Soln E is described by x2 z2 ≤ y ≤ 4− x2 − z2 over a disk D in the xzplane whose radius is given by the intersection of the two surfaces y = 4− x 2 − z 2 and y = x 2 z 2 4− x 2 −z 2 = x 2 z 2 ⇒ x 2 z 2 = 2Plot z=x^2y^2 WolframAlpha Assuming "plot" is a plotting function Use as referring to geometry instead01 Recall ordinary derivatives If y is a function of x then dy dx is the derivative meaning the gradient (slope of the graph) or the rate of change with respect to x 02 Functions of 2
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If x^2 y^2 z^2 2xycosacosb-All equations of the form a x 2 b x c = 0 can be solved using the quadratic formula 2 a − b ± b 2 − 4 a c The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction x^ {2}2xy^ {2}4y=5 x 2 − 2 x y 2 − 4 y = 3Dplot of "x^2y^2z^2=1" Learn more about isosurface;
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Then 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 isF(x,y,z) = x2yz −xy2z decreases in the y direction (a) (1,−1,2), (b) (1,1,1), (c) (−1,1,2), (d) (1,0,1) Definition if nˆ is a unit vector, then nˆ·∇f is called the directional derivative of f in the direction nˆ The directional derivative is the rate of change of f in the direction nˆA Cartesian coordinate system (UK / k ɑː ˈ t iː zj ə n /, US / k ɑːr ˈ t i ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of lengthEach reference line is called a coordinate axis or just axis (plural
Quantitative Aptitude ≫ Algebra ≫ Linear Equation in 2 or more Variables Question (View in Hindi ) If a 2 x b 2 y c 2 z = 9x 121y 81z, where a, b, c are positive integers, then find the value ofY=2^x^x^x^x let y=2^u dy/du = blah blah (rules as above, as you'd normally do) u= x^v du/dv = blah blah v=x^w dv/dw = blah blah w=x^x dw/dx= and so on for similar functions You'll need to fiddle around with the differentiation Then by chain rule 2 reply X start new discussion Page 1 of 1Find dy/dx ycos(x)=x^2y^2 Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate using the Product Rule which states that is where and The derivative of with respect to is Simplify the expression Tap for more steps
You need to evaluate all second degree terms, 3x^2−2xy3y^2 In this case it will work, as the coefficients of x^2 and y^2 are equal, so that the terms 2\cos\theta\sin\theta XY will cancel Question 33 (OR 1st Question) Using the properties of determinants, prove that (y z)2 x2 x2 y2 (z x)2 y2 z2 z2 (x y)2 2xyz (x y z)3 (y z)2 x2 x2 y2 (z x)2 y2 z2 z2 (x y)2 Applying C2 > C2 C1 = (y z)2 x2 (y z)2 x2 y2 (z x)2 y2 y2 z2Click here👆to get an answer to your question ️ If x = ycos2pi 3 = zcos4pi 3, then xy yz zx =
If Y 2 A 2cos 2x B 2sin 2x Then Prove That D 2y Dx 2 Y A 2b 2 Y 3
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Exercise 2 Calculate the curl of the following vector fields F(x,y,z) (click on the green letters for the solutions) (a) F = xi−yj zk, (b) F = y3ixyj −zk, (c) F = xiyj zk p x2 y2 z2, (d) F = x2i2zj −yk Here is a review exercise before the final quiz Exercise 3 Let f be a scalar field and F(x,y,z) and G(x,y,z) be vector fieldsWe take the first equation {eq}x^2 y^2 w^2 z^2 = 1 {/eq} and take the partial derivative wrt x with z as a constant, as denoted in the See full answer belowFind the value of k for which the following systems of equations have infinitely many solutions 7x 4y = 2 (3k 2)x (2k 8)y = 3(k 4) Q12 If one of the zeroes of the cubic polynomial ax3 bx2 cx d is zero, then the ratio of the product of the other two zeroes to
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Expand (xyz)^2 Rewrite as Expand by multiplying each term in the first expression by each term in the second expression Simplify each term Tap for more steps Multiply by Rewrite using the commutative property of multiplication Rewrite using the commutative property of multiplicationExtended 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, musicIntegrate x^2 sin y dx dy, x=0 to 1, y=0 to pi;
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If $x^2 y^2 z^2 = 2xyz$, then at least one of $x$, $y$ or $z$ must be a multiple of 2 Let that one number be x and now $2x$ Also let $x = 2a$Then, $4a^2 y^2 z^2 = 4ayz$ Now assume that one of $y$ or $z$ is odd So the other must be odd as well as odd and odd add upto even and we need an even number to make the equality true It depends on whether we need d/dx or d/dt For d/dt d/dt(ln(x^2y^2)) = 1/(x^2y^2) d/dt(x^2y^2) = 1/(x^2y^2) * (2xdx/dt 2y dy/dt) For d/dx d/dx(ln(x^2y^2)) = 1/(x^2y^2) d/dx(x^2y^2) = 1/(x^2y^2) * (2x 2y dy/dx) Calculus Science Anatomy & Physiology AstronomyGiven x y z = 6 x2 y2 z2 = 16 x3 y3 z3 = 196 Formula used (x y z)2 = x2 y2 z2 Q19 The distance between points P and Q is 485 km If a person starts from point P with the speed of 60 km/h and another person is running with a certain speed from point Q and they both meet after 25 hours then find the speed of the person who starts from point Q
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Complete Factor x^2y^2 Shell, There is a great deal of pattern recognition in factoring, by that I mean looking at an expression and seeing patterns you have seen before and recognizing how to factor them This is true of the "difference of squares" you sent us, x 2 y 2 Once you think you know the factors you can check by multiplicationSOLUTION GIVEN cosA cosB = x, 1 – sin 2 A – sin 2 B = y/2 and cosAcosB = z FORMULA USED cos 2 A = 1 – sin 2 A CALCULATION cosAcosB = z (1) And, cosA cosB = x Taking square on both side cos 2 A cos 2 B 2cosAcosB = x 2 ⇒ 1 – sin 2 A 1 – sin 2 B 2cosAcosB = x 2 x^4y^4z^4 = 25/6 Given { (xyz=1), (x^2y^2z^2=2), (x^3y^3z^3=3) } The elementary symmetric polynomials in x, y and z are xyz, xyyzzx and xyz Once we find these, we can construct any symmetric polynomial in x, y and z We are given xyz, so we just need to derive the other two Note that 2(xyyzzx) = (xyz)^2(x^2y^2z^2) = 1 So xyyzzx = 1/2 Note that 6xyz = (xyz
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In the relation z = f(x,y) the independent variables are x and y and the dependent variable z We have seen in Section 181 that as x and y vary the zvalue traces out a surface Now both of the variables x and y may change simultaneously inducing a change in z However, rather than considerS1=the part of the paraboloid z = 1−x2 −y2 with z = 0 together with S2=disc {(x,y) x2 y2 ≤ 1} Here n is the outward pointing unit normal 5 Solution Applying the Divergence Theorem noting that V is the volume enclosed by S1 and S2 and divF= 2 gives I = Z Z S FndS = Z Z Z V divFdxdydz = Z Z Z V 4dxdydz = 4 Z ZGiven 2^x=3^y=6^z Lets assume that each and every term is equal to k Which implies 2^x=k Now by applying logarithm on both sides we get x=log k to base 2 and 1/x= log 2 to base k And 3^y=k Again by applying logarithm on both sides we get y=lo
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3xy;x 3y) and Sis the the part of z= 5 x2 y2 above the plane z= 1 Assume that Sis oriented upwards Solution If we want to use Stokes' Theorem, we will need to A castiron solid cylinder is given by inequalities \(x^2 y^2 \leq 1, \, 1 \leq z \leq 4\) The temperature at point \((x,y,z)\) in a region containing the cylinder is \(T(x,y,z) = (x^2 y^2)z\) Given that the thermal conductivity of cast iron is 55, find the heat flow across the boundary of the solid if this boundary is oriented outwardUsing x = 2, y = 3, and z = 4, evaluate each expression and match to its corresponding answer SW 1 ху 2 A) 6 2 х(у 2) B) 1 3 2z Зу C) 2 4 x yz D) 14 5 ху— хz E) 12 6 2(г— х) F) 1 7 yz X y G) x y 8
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3D plot x^2y^2z^2=4 Natural Language;Together with x 2 y 2 z 2 = 1 x^2 y^2 z^2 = 1 x 2 y 2 z 2 = 1, we get x = 1 14, y = 2 14, z = 3 14 It is x2 −y2 z2 −2xz = (x2 −2xz z2) −y2 = (x − z)2 −y2 = (x −z y) ⋅ (x −z − y) Answer link
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Given, x^2y^2z^2=2 (xyz)3=2*x2*y2*z3 or, x^2–2*xy^22*yz^22*z=3=1–1–1 or,x (x2)y (y2)z (z2)=1–1–1 Now let us assume, x (x2)=1>x^2*x1=0> (x1)^2=0, or, x=1 y (y2)=1>y^22*y1=0> (y1)^2=0, or y=1 z (z2)=1>z^22*z1=0> (z1)^2=0, or,z=1In general, you are dealing with a function of two random variables So given a joint PDF of math X,\,\,Y /math, math f_{X,Y}(x, y) /math, you can find the CDF of math Z /math, math F_Z(z) /math, by two variable integration If a nFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutor
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The lower bound z = x 2 y 2 z = x 2 y 2 is the upper half of a cone and the upper bound z = 18 − x 2 − y 2 z = 18 − x 2 − y 2 is the upper half of a sphere Therefore, we have 0 ≤ ρ ≤ 18, 0 ≤ ρ ≤ 18, which is 0 ≤ ρ ≤ 3 2 0 ≤ ρ ≤ 3 2 For the ranges of φ, φ, we F p × acts on the set of solution by coordinatewise multiplication, where we have ( c x, c y, c z) = ( x, y, z) iff c = 1 or x = y = z = 0, that is all orbits except that of the trivial solution have length p − 1 We conclude that p − 1 ∣ m − 1, hence together with p ∣ m m ≡ p ( mod p 2 − p) by the Chinese Remainder TheoremMath\overrightarrow{\nabla} F=50x\hat{i}18y\hat{j}32z\hat{k}/math This vector is required to be parallel to math\overrightarrow{PO}=x\hat{i}y\hat{j}z\hat{k
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3dprinting, solidworks f(0,0,0) is 0, not 1 (the isosurface level), so you only get points drawn completing the cones if there are enough points near the origin that happen to have value 1 But when you switch to linspace(,,), the closest coordinates to the origin are at about 105, leaving a gap of about 21Section Stokes' Theorem Problem 1 Use Stokes' Theorem to evaluate ZZ S curl (F) dS where F = (z2;For example, the socalled pythagorean triples (x, y, z) are positive integer solutions to the equation x 2 y 2 = z 2 Here is another Theorem There are no positive integer solutions to the diophantine equation x 2 y 2 = 1 Proof (Proof by Contradiction) Assume to the contrary that there is a solution (x, y) where x and y are positive
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Integrate x/(x1) integrate x sin(x^2) integrate x sqrt(1sqrt(x)) integrate x/(x1)^3 from 0 to infinity; Taking A = α,B = β,C = γ We have cosα = x y z ⇒ 1 cosα = y z x By dividendo and componendo we get 1 −cosα 1 cosα = y z −x x y z ⇒ 2sin2( α 2) 2cos2( α 2) = y z −x x y z ⇒ tan2( α 2) = y z − x x y z SimilarlyExtended 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, music
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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, musicView more examples » Access instant learning tools Get immediate feedback and guidance with stepbystep solutions and Wolfram Problem Generator Learn $\begingroup$ Thanks I appreciate the reply I'm new to this unit and I can see that it would be connected But I'm stuck on the proof In class they provided us with the definition that S is path connected if for every two points a,b there exists a path f 0,1 st f0 = a and f1 = b
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Note that if \omega is a complex cube root of unity, then x^2y^2z^2 xy yz zx = (xy\omega z\omega^2)(xy\omega^2 z\omega) Thus it is sufficient to prove that xy\omega z\omega^2 Note that if ω is a complex cube root of unity, then x 2 y 2 z 2 − x y − y z − z x = ( x y ω z ω 2 ) ( x y ω 2 z ω ) Thus it is sufficient to prove that x y ω z ω 2Integrate 1/(cos(x)2) from 0 to 2pi;It's the equation of sphere The general equation of sphere looks like math(xx_0)^2(yy_0)^2(zz_0)^2=a^2/math Wheremath (x_0,y_0,z_0)/math is the centre of the circle and matha /math is the radious of the circle It's graph looks
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Block Diagram System Functional Di erence Equation System Function UnitSample Response Delay Delay X Y Y X = H (R ) = 1 1 RR 2 y n = x n y n 1 y n 2 H (z) =Noting that this step has yielded cos^2(a) sin^2(a) and can be replaced by 1 using the standard trigonometric identity cos^2(y) sin^2(y) = 1, this leads to the result R = sqrt() Step 3 Solve the equation given for x a From the result in step 2, 4cos(2x ) 2sin(2x) = 1 can be written as sqrt()*cos(2x 266) = 1 b
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