For the equation: 7x2 - 6√3xy + 13y2 - 16 = 0, determine what angle of rotation would eliminate the x′y′-term in a rotated x′y′-system.

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

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Q: Solve for x & y so that the figure is a parallelogram. 2y+ 8 –3x+ 4\ -4x–2/ 5.

A: Given: The given figure is a parallelogram. The property of parallelogram states that: The diagonals…

Q: Graph the image of rhombus QRST after a reflection across the x-axis. 10 8 9. R co 4,

A: NOTE: Refresh your page if you can't see any equations. . write the coordinates of the vertices of…

Q: i. x = sin (y – 5) 2 ii. –3x² + y? – 22 = 6

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Q: Identify the equation without applying a rotation of axes. 4x2-8xy+4y2-3x+6=0

A: Given, function is

Q: Convert the rectangular equation x2 + y2 = 8x to an eq %3D

A: By using the relationship between rectangular coordinates and cylindrical coordinates . We can…

Q: Write the equation with rectangular coordina r = 6cose O x?-y? = 6x %3D O x2+y? = 6x %3D O x²+y² =…

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Q: How far is the center equation 10x^2 -y^2 -5y -11 to its focus?

A: Note: It is assumed that the equation, 10x2-y2-5y-11 is 10x2-y2-5y-11=0.   The conics are generated…

Q: Convert the rectangular equation x2 + y? - 3z2 = 0 to an e %3D

A: Here we use the relationship between rectangular coordinates and spherical coordinates to convert…

Q: Graph the equation, y = cosx y (x.y) 2n y (x,y) 1 0.8 0.6 0.4 0.2 0- -0.2 -0.4 -0.6 -0.8 -1

A: Given:- y =cosx  To find:-  Graph of given function

Q: In the equation 3x2 + 4y2 -18x + 8y +19 = 0, find the center and foci, plot the ends of the axes and…

A: 3x2+4y2-18x+8y+19=0 On simplification, we get…

Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ = 60° in terms of a rotated x′y′-system using θ,…

A: Consider the given equation: Here the objective is to find the equation if the axis is rotated by…

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

A: Given.

Q: 3. What is the length of the minor axis given by the equation + - (y-1) = 17 O 4 units O 2 units O…

A: To find the length of minor axis

Q: For the figure shown, a || b || c. Find x and y. a zy + 14 b У - 8 X,

A: the given figure is: a∥b∥c. we have to find the values of x and y.

Q: In the circle below, VZ = 13 units, ZY = 5 units, and WX = 8 units. Solve %3D %3D for VY. Show your…

A: We will use the fact that, triangle VYZ is a right-angled triangle and use it to find the Value of…

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Given, 3x2 - 10xy + 3y2 - 32 = 0. It is of the form Ax2+Bxy+Cy2+Dx+Ey+F=0   On comparing we get,…

Q: Given the general equation x² + 2x + y? – 2y - 2 0, find its center and radius. O Center (-1,1),…

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Q: Write the appropriate rotation formulas so that in a rotated system the equation 11x2 + 10√3xy + y2…

A: Given Data The equation is 11x2+103xy+y2-4=0.   Compare the equation 11x2+103xy+y2-4=0 with general…

Q: two gears are adjust so that the smaller gear drives the larger one, if the smaller gear (r=3.5)…

A: Let r1 and r2 be the radius of the smaller and larger gears, respectively.Given that, r1 = 3.5 and,…

Q: Given the circles Cx2 + y² – 6x – 4y + 9 = 0 and C2:x² + y2 - 2x- 6y + 9 = 0, Find, (a) the equation…

A: Circle Family of circle Tangent equation

Q: draw the plane given by the equation  x + 2y = 6

A: To draw the plane given by the equation  x + 2y = 6

Q: The equation (x − h)2 + (y − k)2 = r2 is the standard form of the equation of a ________ with center…

A: The equation x-h2+y-k2=r2 is the standard form of the equation of a circle with center (h, k) and…

Q: Find a Cartesian equation for r = 3t – 1, y = 4t + 2.

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Q: The roots of the equation x² - 6x + I = 0 are? The equation of the line of symmetry to the curve y…

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Q: Find the equation that is perpendicular to y = x +3 and passes through the point (-3, -4). %3D Oy =…

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Q: For this rhombus, if <DEA = 2x + 5, what is the correct equation? A, .B O 2x + 5 = x 2x + 5 = 45 O…

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Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Given equation is 34x2-24xy+41y2-25=0. x=x'cosθ-y'sinθ, y=x'sinθ+y'cosθ. Compare the above equation…

Q: On the coordinate plane below, the square ABCD will be rotated 90° clockwise about the origin to…

A: Given data: *A square ABCD is rotated 90 degrees clockwise about the origin to the new position…

Q: 1) For three 2D points A (x1, y1), B (x2, y2) and C (x3, y3), how would you order these points…

A: Given: Three 2D points A(-1,0), B(-2,0) &amp; C(0,0) We have to order these points counterclockwise.…

Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ= 60° in terms of a rotated x′y′-system using θ,…

A: Consider the given equation: 13x2 - 63xy + 7y2 -16=0 Here the objective is to find the equation if…

Q: The secant focus y2 = -6x is

A: Given the equation of a parabola is: y2=-6x To find the secant focus.

Q: sin(r² + y²) dydrdz by converting to a more appropriate coordinate system and then evaluating.

A: Given region of integration is R=x,y,z:-1≤x≤1,-1-x2≤y≤1-x2,0≤z≤1 By changing the cartesian…

Q: The figure was transformed from Quadrant I to Quadrant I. 10 id---7-6-543-2-0 E E7 9 10

A: Given:

Q: For the equation y = x - 3x + 4x + 5, is there any symmetry as to x-axis, y-axis, or origin?

A: An axis of symmetry represents a line about which each part of a function curve is reflection of the…

Q: Translate the axes to eliminate the first degree terms of 3x^(2)+xy+y^(2)-16x-10y+30=0 Find h and k

A: We have to translate the axes to eliminate the first degree terms of 3x2+xy+y2-16x-10y+30=0 To Find…

Q: the general equation От а ircle with center (4,-1) and a rac of 7 units * ) x^2+y^2-5x-5y-31=0 )…

A:

Q: identify the equation without applying a rotation of axes. 4x2-8xy+4y2-3x+6=0

A: Consider the provided equation:

Q: the equation x2+y2+24x+6y-144=0

A: General circle equationx2+y2+2gx+2fy+c=0centre -g,-f and radius r=g2+f2-c

Q: A chicken coop has been built 30 yards south of a farmhouse and is enclosed by a circular fence.…

A: We have to find the equation of the circular fence.

Q: When the axes are rotated through an angle x/4,Find the transformed equation of 3x2+10xy+3y2=9

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Q: Find the angle between the lines whose direction cosines are given by the equations 3L+3+5n=0 and…

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Q: From the given equation of the circle in general form x2 + y2 -6y-7 =0.   complete the square and…

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Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Equation in general form, Ax2+Bxy+Cy2+Dx+Ey+F=0 Where, x=x'cosθ-y'sinθ and y=x'sinθ+y'cosθAnd…

Q: Create the equation of aline that is perpendicular to 2y = 14 + and passes through the point (-2,…

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Q: Find the equation of the bisector of the acute angle formed by the lines 1+2y=3=0 and 2x+y-4=0. 0 a.…

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Q: Find the angle between A = 10a + 2a and B = - 4a + 0. 5a¸ , using dot product. Answer:

A: As we know that, The expression for the angle between the two vectors is: θ=cos-1A→·B→A→B→ Given:…

Q: Find the value of x for the following parallelograms. 5) м 2х -12 6) ВP 3D 17 PD = 17x 10 K D туре…

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Q: Eliminate the parameter and find à corresponding rectangular equation: x = t , y = 2–3 t

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Q: Given the equation, (x-h+v-k)² =r?,what are the coordanates of the center? The coordinates of the…

A: Answer and explanation is given below....