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Find the point at which the line fix)--2x-3 intersects the line g(x) -x (x, y) =(1-3,-x...
Write a program that asks the user the slope and y-intersect of one line y =...
Write a program that asks the user the slope and y-intersect of one line y = a_1x + b_1, the slope and y-intersect of a second line y = a_2x + b_2. The program returns the point of intersection of the two lines, if it exists. Otherwise, the program must print a message to indicate that the two lines do not have a point of intersection. Recall that, if it exists, the point of intersection (x_o, y_o) of two lines...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 pass...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
Find the line through (9, 1, −6) that intersects and is perpendicular to the line x = −1 + t, y =...
Find the line through (9, 1, −6) that intersects and is perpendicular to the line x = −1 + t, y = −3 + t, z = −1 + t. (HINT: If (x0, y0, z0) is the point of intersection, find its coordinates. Enter your answers as a comma-separated list of equations.)
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2...
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y...
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)
Find the point at which the line intersects the given plane. x = y – 2...
Find the point at which the line intersects the given plane. x = y – 2 = 4z; 4x – y + 2z = 12 (x, y, z) = ( (x, y, z) = D
Find the point at which the line with the parametric equations x-1-1, y=1+1, z intersects the...
Find the point at which the line with the parametric equations x-1-1, y=1+1, z intersects the plane with the equation X-y +3.2-4.
determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)=2x^2-5x+3 at exactly one point determine the value(s) of k such that the linear function g(x)=4x+k does not intersect the parabola f(x)=-3x^2-x+4
determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)=2x^2-5x+3 at exactly one pointdetermine the value(s) of k such that the linear function g(x)=4x+k does not intersect the parabola f(x)=-3x^2-x+4
Write a program that asks the user the slope and y-intersect of one line y = a_1x + b_1, the slope and y-intersect of a second line y = a_2x + b_2. The program returns the point of intersection of the two lines, if it exists. Otherwise, the program must print a message to indicate that the two lines do not have a point of intersection. Recall that, if it exists, the point of intersection (x_o, y_o) of two lines...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)
Find the point at which the line intersects the given plane. x = y – 2 = 4z; 4x – y + 2z = 12 (x, y, z) = ( (x, y, z) = D
Find the point at which the line with the parametric equations x-1-1, y=1+1, z intersects the plane with the equation X-y +3.2-4.
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