Find the points on the graph of 3x2 + 10xy + 3y? = 9 closest to the origin.

Q: Put the equation y= a + 20a + 99 into the form y (a - h)" + k: %3D

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Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: In(y) + 2x + In(x) 2 3

A: We need to isolate the y terms, in the given equation,…

Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: find the x- and y-intercepts of the graph of the equation 2x + 3y = 6

A: We to find the x- and y-intercepts of the graph of the equation 2x + 3y = 6

Q: Find the point on the line 2x + 6y + 5 = 0 which is closest to the point (2, 0).

A: Let, (h,k) be the point on the  2x+6y+5=0. That is,

Q: Complete the square to express y= 3x – 10x – 5 in the form y=a(x-h)² +k. Then give the coordinates…

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Q: Find the point on the line – 6x + 2y +1= 0 which is closest to the point (1, – 3).

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Q: Use the given diagram to set up an equation and solve for X. (4x+20Y 40° Equation:

A: Given: To set up: An equation and to solve for x.

Q: Find the x-intercepts of the graph of the equation shown below. y=24x2 – 76x+40 OA. and OB. ,0 and…

A: Consider the equation: y=24x2-76x+40. Find the x-intercept.   x-intercept is the point on the graph…

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Q: Find a, b, and c, so that the graph of the quadratic equation y = ax + bx +c passes through (-2,14).…

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Q: Find the x- and y-intercepts of the graph of the equation. 3x − 4y = 12

A: Find the x- and y-intercepts of the graph of the equation. 3x − 4y = 12

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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Q: Graph the equation 3x - 4y = 8 on the xy-plane

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Q: Approximate the solution(s) to x3-2x+2=0 using a graphing utility

A: x3-2x+2=0

Q: Find the point on the line 2x + 6y + 5 = 0 which is closest to the point (-4, -4). (

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Q: find (y" ) for the following equation 3x²-2y'-y=6 at point (2,1)

A: Take the first derivative of the whole term than find y' at given point after this calculate second…

Q: Find the point on the line -4x + 7y + 1 = 0 which is closest to the point (– 1, 3). %3D

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Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Find a point on the parabola y - x* + 9 which is closest to the origin.

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: Find the equation of the line containing the point P(−2, 2) and perpendicular to the graph of 3x +…

A: The slope of the line 3x + 9y = −2 is given by,

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-8x+7. If there is…

A: The given equation is;  y=x2-8x+7.

Q: - 7x + 12 = 0 %3D AY

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Q: Compute the discriminant. Then determine the number and type of solutions of the given equation.…

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Q: Find the x-intercepts of the graph of the equation shown below y=24x² – 76x+40 OA. and 0* (0) me…

A: Given equation is y=24x2-76x+40. To find the x-intercepts. Solution: The x-intercept is the point…

Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of the…

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Q: The roots of the equation D(4) – 81y = 0 are

A: Here I am attaching image so that you understand each and every step.

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: Show clear and detailed solutions • Determine and draw the graph of the following equation in R3 :…

A: We have to sketch the graph in R3.

Q: 3) Find the vertex of the parabola f(x) = 4x² + 40x+104. Write in correct (x, y) form.

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Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x+4x-5. If there is…

A: The given parabola is: y=x2+4x-5...(1)

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x+8x+12. If there is…

A: The required solution is

Q: Find the equation of the line containing the point  P(−1, 3)  and perpendicular to the graph of…

A: To find the equation of the line containing the point P(-1,3) and perpendicular to 3x+6y=-1

Q: Find the roots of: (D² - 4) (D2)y = 0

A: To find the roots of the given equation D2-4(D-2)y=0

Q: Find the point on the parabola y=x2 closest to (6,3

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Q: Find all solutions of the equation in the interval [0,2π) 2sinxcos2x+2cosxsin2x=1

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Q: Find the x- and y-intercepts of the graph of the equation. y - 2xy + 2x = 1

A: To find x intercept we have to put y = 0. To find y intercept we have to put x = 0.

Q: Approximate the solution(s) to x3 - 2x + 2 = 0 using a graphing utility.

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Q: Use the related graph of each equation to determine its solutions. 14. x? + 4x = 0 15. -2r? – 4x – 5…

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find all points on the x-axis that are 14 units from the point (6, - 7).

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Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x´-8x+12. If there is…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.