10. For the following pair of functions, i) functions intersect (by calculating and stating the points of determine if the curves of the intersection) ii) sketch the functions and identify if the functions do intersect, the regions(s) bounded by the curves. y = x + 4x + 1 3 and y = (hınt: use Newton's method to solve for the points of intersection)

Q: 2. Knowing their linear relationship, find the expression of "C in terms of F using the point-slope…

A: If we have 2 points x0, y0 and x1, y1, then the point-slope form is y-y1=mx-x1, here, m is the slope…

Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…

Q: (b) Find the points that touch the x axis of curve v = u? + pu + (n + 1). Where n=666. Also find the…

A: given the curve in u,v axis is as, v=u2+pu+n+1    where n=666

Q: A rectangle is placed inside a semicircle of radius r, with one side along the diameter. What is the…

A: Given :-  A rectangle is placed inside a semicircle of radius r , with one side along the diameter.…

Q: 3) Find the z-coordinate(s) of the point (s) on the curve y = ³ + 6x² - 2x + 15 where the tangent…

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Q: #8. In each case, sketch the set of points determined by the given conditions (a) /2-1+i/>1 (b)…

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Q: Let Y be a relation defined by a Y b iff a times b is even. Is 5 Y 7 true?

A: Here, the given problem is on relation on set. We will solved the problem  step by step.

Q: Q4/ Find the angle between the curves x² = y & y² = x

A: The curves intersect at (1,1).  Now calculate slope at (1,1):  ddxx21,1=ddxy1,12x1,1=dydx1,1m1=2…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

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Q: In this problem you will get some practice with the logic of sets, i.e., ways of putting sets…

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Q: Let x = a(cost + sin t), y a(sint- teos t). Find C. tant D. cott 38. A. sect B. cost Eliminate the…

A: (38) Given that , x=acost+tsint , y=asint-tcost find dydx=?

Q: Find the equation of the vertical lines that meet the curves y = x³ + 2x² - 4x +5 and 3y = 2x³…

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Q: 5) Find the lengths of the following curves:- 1. y = x 8 from (0,0) to (4,8) -(1010 – 1 )) 27 (ans.…

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Q: 5- 24 1+ A to A' type your answer. B' type your answer. and C' type your answer.

A: The given data is:   From the graph, the coordinate of A2,-3, B5,-4, and C2,-4 To find the…

Q: 5. Show that the sum of the intercepts of the tangent to the parabola (Art. 129), x+y=a¹, is equal…

A: We need to prove given theorem.

Q: Find the equation of the shortest curve that describes the distance between the two points A(x₁, y₁)…

A: Two points :A and B

Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

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Q: Find the shortest distance from the point (2,1) to the curve y = 1+√x.

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Q: 5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact…

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Q: The slope of the tangent line to a plane curve y=f(x) at the point (x,y) is given by 3 - 2 m=- + 16x…

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Q: 8) Find the distance between (3, -2) and (6, 5) Round to the tenths place Substitute into formula

A: To find the distance between the points 3, -2 and 6, 5.

Q: Write down the slope, of tangents of circle x +y2 =25 parallel to order 3x- 54 +8=0

A: