(x^21)^3=x^63x^43x^21 (ab)^3=a^33a^2b3ab^2b^3 (x^21)^3=(x^2)^33(x^2)^23x^21=x^63x^43x^21 How do you find the volume of a prism if the width is x, height is #2x1# and the length if #3x4#? Example 3 y = x 2 3 The "plus 3" means we need to add 3 to all the yvalues that we got for the basic curve y = x 2 The resulting curve is 3 units higher than y = x 2 Note that the vertex of the curve is at (0, 3) on the yaxis Next we see how to move a curve left and right Example 4 y = (x − 1) 2Easy as pi (e) Unlock StepbyStep Natural Language Math Input
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2/x-1 3/y 1=2 3/x-1 2/y 1=13/6-Y' 6 y (x 2 y 2) 2 16 x 2 y = 16 x y 2 6x (x 2 y 2) 2, and Thus, the slope of the line tangent to the graph at the point (1, 1) is , and the equation of the tangent line is y ( 1 ) = (1) ( x ( 1 ) ) or y = x 2 Click HERE to return to the list of problems SOLUTION 11 Begin with x 2 (yx) 3 = 9 If x=1 , then (1) 2 Example 18 Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Term 1) Example 18 Solve the following pair of equations by reducing them to a pair of linear equations 5/ (𝑥 −1) 1/ (𝑦 −2) = 2 6/ (𝑥 −1) – 3/ (𝑦 −2) = 1 5/ (𝑥 − 1) 1/ (𝑦 − 2) = 2 6/ (𝑥 − 1) – 3/ (𝑦 − 2) = 1 So, our
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Chap 3 Two Random Variables where x and y are arbitrary real numbers Properties 1 F XY(−∞,y)=F XY(x,−∞)=0,F XY(∞,∞)=1 (2) since (X(ξ) ≤−∞,Y(ξWe designate (3, 5) as (x 2, y 2) and (4, 2) as (x 1, y 1) Substituting into Equation (1) yields Note that we get the same result if we subsitute 4 and 2 for x 2 and y 2 and 3 and 5 for x 1 and y 1 Lines with various slopes are shown in Figure 78 belowWhich is an instance of the law of total probability Conditioning on the level of densities Example A point of the sphere x 2 y 2 z 2 = 1 is chosen at random according to the uniform distribution on the sphere The random variables X, Y, Z are the coordinates of the random point The joint
P 12) = 47 So the minimum is 7 and the maximum is 47 5 Find the minimum possible distance from the point (4;0;0) to a point on the surface x2y2 z2 = 1Y=3/2x2;y=1/2x2 Simple and best practice solution for y=3/2x2;y=1/2x2 Check how easy it is, to solve this system of equations and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework9 x 2 = 3 2 x 2 = 3 2 ⋅ x 2 = 3 x In this section, we will assume that all variables are positive This allows us to focus on calculating nth roots without the technicalities associated with the principal nth root problem For this reason, we will use the following property for the rest of the section a n n = a, if a ≥ 0 n th root
442 Use the tangent plane to approximate a function of two variables at a point;Extended Keyboard Examples Upload Random 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, musicY=1/x WolframAlpha Area of a circle?
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6 \times \arctan \tan \log 1 2 3\pi e x^{\square} 0 \bold{=} Go Related » Graph » Number Line » Examples » Our online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutesAssuming that x is 1, show the result of the following Boolean expressions (a) Write a Boolean expression that evaluates to true if a number stored in variable num is between 1 and 100 (b) Write a Boolean expression that evaluates to true if a number stored in variable num is between 1 and 100 or the number is negativeLinearequationcalculator y=x en Related Symbolab blog posts High School Math Solutions – Quadratic Equations Calculator, Part 1 A quadratic equation is a second degree polynomial having the general form ax^2 bx c = 0, where a, b, and c
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Answer (1 of 2) 3/x2/y=0 take lcm or multiply both lhs and rhs with xy 3y2x=0 3y=2x substitute 3y=2x in the other equation 2/x2/(2x)=1/6 2/x1/x=1/6 as they are like fractions we can perform subtraction 1/x=1/6 therefore x=6 and substituting x=6 in any eqn find the value of yFor y = 0,1,2,3;Fall 13 S Jamshidi 4 x4 y4 z4 =1 If x,y,z are nonzero, then we can consider Therefore, we have the following equations 1 1=2x2 2 1=2y2 3 1=2z2 4 x4 y4 z4 =1 Remember, we can only make this simplification if all the variables are nonzero!
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Now we can use Equation 51 to find the marginal PMFs P X ( x) = { 1 6 x = 1 3 8 x = 2 11 24 x = 3 0 otherwise P Y ( y) = { 1 2 y = 2 1 4 y = 4 1 4 y = 5 0 otherwise Using the formula for conditional probability, we have P ( Y = 2 X = 1) = P ( X = 1, Y = 2) P ( X Differentiate the following with respect to x sin1 (2 x 13 x)/(1 36 x) continuity and differntiability;9 INNERPRODUCT 2 Angle The angle θ between two vectors xand y is related to the dot product by the formula xT y= kxkkykcosθ 911 Example Find the angle between x= 2,−3T and y= 3,2T Solution We solve the equation above to get
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Z = 1 2 (04) 5s are parallel Solution Reading o the coe cients of the parameters t and s, we see that v 1 = 2i 4j 10k and v 2 = i 2j 5k are the direction vectors for L 1 and L 2 Because v 1 = 2v 2, we conclude that the lines are parallel Example 06Equation of a planeS2(X 1,X2,···,)= 1 n− 1 i=1 (Xi − X¯)2 (4) The observed value of S2 in any sampleis demoted by the lower case letter, ie, s2 133 Sample standard deviation The sample standard deviation is the statisticdefined by S = √ S2 (5) 134 Sample midrange The samplemidrange is the statisticdefined by max(X1,X2,···,)−X(0) = 1 3 Denote by A= −2 1 −5 4 and consider its characteristic polynomial PA(λ
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Y= x(1 x) (1=2;1=4) The region Dis both vertically simple and horizontally simple, but the bounds for yin terms of x are simpler than the bounds for xin terms of y, so when we use Fubini's theorem to evaluate the integral, we take the yintegral on the inside and the xintegral on the outside This gives us ZZ D f(x;y)dA= Z x=1=2 x=0 Z y=x(1Y = 1 4t;(03) L 1 x = 4 2t;
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1 X is called the domain of f 2 Y is called the codomain of f 3 If f(x) = y, then we say y is the image of x The preimage of y is preimage(y) = {x ∈ X f(x) = y} 4 The range of f is the set of images of elements in X In this section we deal with functions from a vector sapce V toReverse order x 1 = y″, x 2 = y′, x 3 = y Deduce the fact that there are multiple ways to rewrite each nth order linear equation into a linear system of n equations y″′ 6y″ y′ − 2y = 0 Answers D11 1 x 1′ = x 2 2 x 1′ = x 2 x 2′ = −5x 1 4 x 2 x 2′ =P(X Y ≥ 1) = Z 1 0 Z 2 1−x (x2 xy 3)dydx = 65 72 (c) We compute the marginal pdfs fX(x) = Z ∞ −∞ f(x,y)dy = ˆR 2 0 (x 2 xy 3)dy = 2x2 2x 3 if 0 ≤ x ≤ 1 0 otherwise fY (y) = Z ∞ −∞ f(x,y)dx = ˆR 1 0 (x 2 xy 3)dx = 1 3 y 6 if 0 ≤ y ≤ 2 0 otherwise 1
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Algebra Graph y=1/3x3 y = − 1 3 x 3 y = 1 3 x 3 Rewrite in slopeintercept form Tap for more steps The slopeintercept form is y = m x b y = m x b, where m m is the slope and b b is the yintercept y = m x b y = m x b Write in y = m x b y = m x b form Tap for more steps2 xy 2 4 5 x y 4 3 f) x 9 x6 – x4 g) 35a4m3 14a3m4 h) 2a2 – a 50 n) 1ay 3 0ay 2 – 40ay i) x 2 y y 3 o) 18mn 30m 2 n 54mn 2 Exercícios 6) Fatore os seguintes polinômios a) cy – y cx – x b) 15 5x 6a 2ax c) 2x2 – x 4xy – 2y d) am m a 1 e) x3 xy2 ax2 ay2 f) a3x a3y Solve the following systems of equations 3/(xy) 2/(xy) =2 9/(xy) 4/(xy) =1 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries
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Ex 32, 12 Given 3 8(x&y@z&w) = 8(x&6@−1&2w) 8(4&xy@zw&3) find the values of x, y, z and w 3 8(x&y@z&w) = 8(x&6@−1&2w) 8(4&xy@zw&3) 8F) Z 2 1 dx Z x3 x f(x,y)dy Z 8 2 dx Z 8 x f(x,y)dy Solucion a) La region de integraci´on, indicada en la figura, es la que verifica el sistema 0 ≤ x ≤ 3, 4x/3 ≤ y ≤You can put this solution on YOUR website!
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Sin (x)cos (y)=05 2x−3y=1 cos (x^2)=y (x−3) (x3)=y^2 y=x^2 If you don't include an equals sign, it will assume you mean " =0 " It has not been well tested, so have fun with it, but don't trust it If it gives you problems, let me know Note it may take a few seconds to finish, because it has to do lots of calculationsThe reason an infinite sum like 1 1/2 1/4 can have a definite value is that one is really looking at the sequence of numbers 1 1 1/2 = 3/2 1 1/2 1/4 = 7/4 1 1/2 1/4 1/8 = 15/8 etc, and this sequence of numbers (1, 3/2, 7/4, 15/8, ) is converging to a limit It is this limit which we call the "value" of theShare It On Facebook Twitter Email 1 Answer 3 votes answered by Jyoti (303k points) selected Nov 9,
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Example 3 Find the equation of the line passing through (6, −1) and parallel to y = 1 2 x 2 Solution Here the given line has slope m = 1 2 , and the slope of a line parallel is m ∥ = 1 2 Since you are given a point and the slope, use the pointslope form of a line to determine the equation2 = λ 3 = −1 Therefore the general solution for the system is x(t) = c 1 2 1 2 e 8t c 2 −1 2 0 e−t c 3 −1 0 1 e −t 16 Solve the following initial value problem Describe the behavior of the solution as t→ ∞ x′ = −2 1 −5 4 x;From the equation 3 (x1)^2 3 (y1)^2 = 6 we divide everything by 3 and get (x1)^2 (y1)^2 = 2 This is the equation of a circle with center at (1, 1) and radius of sqrt (2)
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X^2 2 y^2 = 1 Natural Language;STAT 400 Joint Probability Distributions Fall 17 1 Let X and Y have the joint pdf f X, Y (x, y) = C x 2 y 3, 0 < x < 1, 0 < y < x, zero elsewhere a) What must the value of C be so that f X, Y (x, y) is a valid joint pdf?b) Find P (X Y < 1)c) Let 0 < a < 1 Find P (Y < a X) d) Let a > 1 Find P (Y < a X)e) Let 0 < a < 1 Find P (X Y < a)SOLUTION 1 Begin with x 3 y 3 = 4 Differentiate both sides of the equation, getting D ( x 3 y 3) = D ( 4 ) , D ( x 3) D ( y 3) = D ( 4 ) , (Remember to use the chain rule on D ( y 3) ) 3x 2 3y 2 y' = 0 , so that (Now solve for y' ) 3y 2 y' = 3x 2, and Click HERE to return to the list of problems SOLUTION 2 Begin with (xy) 2 = x y 1 Differentiate both sides
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Learning Objectives 441 Determine the equation of a plane tangent to a given surface at a point;3y=2x1 Geometric figure Straight Line Slope = 1333/00 = 0667 xintercept = 1/2 = yintercept = 1/3 = Rearrange Rearrange the equation by subtracting what is444 Use the total differential to approximate the change in a function of two variables
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Z = 3 10t L 2 x = s y = 6 2s;Graficar f(x) = −2x 2 3x – 3 a = −2, por lo que la gráfica abrirá hacia abajo y será más delgada que f(x) = x 2 c = −3, por lo que se moverá a intersectar el eje y en (0, −3) Antes de hacer la tabla de valores, observa los valores de a y c para tener una(21 x 5) / (3 x 4) = (21 / 3)(x 5 / x 4) Simplify = 7 x (6 x 4)(4 y 2) / (3 x 2)(16 y) Multiply terms in numerator and denominator and simplify (6 x 4)(4 y 2) / (3 x 2)(16 y) = (24 x 4 y 2) / (48 x 2 y) Rewrite as follows = (24 / 48)(x 4 / x 2)(y 2 / y) Simplify = (1 /
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Cancel the common factor Divide ( x − 3) ( x 1) ( x 3) ( x 1) by 1 1 Divide 0 0 by 2 2 If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0 Set the first factor equal to 0 0 and solve443 Explain when a function of two variables is differentiable;(x y) 3 = x 3 3x 2 y 3xy 2 y 3 Example (1 a 2 ) 3 = 1 3 31 2 a 2 31(a 2 ) 2 (a 2 ) 3 = 1 3a 2 3a 4 a 6 (x y z) 2 = x 2 y 2 z 2 2xy 2xz 2yz
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1 3 Thus, T(f)T(g) 6= T(f g), and therefore T is not a linear transformation 2 For the following linear transformations T Rn!Rn, nd a matrix A such that T(~x) = A~x for all ~x 2Rn (a) T R2!R3, T x y = 2 4 x y 3y 4x 5y 3 5 Solution To gure out the matrix for a linear transformation from Rn, we nd the matrix A whose rst column is T(~eThen type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints "True" to let you know that the answer isSteps Using the Quadratic Formula y = \frac { x ^ { 2 } 1 } { x ^ { 2 } 5 x 6 } y = x 2 − 5 x − 6 x 2 − 1 Variable x cannot be equal to any of the values 1,6 since division by zero is not defined Multiply both sides of the equation by \left (x6\right)\left (x1\right) Variable x cannot be equal to any of the values − 1, 6
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Case 2 If y ̸= 0, it follows from 6y = 2 y that = 3 Then 4x 4 = 6x, so x = 2 and y = p 12 We have f( 2;
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