Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of length one), where each step is either vertical (up or down) or horizontal (left or right). How many such paths stay in the first quadrant (x > 0, y > 0)?

Q: The curve y + 22 = 25 is translated to a new position in the plane and the equation of the new curve…

A: Suppose y+x2=k is any function, where k is constant. Then, in the new translated function…

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A:

Q: Find the x-intercept of the line x+3y-5=0 as a point O a. (0,5) O b. (5,0) O c. None O d. (0,5/3)

A: x intercept can be obtained by putting y=0 in the given equation.

Q: Q5) Find the coefficients a, b, c and d such that the curve defined by; y = ax³ + bx² + cx + d,…

A: Given: The curve y=ax3+bx2+cx+d passes through the points 0, 10, 1, 7, 3, -11, 4, -14. To find: The…

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

A:

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

A:

Q: What is the x-coordinate of every point that lies on avertical line through C?

A: The image shows the horizontal and the vertical lines.

Q: 24 The line y = x - 10 intersects the curve x² + y² + 4x + 6y - 40 = 0 at the points A and B. Find…

A: Consider the given equation of curve, x2+y2+4x+6y-40=0 It is given that the line y=x-10 intersects…

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: Find the distance from the point (-4,-6,4) to the line a(t) = ( – 5, 1, − 3)t + (− 7, — 4, 7) FORCYY

A:

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: Let y = d -7 = 7 and u = -7 -2 Compute the distance d from y to the line through u and the origin.…

A: Introduction: Let l be the path connecting the origin to u. We can compute the projection of y onto…