1.) A gateway is a parabolic shape whose vertex is 20 ft. From the ground, (0,20), and the width of the

Q: 1. Put the following equations in standard form and find the center point and the radius: a) x-2x+y…

A: Given that

Q: a. X= 5 6. How long is line segment MN in Figure 2? b. x = 1 figure 2. AY c. 9V7 d. 162 a. 18 b. 9…

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Q: (1-1)? (y-3)? + = 1 10 11

A: Center: (1,3)   Foci: (1,2), (1,4)   Vertices : (1, 3-sqrt(11))    ~ (1,-0.3166) & (1,…

Q: A straight line passes through points A(-1,4) and B(0, -3). Write the equation of the line under:…

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Q: 4) Three planes form a triangular prism with the equations: y = 0 -√3x + y = 0 x + √3y = 4 a. Find…

A: The angle between the planes is the same of the angle between the normals. If n1 and n2 are two…

Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: Complete the coordinates: A(-4,) and B( 6). Then, find the length and midpoint of AB. Show work with…

A: See that, the point A is at 2 unit below the X-axis, which is shown by the bold horizontal line.…

Q: B- Vertices of a triangle are, A(-1, 0, 1), B(3, -2, 0) and C(4, 1, -2). Find 1- Area of Triangle 2-…

A: A detailed solution is given below.

Q: 2. A trucking company needs to determine whether a house trailer will fit that has an opening shaped…

A: In this question we will use basic of calculus i.e concept of parabolic curve. We will first find…

Q: Consider points A(4, -1, 3), B(3, 1, 8), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

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Q: Given the points P=(1,0,1) and Q=(5,-4,3) find an equation for the sphere for which the segment PQ…

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Q: By calculating the lengths of its sides, show that the triangle with vertices at the points A(1, 2),…

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Q: Consider a right triangle whose sides are under the coordinate axes and the hypotenuse under the…

A: Tangent line and maximization area

Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: To which coordinate plane is the plane y = 1 parallel?

A: y=1

Q: 4. What is the equation of a circle with radius 3 and center (3, 0)? A. x2 + y2 – 6x = 0 B. x2 + y?…

A: equation of the circle with radius 3 and center (3, 0) :(x-3)2+(y-0)2 = 32

Q: 12. Graph the two equations and find the points in which the graphs intersect. a) y = -x², y = 2x2-1…

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Find the coordinates of the midpoint of the segment that joins the points a) (a, 0) and (0, b). b)…

A: Givena a, 0 and 0, bb 2a, 0 and 0, 2bMidpoint =x1 +x22 , y1+y22

Q: 1. Consider triangle AABC on the coordinate plane. Let P = (-2, 1) and Q = (2,1). Point P is on side…

A: We are authorized to solve only 3 subpart of question, please repost remaining parts

Q: . Find the angle between the two tangents from the origin to the circle…

A: (a) Any line through (0,0) is y-mx=0. It is a tangent to the circle (x-7)2+(y+1)2=25…

Q: The triangle formed by A(z₁), B(22) and C(23) has its circumcentre at origin. If the perpendicular…

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Q: On the bisector of the second and fourth quadrant determines a point p such that the sum of the…

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Q: 1, In the quadrilateral shown OA = 2a, OB = 2b, OC = 2e. Points P. Q. R and S are the mid-points of…

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Q: (a) Draw AXYZ with XY = 4cm, YZ = 6cm and ZXYZ= 35°. (b) Measure and write down the length of side…

A: Given,  We have to draw ∆XYZ  with  XY = 4 cm ,  YZ = 6 cm   and  ∠XYZ = 35°  (b) Then measure and…

Q: The triangle formed by A(z₁), B(z2) and C(z3) has its circumcentre at origin. If the perpendicular…

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Q: iii) Find the time when it reaches the highest vertical distance and calculate this distance. iv)…

A: Let's find highest vertical distance and draw the graph.