Q9 Find the electric potential inside and outside a uniformly charged spherical shell of radius R? (i) V in =V out =0 (ii) V out (z)= 4πε 01 z q &V in (r)= 4πε 01 R q (iii) V out (z)= ε 0 R 2 zσ &V in (z)= ε 0 R σ (iv) None of the above
Electric potential is given by option is (ii) Vout(z) = 4πε₀ zq and Vin(r) = 4πε₀Rq.
The electric potential is the amount of electrical potential energy that a single charged particle has due to its location in an electric field. The change in electric potential energy in an electric field is given by the formula W = q ΔV, where W is the work done on the particle, q is the charge, and ΔV is the potential difference. Electric Potential Inside and Outside a Spherical Shell. According to Gauss' law, the electric field inside a conductor is zero. As a result, the electric potential is the same throughout the conductor. Consider a uniformly charged spherical shell with a total charge Q and radius R. Since the electric field inside the spherical shell is zero, the electric potential inside the spherical shell is the same throughout as outside. Inside the shell, we have Vin(r) = 4πε₀Rq and outside the shell, we have
Vout(z) = 4πε₀zq.
The electric potential inside and outside a uniformly charged spherical shell of radius R is therefore given by (ii) Vout(z) = 4πε₀ zq and Vin(r) = 4πε₀Rq.
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Combining negatively correlated assets having the same expected return results in a portfolio with ____ level of expected return and ____ level of risk. Select one: a. a higher; a lower b. the same; a lower c. the same; a higher d. a lower; a higher
Combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk.
When assets have a negative correlation, their returns tend to move in opposite directions. By combining these assets in a portfolio, their negative correlation offsets each other's risks to some extent. As a result, the overall risk of the portfolio is reduced.
However, the expected return of the portfolio remains the same as the individual assets, assuming they have the same expected return. This is because the negative correlation does not affect the average return of the assets, only their volatility. The diversification benefits provided by negatively correlated assets help to reduce the overall risk of the portfolio, making it less volatile than the individual assets.
Therefore, combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk. This is a desirable outcome for investors as it allows them to achieve a certain level of return while minimizing the overall risk in their investment portfolio.
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Can someone explain how to convert a quadratic function in standard form to vertex form using the "complete the square" method? Oh, please give steps so I can write them down
The required steps are explained below to convert the quadratic function into a perfect square.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the quadratic function be y = ax² + bx + c.
The first step is to take common the coefficient of x². We have
\(\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c\)
Add and subtract the half of the square the coefficient of x,
\(\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c\)
Then we have
\(\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c\)
These are the required step to get the perfect square of the quadratic function.
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I really need help! Pls! I'd appreciate it! :) Here's the question...
A block of metal has a mass of 1000g and dimensions of 7.5 cm by 6 cm by 10 cm. Use this information to find the density of the metal block.
A machine fills bags with sweets.
There are 4275 sweets.
There are 28 sweets in each full bag.
The machine fills as many bags as possible.
How many sweets are left?
Answer:
19
Step-by-step explanation:
maximum no. of bag filled by 4275 sweets,is
4275/28 ~=152
therefore , there is 4256 sweets in 152 bags
therefore,4275-4256=19 sweets are left
8.4 Area Between Two Curves Homework Name Date Period Problems 1 - 12, Sketch the region bounded by the graphs of the equations and find its area. 1. y = x2: y = 4x 2. y = x + 1: y = 5 3. x=y2; x - y = 2 4. ya = 4+x: y2 + x = 2
the area between first two curves is 10.67-unit, 2nd two curves is 8-unit, 3rd two curves is 7.5 unit, and the last two curves is
How can we calculate the area between two curves?area bounded by two curves means the curves have intersected each other and we can determine the point of intersection of them. In the next we apply the integration with limit formula for the equation of curves in where the point of intersection acts as the upper and lower limit.
Does the area always positive?while determining area we get either negative value or positive value depending on the position of curve in the xy coordinate but in real life the value of area is written as a positive number.
1. the curve y=x² and y=4x
let the two curves intersects each other so x²- 4x= 0
x=0, 4
for this value of x, we determine the values of y
y= 0, 16
now we determine the area between two curves by using the formula, ∫x²dx-∫4xdx
∫₀⁴(x²-4x) dx
[1/3×x³-³4/2×x²]₀⁴
area = -10.67
2. the curves y=x+1 and y=5 is intersected as we need to calculate the area bounded by them, 5=x+1 and x=4
for x=4, we get y= 5
now the area will be ∫₀⁴(x+1-5)dx
[1/2x²- 4x] ⁴
area= -8 unit
3. in case of 3rd two curves, x=y² and x-y=2
y²-y=2, hence y= -1, 2
the x values are x= 1, 4
the area bunded by them is ∫₋²₁{y²-(y-2)}dy
[1/3y³-1/2y²+2y]₋²₁
area =7.5 unit
4. from the last two curves y=4+x, y²= 2-x
hence, the area calculated are 10.67-unit, 8 unit and 7.5 unit respectively.
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it is used to predict the outcome of a variable of interest based on the value of a categorical variable.
The statistical technique used to predict the outcome of a variable of interest based on the value of a categorical variable is called logistic regression.
Logistic regression is a commonly used method when the dependent variable is binary or categorical. It allows us to estimate the probability of an event occurring based on one or more independent variables. The dependent variable, also known as the outcome or response variable, typically takes on two values (e.g., success/failure, yes/no).
To perform logistic regression, we use a mathematical function called the logistic function or sigmoid function, which maps any real-valued number to a value between 0 and 1. The logistic function is defined as:
P(Y=1) = 1 / (1 + e^-(β₀ + β₁X₁ + β₂X₂ + ... + βₖXₖ))
Where:
- P(Y=1) represents the probability of the event occurring.
- β₀, β₁, β₂, ..., βₖ are the coefficients to be estimated.
- X₁, X₂, ..., Xₖ are the independent variables.
To estimate the coefficients, various techniques such as maximum likelihood estimation or gradient descent can be used.
Logistic regression is a powerful statistical technique used to predict the outcome of a variable of interest based on the value of a categorical variable. By estimating the probabilities using the logistic function, we can assess the relationship between the independent variables and the likelihood of an event occurring. Logistic regression provides insights into the impact and significance of the categorical variable on the outcome, enabling prediction and inference in a wide range of fields such as medicine, marketing, and social sciences.
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Verify the following identity. Must show all work for full credit. csc? (x ) cos?
(x) = esc2 (x) - 1
csc²(x) - 1 simplifies to sec²(x). In conclusion, the given identity csc²(x) - 1 = sec²(x) is verified.
To verify the given identity csc²(x) - 1 = sec²(x), we can start with the definition of cosecant (csc) and secant (sec) functions.
The cosecant function is defined as the reciprocal of the sine function: csc(x) = 1/sin(x). The secant function is defined as the reciprocal of the cosine function: sec(x) = 1/cos(x).
Now, let's rewrite the left side of the equation using the definition of csc:
csc²(x) - 1 = (1/sin(x))² - 1 = 1/sin²(x) - 1.
Next, we'll use the Pythagorean identity for sine and cosine: sin²(x) + cos²(x) = 1.
We can rearrange this equation to solve for sin²(x): sin²(x) = 1 - cos²(x).
Now, substitute this expression into the previous equation:
1/sin²(x) - 1 = 1/(1 - cos²(x)) - 1.
To simplify this further, w:
e can use the concept of a common denominator. The common denominator for both terms is (1 - cos²(x)):
1/(1 - cos²(x)) - 1 = (1 - (1 - cos²(x)))/(1 - cos²(x)) = cos²(x)/(1 - cos²(x)).
Now, using the definition of sec, we can rewrite cos²(x)/(1 - cos²(x)) as sec²(x).
Therefore, csc²(x) - 1 simplifies to sec²(x).
In conclusion, the given identity csc²(x) - 1 = sec²(x) is verified.
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A grocery store chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper
Answer:
Step-by-step explanation:
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
Answer:
c. ∠MPN
Step-by-step explanation:
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, ∠MPN is supplementary to ∠NPI.
Anna, Laura and David earn the same monthly salary,
Each month,
Anna saves 19% of her salary and spends the rest of it,
Laura spends 17/20 of her salary and saves the rest of it,
amount of salary David saves : amount of salary he spends = 2 : 8
work out who saves the most of their salary each month,
show how you get your answer
Answer:
David saves the most (20%)
Step-by-step explanation:
The fraction Anna saves is given as 19%.
The fraction Laura saves is 1-(17/20) = 3/20 = 15/100 = 15%.
The fraction David saves is 2/(2+8) = 2/10 = 20/100 = 20%.
David saves the most of his salary each month.
Which excerpt from Samuel Taylor Coleridge's "Kubla Khan" most clearly indicates that he is describing a dream?
A. "A damsel with a dulcimer/In a vision once I saw
B. "In Xanadu did Kubla Khan/a stately pleasure dome decree..."
C. "The shadow of the dome of pleasure/Floated midway on the waves."
D.
"So twice five miles of fertile ground/With walls and towers were girdled round..."
The excerpt from Samuel Taylor Coleridge's "Kubla Khan" that most clearly indicates that he is describing a dream is option A: "A damsel with a dulcimer/In a vision once I saw."
The line "A damsel with a dulcimer/In a vision once I saw" from the poem "Kubla Khan" by Samuel Taylor Coleridge is the excerpt that most clearly indicates that he is describing a dream. This line explicitly mentions a vision, suggesting that the poet is recounting a dreamlike experience. In this line, the poet describes seeing a damsel with a dulcimer in a vision. The word "vision" strongly suggests an experience that is not grounded in reality but rather in the realm of dreams or imagination. It implies that the poet is recounting a scene that he witnessed in his mind's eye, a vision that came to him in a dream-like state. The other options do not directly indicate the dream-like nature of the poem. Option B describes the decree of a pleasure dome by Kubla Khan in Xanadu, but it does not explicitly reference a dream. Option C describes the shadow of the dome of pleasure floating on the waves, which can be interpreted as a surreal image but does not specifically mention a dream. Option D describes the physical characteristics of the fertile ground with walls and towers but does not provide any indication of a dream.
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What are the x-intercept and y-intercept of the line y 4x 5?.
x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.
What is the equation straight line?
The given equation Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the line is y = 4x+5
So the y-intercept is (x=0)
y = 5
And the x-intercept is (y=0)
4x +5 =0
x = -5/4
Hence, the x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.
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A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. (−7.0×104 s2g⋅m2)⋅ΠΠ=? s2kg⋅m2
The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)
What is the value of the missing part in the equation?To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:
\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)
In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.
To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:
1 kg / 1000 g
To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:
\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)
Simplifying this expression, we get:
\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)
Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)
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Write the equation of a line with the slope -3 and y-intercept of 7
O y = 3x + 7
O y=-3x +7
O y = 7x + -3
O y = 3x - 7
Answer:
y = - 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 3 and c = 7 , thus
y = - 3x + 7 ← equation of line
ertanyaan
Use the fifth partial sum of the exponential series to approximate each value. Round to three decimal places.
�
−
2.5
e
−2.5
using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).
To approximate the value of e^(-2.5) using the fifth partial sum of the exponential series, we can use the formula:
e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + (x^4 / 4!) + ... + (x^n / n!)
In this case, we have x = -2.5. Let's calculate the fifth partial sum:
e^(-2.5) ≈ 1 + (-2.5) + (-2.5^2 / 2!) + (-2.5^3 / 3!) + (-2.5^4 / 4!)
Using a calculator or performing the calculations step by step:
e^(-2.5) ≈ 1 + (-2.5) + (6.25 / 2) + (-15.625 / 6) + (39.0625 / 24)
e^(-2.5) ≈ 1 - 2.5 + 3.125 - 2.60417 + 1.6276
e^(-2.5) ≈ 1.64893
Therefore, using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).
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how does hermite interpolation differ from ordinary interpolation? how does a cubic spline interpolant differ from a hermite cubic interpolant?
it does not use the additional information provided by the second derivative to ensure continuity between the interpolating polynomials, which can result in a less smooth interpolant than a cubic spline.
Hermite interpolation and ordinary interpolation are both methods used to find an approximation of a function based on a given set of data points. However, they differ in the way they approach the problem.
In ordinary interpolation, a unique polynomial of degree n-1 (where n is the number of data points) is constructed that passes through all the given data points. The polynomial is then used to approximate the function between the data points. The drawback of ordinary interpolation is that it can result in a very oscillatory or wiggly interpolant, especially when the data points are unequally spaced.
On the other hand, Hermite interpolation constructs a polynomial of degree 2n-1 that not only passes through all the given data points but also includes the values of the first n-1 derivatives at each data point. This additional information allows Hermite interpolation to produce a smoother interpolant that more accurately represents the behavior of the function.
A cubic spline interpolant is a type of piecewise interpolation where a polynomial of degree 3 is used to approximate the function between each adjacent pair of data points. The splines are connected at the data points such that the function and its first and second derivatives are continuous across the entire range of data points.
In contrast, a Hermite cubic interpolant constructs a single polynomial of degree 3 that passes through all the given data points and includes the values of the first derivative at each data point. Therefore, it does not use the additional information provided by the second derivative to ensure continuity between the interpolating polynomials, which can result in a less smooth interpolant than a cubic spline.
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27 is 30% of what number?
A 8585
B 9292
C 1212
D 90
Answer:
27 is 30% of what number?
D. 90
Step-by-step explanation:
You're welcome.
3/5x+2=5.6 what is x?
Answer:
x= 1/6
Step-by-step explanation:
Multiply all the numbers by x and cancel:
3/5 + 2x =5.6x
2x + 3/5 = 5.6x (Simplify both sides of the equation)
2x + 3/5 - 5.6x = 5.6x - 5.6x (Subtract 5.6x from both sides)
-3.6x + 3/5 = 0
-3.6x + 3/5 - 3/5 = 0 - 3/5 (Subtract 3/5 from both sides)
-3.6 = -3/5
-3.6x/-3.6 = -3/5 / -3.6 (Divide both sides by -3.6)
x = 1/6
Patrice bought a can of soda using the following coins. $20 $20 , $10, $10, $5.
how much money did she spend ?
A. $45
B. $65
C. $55
Answer: B. $65
Simply add the values given to get: 20+20+10+10+5 = 40+20+5 = 65
Given that,
Patrice bought a can of soda using the following coins.
→ $20, $20, $10, $10, and $5.
We have to,
find the amount of money she spend.
Now add all coins,
→ {20 + 20} + {10 + 10 + 5}
→ 40 + 25
→ $ 65
Hence, option (B) is the answer.
Look at the photo to answer the question.
Step-by-step explanation:
A = 1
B = 0
C = AB
I think this is the answer
Write an equation in the form ax? + bc+c=0 if the roots are r1= - 7 and r2 = -5
Answer:
A
Step-by-step explanation:
PLEASE SOLVE USING DETERMINANT
One large jar and two small jars together can hold 8 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 2 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 8 and row 2 is 2.
Use matrices to solve the equation and determine how many ounces of jam are in each type of jar. Show or explain all necessary steps.
PLEASE SOLVE USING DETERMINANT
The number of ounces of jam that all of the jar can hold is about 4 large jars and 2 small jars.
What is Matrix equation ?A matrix represents a mathematical entity or characteristic through a table or array of expressions, numbers, or symbols arranged in rows and columns.
So, from the given matrix in the question, one has to compare the equations, So we have:
l + 2s = 8 ...........(i)
l - s = 2 .............(ii)
Then do subtract the second equation from the first, to remove l
3s = 6
s = 2
So also substitute 2 for s in l - s = 2
l - 2 = 2
Then sum up the 2 to both sides
l = 4
Therefore, the number of ounces of jam that each jar can hold is about 4 large jars and 2 small jars.
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50 POINTS! HELP ME PLZZ I NEED HELP WITH THIS!
Answer:
C
Step-by-step explanation:
The answer is c because:
1) Associative property means you get the same value in anyway the numbers are grouped.
2) C is grouped in another way, however, you get the same answer with both expressions.
Hope this helps!
Please help giving up 20 points for answers
Answer:
Question 2: 6x-21
Question 1: -9x+3
Step-by-step explanation:
Which expression is equivalent to -3x+9?
A.-3(x+9)
B.-3(x-3)
C.-3(x+12)
D.3(-x-3)
Explanation:
Use the distributive property to pull out the -3
When going in reverse like this, we divide each term by -3
-3x/(-3) = x
9/(-3) = -3
So -3x+9 = -3(x-3)
We can verify this by multiplying the -3 outside with each term inside
-3 times x = -3x
-3 times -3 = 9
This shows how -3(x-3) turns into -3x+9 again.
What is 230 kilometers converted to meters per minute?
Your answer would be 230,000
In Triangle XYZ, measure of angle X = 49° , XY = 18°, and
YZ = 14°. Find the measure of angle Y.
Answer:
There are two choices for angle Y: \(Y \approx 54.987^{\circ}\) for \(XZ \approx 15.193\), \(Y \approx 27.008^{\circ}\) for \(XZ \approx 8.424\).
Step-by-step explanation:
There are mistakes in the statement, correct form is now described:
In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:
The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:
\(YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X\) (1)
If we know that \(X = 49^{\circ}\), \(XY = 18\) and \(YZ = 14\), then we have the following second order polynomial:
\(14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}\)
\(XZ^{2}-23.618\cdot XZ +128 = 0\) (2)
By the Quadratic Formula we have the following result:
\(XZ \approx 15.193\,\lor\,XZ \approx 8.424\)
There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:
\(XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y\)
\(\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}\)
\(Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)\)
1) \(XZ \approx 15.193\)
\(Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]\)
\(Y \approx 54.987^{\circ}\)
2) \(XZ \approx 8.424\)
\(Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]\)
\(Y \approx 27.008^{\circ}\)
There are two choices for angle Y: \(Y \approx 54.987^{\circ}\) for \(XZ \approx 15.193\), \(Y \approx 27.008^{\circ}\) for \(XZ \approx 8.424\).
6.411
The rounded answer is
Answer:
Step-by-step explanation:
6.411=
6.411=6.4
3. Multiply (2x - 3) by (x2 - 2x + 1)
a. 2x3+ 7x2 - 8x + 3
b. 2x3- 7x2 + 8x - 3
c. X+ 7x2 - 6x + 3
d. 3x - 7x2 + 8x - 3
Answer:
B.2\(x^3\) - 7\(x^2\) + 8x -3
Step-by-step explanation:
To multiply a binomial (2 terms) by a trinomial (3 terms):
Multiply the first term of the binomial by the each term of the trinomial.
Multiply the second term of the binomial by each term of the trinomial.
Combine the expressions and simplify.
(2x-3)*(\(x^2\)-2x+1)
(2x * \(x^2\)) + (2x * -2x) + (2x * 1)
(2\(x^3\)) + (-4\(x^2\)) + (2x)
(2x-3) * (\(x^2\)-2x+1)
(-3 * \(x^2\)) + (-3 * -2x) + (-3 * 1)
(-3\(x^2\)) + (6x) + (-3)
[2\(x^3\) + -4\(x^2\) + 2x] + [-3\(x^2\) + 6x + -3]
2\(x^3\) - 7\(x^2\) + 8x -3
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