Y-3's latest collection daringly reimagines the brand's signature codes. adidas and Yohji Yamamoto continue their industry defining partnership with a triumphant offering of audacious sportswear, reimagined through a distinctly avant-garde lens. This season, Y-3 shines a light on its most iconic color, contrasting the luminosity of Orange with ... x^{2}-x-6=0 -x+3\gt 2x+1 ; line\:(1,\:2),\:(3,\:1) f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More Buy Tronxy Silent Mainboard with Wire Cable for XY-3 PRO/XY-3 SE Series in China. Check Tronxy Silent Mainboard with Wire Cable for ...Solve for one of the variables in the first equation (in this case, I will solve for X): X = Y + 3. Then use that value of X in the second equation to solve for Y: X + 3Y = 9. (Y + 3) + 3Y = 9. 4Y + 3 = 9. 4Y = 6. Y = 1.5. Use the value of Y …Click here:point_up_2:to get an answer to your question :writing_hand:find the value of x3 y3 12xy 64 when x y You should plug in any number for x which can be positive or negative numbers. Explanation: graph{y=-x-3 [-10, 10, -5, 5]} So you can plug in any numbers for x.Detailed step by step solution for expand ln((xy)^3)Y-3 brings sports style to the street. Fueled by the innovations of adidas and expressed in the style of Yohji Yamamoto, Y-3 creates progressive apparel, footwear and accessories—a vision driven by both the sports icon and the renowned designer. Founded in 2002, Y-3 established the category of fashion sportswear—one it continues to redefine ...Detailed step by step solution for expand ln((xy)^3)Graph y=-3. y = −3 y = - 3. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: 0 0. y-intercept: (0,−3) ( 0, - 3) Find two points on the line. x y 0 −3 1 −3 x y 0 - 3 1 - 3. Graph the line using the slope, y-intercept, and two points. This is an identity, it will work for any values of x and y. Explanation: There are several methods for solving simultaneous equations, but in this case I like the idea that y = y ... 4x+y=3 Geometric figure: Straight Line Slope = -8.000/2.000 = -4.000 x-intercept = 3/4 = 0.75000 y-intercept = 3/1 = 3.00000 Rearrange: Rearrange the equation by ... Solution. Verified by Toppr. We know the corollary: if a+b+c = 0 then a3 +b3 +c3 = 3abc. Using the above identity taking a =x−y, b = y−z and c =z−x, we have a+b+c = x−y+y−z+z−x = 0 then the equation (x−y)3 +(y−z)3 +(z−x)3 can be factorised as follows: (x−y)3 +(y−z)3 +(z−x)3 = 3(x −y)(y−z)(z−x) Hence, (x−y)3 +(y ...Amazon.com: Pokémon XY Mega 3-Movie Collection (BD) : Various, Various: Movies & TV.Question 3: For a linear equation y = 2x + 6, find the point where the straight line meets y-axis on the graph. Answer: On y-axis, the x-coordinate of the point is 0. Therefore, we can find the intersection point of y-axis and y = 2x + 6 by simply putting the value of x as 0 and finding the value of y. y = 2(0)+6 = 0 + 6 = 6.This is an identity, it will work for any values of x and y. Explanation: There are several methods for solving simultaneous equations, but in this case I like the idea that y = y ... 4x+y=3 Geometric figure: Straight Line Slope = -8.000/2.000 = -4.000 x-intercept = 3/4 = 0.75000 y-intercept = 3/1 = 3.00000 Rearrange: Rearrange the equation by ... Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Tap for more steps... x y 0 0 5 3 x y 0 0 5 3. Graph the line using the slope and the y-intercept, or the points. Slope: 3 5 3 5. y-intercept: (0,0) ( 0, 0) x y 0 0 5 3 x y 0 0 5 3.Nov 28, 2017 ... A math video lesson on Systems of Two Equations. This video solves by graphing x-y=3 and 7x-y=-3 #solvebygraphing ...In mathematics, the cube of sum of two terms is expressed as the cube of binomial $x+y$. It is read as $x$ plus $y$ whole cube. It is mainly used in mathematics as a formula for expanding cube of sum of any two terms in their terms. ${(x+y)}^3$ $\,=\,$ $x^3+y^3+3x^2y+3xy^2$ Proofs. The cube of $x$ plus $y$ identity can be proved in two ... 5,471 likes, 484 comments - megha_ghimire54_official on February 21, 2024: "Me teri hogai waii ♥️ #transformation #lovethissong #meghu54 #reels #motivation #nev..."3x-4y=8 Geometric figure: Straight Line Slope = 1.500/2.000 = 0.750 x-intercept = 8/3 = 2.66667 y-intercept = 8/-4 = 2/-1 = -2.00000 Rearrange: Rearrange the equation by subtracting ... Let f (z) = sin(z + 1) be a function of a complex variable z = a + bi. How do you write the function f (z) = x + iy where x and y are real numbers? https://www ... Oct 14, 2020 ... Prove the following statement: Let x,y be real numbers. Prove (x-y)^5 + (x-y)^3 = 0 if and only if x = y.Calculadora gratuita de derivadas – derivar funções com todos os passos. Digite qualquer derivada para obter solução, passos e gráfico.Main topic: Two-variable linear equations. Learn how to solve two-variable linear equations problems step by step online. Solve the equation x+y=3. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x from both sides of the equation. x+2y=3 Geometric figure: Straight Line Slope = -1.000/2.000 = -0.500 x-intercept = 3/1 = 3.00000 y-intercept = 3/2 = 1.50000 Rearrange: Rearrange the equation by subtracting what is ... How do you solve 2x + 2y = 3 and x − 4y = −1 ? x = 1; y = 1/2 Explanation: 2x+2y = 3 x−4y = −1 From the 2nd equation: x = 4y −1 put this x to the 1st ...Solution. Verified by Toppr. (x+y)3 −(x3 +y3) (x3 +y3 +3xy(x+y)−x3 −y3. 3xy(x+y) So, above term is factor of 3xy. Answer (D) 3xy. Was this answer helpful? 17. x − y = 3 ----- eq 2. Using elimation method: eq 2 x 2. 2 (x − y)= 2(3 ) 2x - 2y = 6 ---- eq 3. eq 1 + eq 3. 4x + 2y + 2x - 2y = 6 + 6. 6x = 12. x = 2 (sub this back into eq 2) x − y = 3. 2 − y = 3-y = 3 - 2-y = 1. y = -1. heart outlined.x+y=27 y=x+3. en. Related Symbolab blog posts. High School Math Solutions – Systems of Equations Calculator, Nonlinear. In a previous post, we learned about how to solve a system of linear equations. In this post, we will learn how... Read More. Enter a …x^{2}-x-6=0 -x+3\gt 2x+1 ; line\:(1,\:2),\:(3,\:1) f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More Minus one is less than or equal to x, which is less than or equal to three., Draw the graph of 𝒚 = 2𝒙 – 5 for values of 𝒙 from -1 to 3. This is written as the inequality -1 ≤ 𝒙 ≤ 3An infinite number of solutions exist. Explanation: We can start by using substitution. The first equation solves easily for y , so just subtract 2x from both ... 3x-2y=0 Geometric figure: Straight Line Slope = 3.000/2.000 = 1.500 x-intercept = 0/3 = 0.00000 y-intercept = 0/-2 = -0.00000 Step by step solution : Step 1 :Equation of a Straight ...Algebra. Graph y=-x-6. y = −x − 6 y = - x - 6. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: −1 - 1. y-intercept: (0,−6) ( 0, - 6) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.The X and Y chromosomes, commonly referred to as the sex chromosomes, are one such pair. They determine the biological sex, reproductive organs, and sexual characteristics that develop in a person.A system of equations is linear if all of the equations are linear functions, meaning that the variables only appear to the first power and are not multiplied or divided together. If any equation is not linear, then the system is nonlinear. Show more.How to Solve the Bernoulli Differential Equation y' + xy = xy^2If you enjoyed this video please consider liking, sharing, and subscribing.Udemy Courses Via M...Use implicit differentiation to find the largest y-value in the loop of the Folium of Descartes, which is given by : x3 + y3 − 3xy = 0. First, we do the implicit derivative to simplify our equation. Because maxima/minima occur when f ′(x)= 0, we take the implicit derivative and set it equal to 0.5,471 likes, 484 comments - megha_ghimire54_official on February 21, 2024: "Me teri hogai waii ♥️ #transformation #lovethissong #meghu54 #reels #motivation #nev..."Intuitively, the vertex form of a parabola is the one that includes the vertex’s details inside.We can write the vertex form equation as: y = a·(x-h)² + k.. As you can see, we need to know three parameters to write a quadratic vertex form.One of them is a, the same as in the standard form.It tells us whether the parabola is opening up (a > 0) or down (a < …How to Solve the Bernoulli Differential Equation y' + xy = xy^2If you enjoyed this video please consider liking, sharing, and subscribing.Udemy Courses Via M...Solution. Verified by Toppr. (x+y)3 −(x3 +y3) (x3 +y3 +3xy(x+y)−x3 −y3. 3xy(x+y) So, above term is factor of 3xy. Answer (D) 3xy. Was this answer helpful? 17. x − y = 3 ----- eq 2. Using elimation method: eq 2 x 2. 2 (x − y)= 2(3 ) 2x - 2y = 6 ---- eq 3. eq 1 + eq 3. 4x + 2y + 2x - 2y = 6 + 6. 6x = 12. x = 2 (sub this back into eq 2) x − y = 3. 2 − y = 3-y = 3 - 2-y = 1. y = -1. heart outlined.Derivative Calculator. Step 1: Enter the function you want to find the derivative of in the editor. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding of the function by using our graphing tool.Tap for more steps... x⋅x+x(−y)+yx+y(−y) x ⋅ x + x ( - y) + y x + y ( - y) Simplify terms. Tap for more steps... x2 − y2 x 2 - y 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.4. @CharlieParker: Intuitively, if x and y have the same sign then | | x | − | y | | is the same as | x − y | (the distance between x and y when plotted on the real line). If they are different, then the distance between x and y is larger than the distance between x (say x ≥ 0) and the reflected version of y, i.e. | y |.May 21, 2018 · Easiest way: plot (0,3) and (3,0) on a graph; connect them with a line. We're looking for all pairs of numbers that add to 3. There are infinitely many (x,y) pairs that work; we want to show where they are on an x"-"y plane. Two pairs are easy to find. We know that 0 + 3=3 and we know 3+0=3. That means the points (0,3) and (3,0) are both on our graph. We plot those points: graph{(x^2+(y-3)^2 ... Free math problem solver answers your algebra homework questions with step-by-step explanations. Graph y=x^3-3. Step 1. Find the point at . Tap for more steps... Step 1.1. Replace the variable with in the expression. Step 1.2. Simplify the result. Tap for more ... Teams. Q&A for work. Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams(x + y) 3 + (y + z) 3 + (z + x) 3 − 3(x + y) (y + z) (z + x) = (x3 + y3 + z3 − 3xyz). Q. Factorize: x 3 + y 3 + z 3 = 3 x y z. Q. The expansion of x 3 + y 3 + z 3-3xyz is. Q. How (x 3 +y 3)+z 3-3xyz = [(x+y) 3-3xy(x+y)]+z 3-3xyz. Q. If X3+y3+z3=3xyz then. View More. Join BYJU'S Learning ProgramAug 7, 2021 ... xy = 3 cone ellipsoid O hyperboloid O elliptic cylinder O hyperbolic cylinder parabolic cylinder elliptic paraboloid O ...Sep 24, 2023 ... Your browser can't play this video. Learn more.Oct 4, 2022 · In this video we'll draw the graph for x + y = 3.First, we will use a table of values to plot points on the graph. Once we have two or three points, we can d... Algebra. Graph y=2x-3. y = 2x − 3 y = 2 x - 3. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: 2 2. y-intercept: (0,−3) ( 0, - 3) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Solve by Substitution x^2-y=3 , x-y=-3 | Mathway. This website uses cookies to ensure you get the best experience on our website. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.x^{3}-y^{3} en. Related Symbolab blog posts. My Notebook, the Symbolab way. Math notebooks have been around for hundreds of years. You write down problems, solutions ... Algebra. Graph y=x+3. y = x + 3 y = x + 3. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: 1 1. y-intercept: (0,3) ( 0, 3) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Nov 28, 2017 ... A math video lesson on Systems of Two Equations. This video solves by graphing x-y=3 and 7x-y=-3 #solvebygraphing ...A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities. Given tables are . Table 1: x 3 3 3 3 3. y -2 …Rewrite in slope-intercept form. Tap for more steps... y = x− 4 y = x - 4. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: 1 1. y-intercept: (0,−4) ( 0, - 4) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Algebra Factor (x+y)^3+ (x-y)^3 (x + y)3 + (x - y)3 Since both terms are perfect cubes, factor using the sum of cubes formula, a3 + b3 = (a + b)(a2 - ab + b2) where a = x + y …Free Function Transformation Calculator - describe function transformation to the parent function step-by-step.If x = x(y) is the solution of the differential equation y \(\frac{dx}{dy}\) = 2x + y 3 (y + 1)e y, x(1) = 0; then x(e) is equal to: (A) e 3 (e e - 1) (B) e e (e 3 - 1) (C) e 2 (e e + 1) (D) e e (e 2 - 1) jee main 2022; Share It On Facebook Twitter Email. Play Quiz Game > 1 …y=x^3. Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Apr 29, 2020 ... x-y=3 written in function notation x being the independent variable.Godzilla x Kong: The New Empire: Directed by Adam Wingard. With Rebecca Hall, Dan Stevens, Rachel House, Brian Tyree Henry. Two ancient titans, Godzilla and Kong, clash in an epic battle as humans unravel their …If x y+ y x = -2 and x, y ≠ 0, then x3+y3 +3xy (x + y) is equal to: Q. expand. x(x−y)3+3xy(x−y) Q. Factorize: 3. x x 3 - y 3 + 3 x y ( x - y) Q.For example: [x*y for x in range(10) for y in range(x, x+10)]. To ensure the comprehension always results in a container of the appropriate type, yield and yield from expressions are prohibited in the implicitly nested scope. Since Python 3.6, in an async def function, an async for clause may be used to iterate over a asynchronous iterator.Send us Feedback. Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step.Get Step by Step Now. Starting at $5/month. Get step-by-step answers and hints for your math homework problems. Learn the basics, check your work, gain insight on different ways to solve problems. For chemistry, calculus, algebra, trigonometry, equation solving, basic math and more.Oct 14, 2020 ... Prove the following statement: Let x,y be real numbers. Prove (x-y)^5 + (x-y)^3 = 0 if and only if x = y.Section 6.3 : Volume With Rings. For each of the following problems use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis. Rotate the region bounded by y =√x y = x, y = 3 y = 3 and the y y -axis about the y y -axis. Solution.In mathematics, the cube of sum of two terms is expressed as the cube of binomial $x+y$. It is read as $x$ plus $y$ whole cube. It is mainly used in mathematics as a formula for expanding cube of sum of any two terms in their terms. ${(x+y)}^3$ $\,=\,$ $x^3+y^3+3x^2y+3xy^2$ Proofs. The cube of $x$ plus $y$ identity can be proved in two ... Note. Go to the end to download the full example code. contour(X, Y, Z)# See contour.. import matplotlib.pyplot as plt import numpy as np plt. style. use ('_mpl ...A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities. Given tables are . Table 1: x 3 3 3 3 3. y -2 …The equations of the transverse and conjugate axes of a hyperbola are respectively x+2y−3 = 0, 2x−y+4 = 0 and their respective lengths are √2 & 2 √3. The equation of the hyperbola is. View Solution. Q 3. Q. If x:y = 3:4, find (4x+5y) : (5x-2y) View Solution. Q 4. If 1×22 +2×32 +3×42 +⋯+n(n+1)2 12 ×2+22 ×3+32 ×4+⋯+n2(n+1) = 8 7 ...Tap for more steps... x⋅x+x(−y)+yx+y(−y) x ⋅ x + x ( - y) + y x + y ( - y) Simplify terms. Tap for more steps... x2 − y2 x 2 - y 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.In this math video lesson I show the student how to graph the equation x+y=3. This equation is in standard form and I covert that to slope intercept form to graph …Algebra. Graph y=-x-6. y = −x − 6 y = - x - 6. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: −1 - 1. y-intercept: (0,−6) ( 0, - 6) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. May 21, 2018 · Easiest way: plot (0,3) and (3,0) on a graph; connect them with a line. We're looking for all pairs of numbers that add to 3. There are infinitely many (x,y) pairs that work; we want to show where they are on an x"-"y plane. Two pairs are easy to find. We know that 0 + 3=3 and we know 3+0=3. That means the points (0,3) and (3,0) are both on our graph. We plot those points: graph{(x^2+(y-3)^2 ... $$ x(x+y)^3 -3x^2y(x+y) $$ $$= x(x+y)(x^2+y^2 -xy)$$ Was this answer helpful? 34. Similar Questions. Q1. Factorise x (x ...
Explanation: (x −y)3 = (x − y)(x −y)(x −y) Expand the first two brackets: (x −y)(x − y) = x2 −xy −xy + y2 ⇒ x2 +y2 − 2xy Multiply the result by the last two brackets: (x2 + y2 −2xy)(x − y) = x3 − x2y + xy2 − …. Ddlg video
Graph y=x^3-3. Step 1. Find the point at . Tap for more steps... Step 1.1. Replace the variable with in the expression. Step 1.2. Simplify the result. Tap for more ... 2x-y=0 Geometric figure: Straight Line Slope = 2 x-intercept = 0/2 = 0.00000 y-intercept = 0/-1 = -0.00000 Step by step solution : Step 1 :Equation of a Straight Line ... 2x-y=1 Geometric figure: Straight Line Slope = 2 x-intercept = 1/2 = 0.50000 y-intercept = 1/-1 = -1.00000 Rearrange: Rearrange the equation by subtracting what is to the ...Use implicit differentiation to find the largest y-value in the loop of the Folium of Descartes, which is given by : x3 + y3 − 3xy = 0. First, we do the implicit derivative to simplify our equation. Because maxima/minima occur when f ′(x)= 0, we take the implicit derivative and set it equal to 0.Godzilla x Kong: The New Empire: Directed by Adam Wingard. With Rebecca Hall, Dan Stevens, Rachel House, Brian Tyree Henry. Two ancient titans, Godzilla and Kong, clash in an epic battle as humans unravel their …Oversaturation isn’t good for anyone, even the in-love, in-demand, ever-adorable Swift. Plus, she just announced a new record for release in April. “The Tortured …Question 3: For a linear equation y = 2x + 6, find the point where the straight line meets y-axis on the graph. Answer: On y-axis, the x-coordinate of the point is 0. Therefore, we can find the intersection point of y-axis and y = 2x + 6 by simply putting the value of x as 0 and finding the value of y. y = 2(0)+6 = 0 + 6 = 6.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Let's practice translations on a coordinate plane. A translation is a way to move a point or shape by a certain number of units in a certain direction. For example, we can translate a point by moving it 5 units left and 3 units up. We describe this translation algebraically using the coordinates (x-5, y+3).Algebra. Solve for x (x+y)/3=5. x + y 3 = 5 x + y 3 = 5. Multiply both sides of the equation by 3 3. 3 x+y 3 = 3⋅5 3 x + y 3 = 3 ⋅ 5. Simplify both sides of the equation. Tap for more steps... x+y = 15 x + y = 15. Subtract y y from both sides of the equation.In fact |x − y|2 = (x − y)2 | x − y | 2 = ( x − y) 2, so nothing to gain from that. If you're familiar with the triangle inequality, this actually is the triangle inequality for x x and −y − y, since | − y| =|y| | − y | = | y |. – Matt Samuel. Dec 18, 2018 at 4:26. so does it follow to say |x − y|=|x + (-y)|≤ |x|+|-y|...Graph y=3. y = 3 y = 3. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... Slope: 0 0. y-intercept: (0,3) ( 0, 3) Find two points on the line. x y 0 3 1 3 x y 0 3 1 3. Graph the line using the slope, y-intercept, and two points.In terms of display, the Legion Y9000X (2024) boasts a 16-inch gaming screen that supports a 100% DCI-P3 wide color gamut, 165Hz refresh rate, Dolby Vision, …Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Main topic: Two-variable linear equations. Learn how to solve two-variable linear equations problems step by step online. Solve the equation x+y=3. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x from both sides of the equation. x^3 + x^2 y + x y^2 + y^3. Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….Given, x 3 + y 3 = (x + y) (x 2 − x y + y 2) First take R.H.S (x + y) (x 2 − x y + y 2) To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial. = x. x 2 − x 2 y + x. y 2 + y. x 2 − x. y 2 + y. y 2 = x 3 − x 2 y + x y 2 + x 2 y − x y 2 + y 3 ... a. In Read more. which function has the most rapid rate of change? y=6 (2^x) y=4 (2^x) y=2 (3^x) y=3 (4^x) Top answer: The function with the most rapid rate of change is y = 6 (2^x) because the coefficient 6 in front of Read more. Consider the two functions shown here.$\begingroup$ An edit by Derek Ehle changed the original $$(x+y)^n = \sum_{k=0}^n x^k y^{n-k}$$ in this posting, not to $$(x+y)^n = \sum_{k=0}^n \binom n k x^ky^{n-k},$$ which would have made the question incomprehensible, but to $$(x+y)^n = \sum_{k=0}^n (^n_k) x^ky^{n-k},$$ with the notation (^n_k), which also makes it incompehensible.That required approval and approved it. The $\boldsymbol{ y = x}$ reflection projects the pre-image over the diagonal line that passes through the origin and represents $\boldsymbol{ y = x}$. This results in switching the places of the x and y coordinates on the coordinate system.math. remainder (x, y) ¶ Return the IEEE 754-style remainder of x with respect to y. For finite x and finite nonzero y, this is the difference x-n*y, where n is the closest integer to the exact value of the quotient x / y. If x / y is exactly halfway between two consecutive integers, the nearest even integer is used for n.Solve the system by elimination. {x + y = 10 x − y = 12 { x + y = 10 x − y = 12. Both equations are in standard form. The coefficients of y are already opposites. Add the two equations to eliminate y. The resulting equation has only 1 variable, x. Solve for x, the remaining variable..