What is the coefficient of x³y² in the expansion of (2x+y)5?
O A 2
OB. 5
OC. 40
OD. 80
OE. It does not exist.
SUBMI

Answer:

A

Step-by-step explanation:

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The answer is not among the given options, so it seems there may be a typo or missing information in the question.

To find the length of WT, we can use the properties of parallelograms. In a parallelogram, the diagonals bisect each other. This means that RW is equal in length to WT and RT is equal in length to SU. Given that RW = 2x + 2 and RT = 32 + 8, we can set up the equation: 2x + 2 = 32 + 8

Simplifying the equation: 2x = 40 - 2, 2x = 38, x = 38/2, x = 19. Now, we can substitute the value of x back into the equation for WT: WT = 2x + 2, WT = 2(19) + 2, WT = 38 + 2, WT = 40

Therefore, the length of WT is 40. The answer is not among the given options, so it seems there may be a typo or missing information in the question.

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B. The set is linearly independent describe the set. Given vectors are,{[ 1], [-2], [0], [ 0]}{[-5] [ 6] [0] [-7]}{[ 0] [ 0] [0] [ 4]}

To determine if the set of vectors shown to the right is a basis for R3 or not. We can check the rank of the matrix which is obtained by placing the given vectors as column vectors of a matrix and then taking the transpose of that matrix.

Then check the rank of that matrix and compare it with the number of given vectors, if rank is same as the number of vectors given then it forms a basis for R3.

To check the linearly independence and span, we can obtain the echelon form of the matrix and compare the pivot and non-pivot columns of that matrix.If the number of pivot columns is equal to the number of vectors, then they are linearly independent otherwise linearly dependent.Let A be the matrix obtained by placing given vectors as its column vectors and taking transpose of it. i.e

\[A = \begin{bmatrix}1 & -5 & 0\\-2 & 6 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]Let us obtain the echelon form of the matrix A,\[A = \begin{bmatrix}1 & -5 & 0\\-2 & 6 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\mathop{\xrightarrow{{R_2}+2{R_1}}}\begin{bmatrix}1 & -5 & 0\\0 & -4 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]\[\mathop{\xrightarrow{-\frac{1}{4}R_2}}\begin{bmatrix}1 & -5 & 0\\0 & 1 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\mathop{\xrightarrow{{R_1}+5{R_2}}}\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 0\\0 & -7 & 4\end{bmatrix}\]

As the rank of matrix A is 2 and we have 3 vectors in the given set, so the given vectors do not form a basis for R3.Also, we can see that the first two columns of echelon form matrix contain pivot elements and the last column does not have a pivot element. Therefore, we can say that the given set of vectors are linearly independent but they do not span R3. The given options are,

A. The set is a basis for R3 (False)

B. The set is linearly independent (True)

C. The set spans R3 (False)

D. None of the above are true (False) Hence, the correct options is (B).

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The dimension the  a box with a square end the largest possible volume is 10 ×10 × 23.3

First, we will need to complete the question.

Let us assume that its dimensions are h by h by w and its girth is 2h + 2w.

Volume = h²w

Where h is the length

w is the girth

From the information given, we have;

Length + girth = 90

w+(2h+2w) = 90

2h + 3w = 90

Make 'w' the subject

w = 90- 2h/3

w = 30 - 2h/3

Substitute the values

Volume = h²(30 - 2h/3)

expand the bracket

Volume = 30h² - 2h³/3

Find the differential value

Volume = 60h - 6h²

h = 10

Substitute the values

w =  30 - 2h/3

w = 30 - 2(10)/3

w = 30 - 20/3

w = 23.3 in

The dimensions are 10 ×10 × 23.3

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If a Markov chain has a valid transition matrix without absorbing states, we can find the steady-state probabilities by solving the equation πP = π or by using other methods such as eigenvalues and eigenvectors.

Let's denote the transition matrix as P. In your case, the given transition matrix is:

P = [0.6 0.3 0.1

0.1 0.8 0.1

0.6 0 0.4]

To find the steady-state probabilities, we need to solve the equation πP = π, where π is the probability vector we want to find.

πP = π

π(P - I) = 0

By finding the null space of (P - I), we can find the steady-state probabilities. However, the given matrix P does not have a steady-state distribution because one of its rows (the third row) contains only zeros. This means that state 3 is an absorbing state, meaning once you reach state 3, you can never leave it.

In such cases, the long-term behavior of the Markov chain depends on the initial distribution. If we start with a non-zero probability in state 3, the chain will remain in state 3 forever. If the initial distribution does not have a non-zero probability in state 3, the chain will never reach that state.

Therefore, for the given transition matrix, we cannot calculate the long-term probabilities for each state since there is an absorbing state present. It's important to note that the presence of an absorbing state affects the long-term behavior of the Markov chain.

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To determine the probability of event A, we need to add the probabilities of the sample points e1, e4, and e6:

P(A) = P(e1) + P(e4) + P(e6)

To determine the probability of event B, we need to add the probabilities of the sample points e2, e4, and e7:

P(B) = P(e2) + P(e4) + P(e7)

To determine the probability of event C, we need to add the probabilities of the sample points e2, e3, e5, and e7:

P(C) = P(e2) + P(e3) + P(e5) + P(e7)

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The expanded form of the expression \((0.1x^4 - \frac{1}{2}x^3)^3\) is,

\(0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9\)

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know, (a - b)³ = a³ - 3a²b + 3ab² - b³.

Given, \((0.1x^4 - \frac{1}{2}x^3)^3\).

Here, \(a = 0.1x^4\) and \(b = \frac{1}{2}x^3\).

Therefore, \((0.1x^4 - \frac{1}{2}x^3)^3\).

\(= (0.1x^4)^3 - (\frac{1}{2}x^3)^3 - 3.(0.1x^4)^2.\frac{1}{2}x^3 + 3.(0.1x^4).(\frac{1}{2}x^3)^2\).

\(= 0.001x^{12} - 0.125x^9 - 0.015x^{11} - 0.15x^{10}\).

\(= 0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9\).

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1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 =  ⁷/₉(x + 4)

1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0

Thus, let us rearrange to find the slope.

7x − 9y − 8 = 0

⇒ 9y = 7x - 8

⇒ y = ⁷/₉x - ⁸/₉

Slope; m = ⁷/₉

Now,  the point slope formula is;

y − y₁ = m(x − x₁)

where;

y₁ is the y-coordinate

x₁ is the x-coordinate

m is the slope

Thus the line Passing through (−4,4) is;

y - 4 =  ⁷/₉(x + 4)

2) The equation in general form is;

y = 4 + ⁷/₉x + ²⁸/₉

y = ⁷/₉x + ⁶⁴/₉

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The system has a single solution and the solution set is (-1, 3).

From the second equation, we can solve for y:

y = -3x

Substituting this expression into the first equation in place of y, we get:

4x + 1 = -(-3x)

Simplifying, we get:

4x + 1 = 3x

Subtracting 3x from both sides, we get:

x + 1 = 0

Solving for x, we get:

x = -1

Now we can use either of the original equations to solve for y. Using the second equation:

3(-1) + y = 0

-3 + y = 0

y = 3

So the solution to the system is (-1, 3).

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Answer:

2

Step-by-step explanation:

Since rounding to the one place relies on the decimal part, the part to focus on is the .5

becuase anything greater or equal to 5 is rounded up, the answer is 2

1.5 rounded to one decimal place will be 2.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Given a fraction number 1.5 that needed to be rounded to one decimal place. Since it's at the equidistance from the nearest whole number then we will follow the even number rule.

Rounds towards the nearest neighbor, but if equidistant, it rounds towards the even number. Both 1.5 and 2.5 are rounded to 2

therefore, 1.5 will be 2, when rounded to the nearest tenth.

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The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

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Answer:

5381.6

Step-by-step explanation:

\((2.1 × 1016) + (3.2 × 1015)\)

\( = 5381.6\)

Given:

Alexandra bought a television set for $724 in Boston.

The sales tax rate was 6.25% of the purchase price.

So, the sales tax =

The total cost =

So, the answer will be The total cost = 769.25

Answer:

False

Step-by-step explanation:

68% falls between the first standard deviation from the mean.

plus minus two would fall under 95%

Answer:

Step-by-step explanation:

If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.

275 - 6 = 269

Use tangent with the given angle and the new height. The distance is x.

tan15 = 269/x

x = 269/tan15

x = 1004ft

The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.

Hence option C is correct.

According to the information given,

We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.

Carlos's height of 6 feet can be used as one side of the triangle,

And we can use the tangent function to find the length of the adjacent side.

A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).

So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:

tan(15) = height of the tree / distance from Carlos to the tree

Distance from Carlos to the tree = height of the tree / tan(15)

Plugging in the values given:

Distance from Carlos to the tree = 275 / tan(15)

                                                      ≈ 1026

Therefore,

The nearest foot to the distance from Carlos to the tree is option C. 1026.

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A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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Parvati must donate approximately $12,166.13 today in order to fund an ongoing annual bursary of $2,750, starting in five years, considering an interest rate of 4%. This donation amount will ensure that the first payment can be made on time.

To calculate the amount Parvati must donate today for the first payment to start in five years and fund an ongoing annual bursary of $2,750, we can use the concept of present value. The present value (PV) is the current value of a future stream of cash flows, taking into account the time value of money and the interest rate.

In this case, Parvati wants to donate an amount today that will provide an annual payment of $2,750, starting in five years. The interest rate is 4%.

To calculate the present value, we can use the formula for the present value of an ordinary annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r],

where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

Using the given values:

PMT = $2,750,

r = 4% (annual interest rate),

n = 5 (number of years until the first payment).

Substituting these values into the formula:

PV = $2,750 * [(1 - (1 + 0.04)^(-5)) / 0.04].

Now, let's calculate this expression to find the amount Parvati must donate today for the ongoing annual bursary.

PV = PMT * [(1 - (1 + r)^(-n)) / r].

Substituting the given values into the formula:

PMT = $2,750,

r = 4% = 0.04 (annual interest rate),

n = 5 (number of years until the first payment).

PV = $2,750 * [(1 - (1 + 0.04)^(-5)) / 0.04].

Now, let's calculate this expression step by step

1 + 0.04 = 1.04,

1.04^(-5) ≈ 0.8227,

1 - 0.8227 ≈ 0.1773.

Now, let's substitute these values back into the equation:

PV = $2,750 * (0.1773 / 0.04).

Dividing 0.1773 by 0.04:

PV ≈ $2,750 * 4.4325.

Calculating the final result:

PV ≈ $12,166.13.

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a) The physical meaning of a solution Ψ(x,t) is the same as e^iΔΨ(x,t), where Δ is real.

b) Solutions of the time-independent Schrödinger equation can be taken as real functions.

c) The expectation value of momentum in a stationary state is zero.

d) If V(x) is an even function, ψ(x) can be either even or odd.

a) The physical observables and probabilities in quantum mechanics are determined by the magnitude of the wavefunction squared, |Ψ(x,t)|^2. The phase of the wavefunction, represented by e^iΔ, only affects the overall complex coefficient of the wavefunction and cancels out when calculating probabilities or observables. Therefore, different wavefunctions that differ only by an overall phase have the same physical meaning.

b) The time-independent Schrödinger equation represents stationary states, where the wavefunction does not change with time. Taking the complex conjugate of the wavefunction, ψ(x)∗, still satisfies the equation. As the complex conjugate of a real function is itself, this implies that the solutions can be taken to be real.

c) In a stationary state, the wavefunction does not evolve with time. The expectation value of momentum is given by the integral of the product of the complex conjugate of the wavefunction and the momentum operator. Since the wavefunction does not change with time, its derivative with respect to time is zero, resulting in an expectation value of momentum of zero.

d) The potential V(x) being an even function implies that it has symmetry around the origin. This symmetry allows for the wavefunction to also have the same symmetry. It can be represented as either an even function (symmetric about the origin) or an odd function (antisymmetric about the origin) to satisfy the Schrödinger equation.

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According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

\(k=1+log_{2} n\)

Here, n is equal to 66 and by substituting the value to the equation we get:

\(k=1+log_{2} (66)\)

k = 7.0444

k ≈ 7

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Answer:

x+50°=180°{alternate enterior angle}

x=180-50

x=130°

hope it helps ....

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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Answer:

  B.  Option 2 (only)

Step-by-step explanation:

A geometric sequence is a sequence of terms that have a common ratio.

The deposits are ...

  100, 50, 50, 50, ...

The ratios of terms of this sequence are ...

  1/2, 1, 1, 1

So, the ratio is not constant, and the sequence is not geometric.

__

The deposits are ...

  5, 10, 20, 40, ...

The ratios of terms of this sequence are ...

  10/5 = 2, 20/10 = 2, 40/20 = 2, ...

The ratio is constant, so the sequence of deposits for Option 2 is geometric.

Answer:

D

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length ) , then

V = 14³ = 2744 cm³

Answer:

D. 2744 cm³

Step-by-step explanation:

volume can be found by multiplying length × width × height

because we know that this is a cube, all side lengths are the same (meaning length, width, and height will all be the same)

so, we know our side length is 14cm, meaning that all of our measurements {length/width/height} are 14cm

length × width × height = volume

14 × 14 × 14 = 2744

when we write volume, we write it as cubed (x³)

{similarly, when we write area,  we write it as squared (x²)}

so, we would write the volume of this cube to be 2744 cm³

(option D)

hope this helps! have a lovely day :)

Ans of your question . in which class do u read?

Hey there!

1/2(8 - 6y) + 1/5(10y - 25)

DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES

= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)

= 4 - 3y + 2y - 5

COMBINE the LIKE TERMS

= (-3y + 2y) + (4 - 5)

= -3y + 2y + 4 - 5

= -1y - 1

≈ -y - 1

Therefore, your answer is: -y - 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

the expected total score from the game is 8.

Let X be the number of heads in 97 coin flips, and let Y be the sum of the dice rolls for each head. Since each coin flip and each dice roll is independent and has a well-defined probability distribution, we can use the linearity of expectation to compute the expected value of Y:

E(Y) = E(Y | X = 0) P(X = 0) + E(Y | X = 1) P(X = 1) + ... + E(Y | X = 97) P(X = 97)

The probability distribution of X is a binomial distribution with n = 97 and p = 1/2, so we have:

P(X = k) = (97 choose k) (1/2)^97

The conditional probability distribution of Y given X = k is the sum of the probability distributions of k independent dice rolls, each of which has a uniform distribution from 1 to 6. Therefore:

E(Y | X = k) = 4k * (1/6) + 4(6-k) * (1/2) * (1/6) + 4(1-k) * (1/3) * (1/6)

Simplifying and substituting, we get:

E(Y) = [4 * (1/6) * sum(k=0 to 97) (k * (97 choose k) * (1/2)^97)] + [4 * (1/6) * sum(k=0 to 97) ((6-k) * (97 choose k) * (1/2)^97)] + [4 * (1/6) * sum(k=0 to 97) ((1-k) * (97 choose k) * (1/2)^97)]

E(Y) = 4 * (1/6) * [sum(k=0 to 97) (k * (97 choose k) * (1/2)^96)] + 4 * (1/6) * [sum(k=0 to 97) ((6-k) * (97 choose k) * (1/2)^96)] + 4 * (1/6) * [sum(k=0 to 97) ((1-k) * (97 choose k) * (1/2)^96)]

We can evaluate the three sums using the binomial theorem:

sum(k=0 to 97) (k * (97 choose k) * (1/2)^96) = 48

sum(k=0 to 97) ((6-k) * (97 choose k) * (1/2)^96) = 24

sum(k=0 to 97) ((1-k) * (97 choose k) * (1/2)^96) = -24

Substituting back, we get:

E(Y) = 4 * (1/6) * (48 + 24 - 24) = 8

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Answer:

-12√3n

Step-by-step explanation:

We want to write this in its simplest form

48 = 16 * 3

√(48) = √16*3

√48 = 4 √3

so we have

-3 * 4 √3n

=

-12√3n

Answer:

81πinc^3

Step-by-step explanation:

Volume of glass = π(3)^2(12) = 108πin^3

Volume of water in glass = π(3)^2(3) = 27πin^3

Volume needed to fill completely = 108π - 27π = 81π^3

Topic: Mensuration

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