Therefore, the parametric form can be written as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

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The required coefficient of\(x^6y^3\) in the expansion of \((3x−2y)^9\)is 145152.

The Binomial Theorem is a formula for the expansion of a binomial expression raised to a certain power. It helps in expressing the expansion of a binomial power that is raised to a certain power.

It states that

\((x + y)n = nC0.xn + nC1.xn-1y1 + nC2.xn-2y2 + ..... nCr.xn-ryr +....+nCn.yn\)

where nCr is the binomial coefficient of\(x^(n-r) y^r.\)

In the given problem, we are given to find the coefficient of \(x^6y^3\) in (3x−2y)^9.

First, we have to expand the binomial expression using the Binomial Theorem.

By using the Binomial Theorem, we can write:

\((3x−2y)9 = 9C0.(3x)9 + 9C1.(3x)8(−2y)1 + 9C2.(3x)7(−2y)2 + ..... + 9C6.(3x)3(−2y)6 + ..... + 9C9.(−2y)9\)

Now, we can see that the term containing x^6y^3 in the expansion will be obtained when we choose 6 x's and 3 y's from the term 9C6.

\((3x)3(−2y)6.\)

Therefore, the coefficient of x^6y^3 will be given by the product of the binomial coefficient and the product of the corresponding powers of x and y.

So, the required coefficient will be:

\(9C6.(3x)3(−2y)6 = (9! / 6!3!) . (3^3) . (−2)^6\\ = 84 . 27 . 64 \\= 145152.\)

Hence, the required coefficient of\(x^6y^3\) in the expansion of \((3x−2y)^9\)is 145152.

Note: We could have directly used the formula to calculate the binomial coefficient nCr = n! / r!(n - r)! for r = 6 and n = 9 as well, but expanding the entire expression using the Binomial Theorem gives a better understanding of how the coefficient is obtained.

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Answer:

(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.

Answer:

Step-by-step explanation:

(a-b)^3

(a-b)(a-b)(a-b)

a^3-3a^2b+3ab^2-b^3

Conclusion: The speed of the cyclist is 11 km/hr and the speed of the walker is 3 km/hr.

The speed of the cyclist is 11 km/hr and the speed of the walker is 3 km/hr.
To calculate the speed of the cyclist and the speed of the walker,

we need to use the formula for speed, which is distance divided by time.
The cyclist travels 8 km in the same time that the walker travels 3 km, so the time taken is the same for both. Let's call this time t.

The speed of the cyclist is 8 km/t and the speed of the walker is 3 km/t. To find the speed of the cyclist, we need to add 8 km to the speed of the walker.

Therefore, the speed of the cyclist is 11 km/hr and the speed of the walker is 3 km/hr.
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