Find the slope of the tangent to a parabola y = x 2 at a point on the curve where x = ½ A 0 93 Find the acute angle that the curve y = 1 – 3x 2 cut the xaxisThe base is the region enclosed by y = x 2 y = x 2 and y = 9 y = 9 Slices perpendicular to the xaxis are right isosceles triangles The intersection of one of these slices and the base is the leg of the triangle 73 The base is the area between y = x y = x and y = x 2 y = x 2Find the area of the finite part of the paraboloid y = x2 z2 cut off by the plane y = 16 Hint Project the surface onto the xzplane Expert Answer % (16 ratings) Previous question Next question Get more help from Chegg Solve it with our calculus problem solver and calculator
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The line x+y=2 cuts the parabola-Example 57 Find the area of the ellipse cut on the plane 2x 3y 6z = 60 by the circular cylinder x 2 = y 2 = 2x Solution ThesurfaceS liesin theplane 2x3y6z = 60soweusethisto calculatedS =Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
Solution Suppose You Have Inches By 16 Inches Cardboard You Need To Cut An Identical Square In Each Corner To Form An Open Box With A Total Volume Of 384 Cubic
Hi Mike, y = x 2 2 is a quadratic equation of the form y = ax 2 bx c, let a = 1, b = 0 and c = 2 You can certainly plot the graph by using values of x from 2 to 2 but I want to show you another way I expect that you know the graph of y = x 2 If you compare the functions y = x 2 and y = x 2 2, call them (1) and (2), the difference is that in (2) for each value of x the Example 2 y = x 2 − 2 The only difference with the first graph that I drew (y = x 2) and this one (y = x 2 − 2) is the "minus 2" The "minus 2" means that all the yvalues for the graph need to be moved down by 2 units So we just take our first curve and move it down 2 units Our new curve's vertex is at −2 on the yaxisClick here👆to get an answer to your question ️ If the line y √(3)x 3 = 0 cuts the parabola y^2 = x 2 at A and B , the PA PB is equal to If P = √(3), 0)
You have x2 −y2 = (x y)(x −y) So in your case x2 − y2 x −y = (x y)(x − y) x − y = x y Answer link Rewrite as x^22xy=0 This is a quadratic equation in variable x Don't be confused, I'm just pointing out that we will temporarily be thinking of y as a constant (a number) We would solve by factoring if we could, but we can't so we'll use the quadratic formula, which says that the solutions to 2x^2 bx c = 0 are x=(bsqrt(b^24ac))/(2a)Y= x2 left of x= 1 We reverse the order of integration, so that Z 1 0 Z 1 p y p x3 1 dxdy= Z 1 0 Z x2 0 p x3 1 dydx = Z 1 0 x2 p x3 1 dx = 2 9 (x3 1)3=2j1 0 = 2 9 (23=2 1) c) The integral representing the volume bounded by ˆ= 1 cos˚(in spherical coordinates)
Divide 0 0 by 4 4 Multiply − 1 1 by 0 0 Add − 2 2 and 0 0 Substitute the values of a a, d d, and e e into the vertex form a ( x d) 2 e a ( x d) 2 e Set y y equal to the new right side Use the vertex form, y = a ( x − h) 2 k y = a ( x h) 2 k, to determine the values of a a, h h, and k kAnswer to Find the area of the finite part of the paraboloid y = x^2 z^2 cut off by the plane y = 81 (Hint Project the surface onto theVolume V of the solid generated by revolving the area cut off by latus rectum (x = a) of the parabola y^2 = 4ax, about its axis, which is x axis, is given by the formula;
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreStart your free trial In partnership with Prove that the curves x = y 2 and xy = k cut at right angles if 8k 2 = 1 Hint Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other
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Solution Suppose You Have Inches By 16 Inches Cardboard You Need To Cut An Identical Square In Each Corner To Form An Open Box With A Total Volume Of 384 Cubic
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Surface area and surface integrals (Sect 165) I Review Arc length and line integrals I Review Double integral of a scalar function I The area of a surface in space Review Double integral of a scalar function I The double integral of a function f R ⊂ R2 → R on a region R ⊂ R2, which is the volume under the graph of f and above the z = 0 plane, and is given byQuestion for what value(s) of k will the graph of y = x^23xk a) touch the xaxis b) never meet the xaxis? Ex 63, 23 Prove that the curves 𝑥=𝑦2 & 𝑥𝑦=𝑘 cut at right angles if 8𝑘2 = 1We need to show that the curves cut at right angles Two Curve intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other First we Calculate the point of inters
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Solve Quadratic Equation by Completing The Square 22 Solving x26x10 = 0 by Completing The Square Subtract 10 from both side of the equation x26x = 10 Now the clever bit Take the coefficient of x , which is 6 , divide by two, giving 3 , and finally square it giving 9 Add 9 to both sides of the equation On the right hand side we haveFind the area of the finite part of the paraboloid {eq}y = x^2 z^2 {/eq} cut off by the plane y = 16 (Hint Project the surface onto the xzplane) Section 52 Line Integrals Part I In this section we are now going to introduce a new kind of integral However, before we do that it is important to note that you will need to remember how to parameterize equations, or put another way, you will need to be able to write down a set of parametric equations for a given curve
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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!These should be our limits of integration Hence, the volume of the solid is Z 2 0 A(x)dx= Z 2 0 ˇ 2x2 x3 dx = ˇ 2 3 x3 x4 4 2 0 = ˇ 16 3 16 4 = 4ˇ 3 7Let V(b) be the volume obtained by rotating the area between the xaxis and the graph of y= 1 x3 from x= 1 to x= baround the xaxisCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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M = 68 m = 78 m = 102 m = 112 c What is the equation, in pointslope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?Related » Graph » Number Line » Examples » Our online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!This is always true with real numbers, but not always for imaginary numbers We have ( x y) 2 = ( x y) ( x y) = x y x y = x x y y = x 2 × y 2 (xy)^2= (xy) (xy)=x {\color {#D61F06} {yx}} y=x {\color {#D61F06} {xy}}y=x^2 \times y^2\ _\square (xy)2 = (xy)(xy) = xyxy = xxyy = x2 ×y2 For noncommutative operators under some algebraic
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We can do this because we are not multiplying by zeroCalculus Multivariable Calculus Find the area of the finite part of the paraboloid y = x 2 z 2 cut off by the plane y = 25 Hint Project the surface onto the xzplane more_vert Find the area of the finite part of the paraboloid y = x 2 z 2 cut off by the plane yFactor x^2y^2 x2 − y2 x 2 y 2 Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (ab)(a−b) a 2 b 2 = ( a b) ( a
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12 18 81 99 b Two parallel lines are crossed by a transversal What is the value of m?If the Curve Ay X2 = 7 and X3 = Y Cut Orthogonally at (1, 1), Then a is Equal to (A) 1 (B) −6 6 (D) 0 Mathematics Advertisement Remove all ads Advertisement Remove all adsReason x/y y/x = 2 Given x≠0 and y≠0 Because then the original question would be dividing by zero xy≠0 Because neither factor is zero (xy) (x/y y/x) = (xy) 2 Multiply both sides of given equation by (xy);
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Y= x 2 z cut o by the plane y= 25 Solution Surface lies above the disk x 2 z in the xzplane A(S) = Z Z D p f2 x f z 2dA= Z Z p 4x2 4y2 1da Converting to polar coords get Z 2ˇ 0 Z 5 0 p 4r2 1rdrd = ˇ=8(101 p 101 1) Section 167 2A) It will touch the xaxis when the polynomial has only one solution If the polynomial has only one solution, then the discriminant isV= (π)∫y^2dx, within limit x = 0 to a = (π)∫(4ax)dx, limits 0 to a = 4
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For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side a b can be cut into a square of side a, a square of side b, and two rectangles with sides a and bWith n = 3, the theorem states that a cube of side a b can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × bY = x 2 2 First, we find the critical points on D We begin by finding the partials and setting them equal to zero • fx(x,y)=1y =0 • fy(x,y)=1x =0 The only critical point on D is (1,1) Notice that f(1,1) = 1 Now, we find the extreme points on the boundary We will use the information in our picture to help us From (0 ,0) to (0,2), theAnswer by jim_thompson5910() (Show Source) You can put this solution on YOUR website!
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F (x,y) is the height of the graph along the z axis The first line is z=f (x,y)=x0², or, z=x, which is a line that rises up above the xy plane at a 45 degree angle and is positioned directly over the x axis (since the x axis is where y=0) When x=0, z=0, when x=1, z=1, when x=2, z=2 That means there is a curtain along the x axis whoseWhat must be the value of x so that lines c and d are parallel lines cut by transversal p?This is the 3rd video I sent to a graduating Grade 12 when her graduation in was cancelled because of COVID19 Her Mom asked those who knew her or taug
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Here we can clearly see that the quadratic function y = x^{2} does not cut the xaxis But the graph of the quadratic function y = x^{2} touches the xaxis at point C (0,0) Therefore the zero of the quadratic function y = x^{2} is x = 0 Now you may think that y = x^{2} has one zero which is x = 0 and we know that a quadratic function has 2 zerosCalculus Calculus Early Transcendentals Find the area of the finite part of the paraboloid y = x 2 z 2 cut off by the plane y = 25 Hint Project the surface onto the xzplane more_vert Find the area of the finite part of the paraboloid y = x 2 z 2 cut off by the plane y = 25 Hint Project the surface onto the xzplane The second geometric interpretation of a double integral is the following Area of D = ∬ D dA This is easy to see why this is true in general Let's suppose that we want to find the area of the region shown below From Calculus I we know that this area can be found by the integral, A = ∫b ag2(x) − g1(x)dx
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