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- Points of Intersection Sketch the circle x2+y2=4. Then find the values of C so that the parabola y=x2+C intersects the circle at the given number of points. (a) 0 points (b) 1 point (c) 2 points (d) 3 points (e) 4 pointsFast pls solve this question correctly in 5 min pls I will give u like for sure Nid Find an equation of the plane. The plane through the point (−3, 7, 10) and perpendicular to the line x = 1 + ty = 2t, z = 1 − 2t.A bird is hunting for fish in a pond. She swoops down from a height and picks up a fish from the water surface and flies back up, all along a path y=4x2−(2k+2)x+1, where k≥0, y is its height from the water surface, and x is the horizontal distance from a fixed origin which is in the plane of the path. Then, the value of k can be:
- Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. y0, z0 Choose the correct answer below. The xy-plane The point (0,0,0) The x-axis The xz-plane The z-axis The yz-plane The y-axisA plane α passes through the points A = (1,1,1), B = (−1,1,4), and C = (2,2,0). A)Find a parameter formulation for the plane. B)Find an equation for the planet. The lines l and m are given by the parameter productions l:x = 2 + 3ty = −1 + tz = −1 −tog m:x = 2 −2ty = −1 −4tz = −1 + t c) Find the minimum distance from each of the lines to the planeQuadrilateral ABCD has vertices A(0,5) B(1,2) C(3,2) and D(2,5). Quadrilateral ABCD is rotated 90 counterclockwise about the origin. Which statement about what happens when point A is rotated is true?A.The x-coordinate of vertex A does not changeB.The y-coordinate of vertex A does not changeC.The image of vertex A remains on the y-axisD.The image of vertex A is a point on the x-axis
- Topic is: PrecalculusThe topic to be discussed is: Analytic Geometry. Question 7Given: (x-2)2/9 + (y-4)2/16= 1What is the center?(2,0) (0,4) (0,0) (2,4) Question 8Given: (x2-2)2/4 + (y-4)2/16= 1Where can you find one of the vertices?(0,4) (-2,4) (2,4) (2,0)Weather Satellites Earth is represented on a map of aportion of the solar system so that its surface is the circlewith equation x2 + y2 + 2x + 4y - 4091 = 0. A weathersatellite circles 0.6 unit above Earth with the center of itscircular orbit at the center of Earth. Find the equation forthe orbit of the satellite on this mapA Ferris wheel at a theme park rotates in an anticlockwise direction at a constant rate. People enter the cars of the Ferris wheel from a platform which is above ground level. The Ferris wheel does not stop at any time. The Ferris wheel has 16 cars, spaced evenly around the circular structure. A spider attached itself to the point P on the side of car C when the point P was at its lowest point at time 1.00 pm. The height, h metres, of the point P above ground level, at time t hours after 1.00 pm is given by h(t)=62+60 sin(((5t-1)pi)/2) a) Write down the maximum height, in metres, of the point P above ground level. b)Write down the minimum height, in metres, of the point P above ground level. c) At what time, after 1.00 pm, does point P first return to its lowest point? d)Find the time, after 1.00 pm, when P first reaches a height of 92 metres above ground level. e)Find the number of minutes during one rotation that P is at least 92 metres above ground level.
- 3) Suppose plane ?1 contains the points ?(5, 0, −1), ?(2, 3, 2), and ?(−2, 1, −4), and assume ?1 is the tangent plane to a function ? = ?(?, ?) at the point ?. Find a possible formula for ?(?, ?) that is NOT linear (there are many correct answers!).Parametric equations including t ∈ (−∞, ∞) and s ∈ (−∞, ∞) x = a1s + b1, y = a2s + b2, z = a3s + b3 and x = c1t + d1, y = c2t + d2, z = c3t + d Show that the following equality is satisfied if the lines given by , intersect or are parallel to each other a1 c1 b1 − d1 a2 c2 b2 − d2 a3 c3 b3 − d3 = 0.You Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (7,0) in the xy -plane, Springfield is at (0,4) , and Shelbyville is at (0,-4) . The cable runs from Centerville to some point (x,0) on the x -axis where it splits into two branches going to Springfield and Shelbyville. Find the (x,0)location that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of x : f(x)=