2 Let PÅ be a tangent line which is tangent to a circle at the point A. Let DĆ be a secant line intersecting the circle at points C and D and intersecting the tangent line at P. Prove (PA)² = (PC)(PD) and < APC = ÷(DA – CA).

Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

A:

Q: Find the equation of the tangent line to the cycloid generated by a circle of radius r = 1 at i =…

A: The solution is given as follows

Q: Determine the slope of the tangent line to the curve of sin(x + y) = y2cos(x)  at  the point (x,y) =…

A: Topic = Derivative

Q: make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at…

A: make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at…

Q: Find equations of the tangent line and normal line to the curve at the given point. y = 6 cos x , (…

A:

Q: Find the tangent line to y = x -x+7 at x = 7. ,2 The tangent line to y = Vx -x + 7 at x = 7 is y =

A: We have to find tangent line

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: (a) Find the equation of the tangent line to the curvey = 2 sec x – 4 cos x at the point (, 2) %3D

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Let L be the tangent line to the graph of the function y = ln x at the point (a, b), where c is the…

A: Given function y = ln(x) L be the tangent line to the graph of the function y = ln(x) at ( a, b ).…

Q: Show that the curve y=|x| has no tangent line at the origin.

A: We show that y = |x| is not differentiable at origin.  Therefore there will be no tangent line at…

Q: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: At how many different values of x does the curve y = x +2x have a tangent line parallel to the line…

A: Given equation of curve is Differentiating with respect to x, we get

Q: 7. Find the points on the curve y ve y = -x where the tangent line is parallel to the line y=

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: At how many different values of x does the curve y =x+ 2x have a tangent line parallel to the line…

A:

Q: Tangents are drawn from the origin to the curbe y=sin x.Prove that their points of contact lie on…

A:

Q: Tangents are drawn from the origin to the curbe y = sin x.Prove that their points of contact lie on…

A:

Q: Find the slope of the tangent line to the curve 2 sin(z) + 5 cos(y) – 4 sin(z) cos(y) + z = 7m at…

A:

Q: 3. Find the equations of the tangent and normal lines to the curve f(x) = /2* +cos(x*) at(0,/2).…

A:

Q: Find equations for the lines that are tangent and normal to the graph of

A: Given equation of the function is: fx=tan xx Differentiating with respect to x we get, f'x=x…

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: 45. Find all points on the curve z'y +ry% 2 where the slope of the tangent line is -1.

A:

Q: How many tangent lines to the curve y = x+3 pass through the point (1, 2)? At which exact points do…

A: Take the derivative of the given curve and satisfy the equation of tangent then solve for points.

Q: Find the slope of the tangent line to the curve 5 sin(æ) + 3 cos(y) – 4 sin(x) cos(y) + x = 7n at…

A:

Q: Show that the tangent lines to the curve y = (paisin x)/x at x = pai and x = -pai intersect at right…

A: y=π sinxx Differentiating with respect to x, we get dydx=ddxπ…

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the line y= 4x - 3.…

A:

Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Find equation for the tangent line at (-l,1) , then an to the curve y= | sketch them togethor

A: Recall: Slope -point intercept form: y-y1=m(x-x1) ; where (x1,y1) is given point and 'm' is the…

Q: Let y= 3 cos x-5 cot x+ csc x tan x, then the slope of the tangent line at x = is 4

A:

Q: Find the equation of the tangent line to the graph of y = f(x) = tan(x) at the point a = 1/3. Give…

A: Given that: y=f(x)=π3

Q: Let point E lie in the exterior of OP. How many tangent lines can be constructed to OP from point E?

A: two tangent line can be drawn to a circle from a point E outside of the circle.

Q: Find the slope of the tangent line to the curve 5 sin(x) + 5 cos(y) – 6 sin(x) cos(y) + x = 6T at…

A:

Q: Let ℓ be the tangent line to the parabola y= x2 at the point (1 ,1). The angle of inclination of ℓ…

A: Given equation of parabola,y = x2       ................(1)Slope of line l is m,m = tanϕ = dydxat…

Q: nd analytically using limits the slope of the tangent line to the curve y= x

A: Here we have to Find analytically using limits the slope of the tangent line to the curve y=x2+3x At…

Q: 61. Find the lines that are tangent and normal to the curve y = 2 tan( 7x/4) at x = 1. . %3D TTX

A: The given curve is  y = 2.tan(πx/4) Thr given point x = 1 At x = 1, y = 2*tan(π/4) y = 2 Point is =…

Q: Find points of horizontal and vertical tangent lines r = 1- cos(0) %3|

A:

Q: IT Find the length of the curve y= in (cos x ), 0 < x < 4

A:

Q: Find the slope of the tangent line to the curve 5 sin(z) + 4 cos(y)- 5 sin(z) cos(y) + z = 3x at the…

A: Consider the curve  5sinx+4cosy−5sinxcosy+x=3π

Q: 4. Find the slope of the tangent line to r = cos 0 at 0 = 3 %3D

A:

Q: Find the tangent line to x^6 + y^6=2 at (1, 1).

A: Given : x6+y6 = 2

Q: 1. Given y = sin(x In.x), what is the slope of the tangent line at (e, 0)? (The red line.) 2. Given…

A:

Q: find the line tangent to the curve y=cos(x) at the point (π/4, 1/√2)

A:

Q: Find an equation for the tangent line to the curve + xy - y = 1 at the point (2, 3). %3D

A:

Q: 7. Find all points (x, y) where the curve y = xe has a horizontal tangent line. 2

A:

Q: 5. Find the equation of the tangent line and normal line to the curve f(x)= at the point(,4).

A: The tangent line is horizontal where y'=0. So at first we differentiate the given curve and equate…

Q: Find all​ x-coordinates of points​ (x,y) on the curve y=(x−2)4(x−5)-3 where the tangent line is…

A: Given,          y=x-24x-5-3 where the tangent line is horizontal.

Q: A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point (1,4)

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.