Suppose the angle formed by the line y = 8x and the positive x-axis is 0. Find the tangent of 0. > 10 (1, 7) 4. 6. tangent of 0 = 4. 2.

Q: If the normal to the curve y=f (x) at the point(3,4) makes an angle of 3/4pi with the positive…

A: Near the point of tangency, say (x0, y0), the slope f'(x) of the curve f(x) is approximately equal…

Q: Find the points where the tangent is parallel to OX. y = x4 - 8x3 + 22x2 - 24x + 9

A: Given: y=x4-8x3+22x2-24x+9.

Q: Given circle x+y= 25, find the slopes of the tangents to the two points on the circle where x =-3.'…

A: Consider the given circle x2+y2=25. Obtain the slopes of the tangent to the two points in the circle…

Q: 31° C D

A: Given:

Q: y 2 = 5x at (2, –1)

A: Find the tangent line to the given circle as directed. 2x 2 + 2y 2 =  5x  at (2, –1)

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=0 in the given equation So the point satisfies the equation

Q: B-Find the point on the curve y = x + x?- 1 where the tangent parallel to the x- axis. Q 2/ La…

A:

Q: Find the slope of the line tangent to the curve at the given point. 7.) r = 4cos(0); (2, #) 7.) 8.)…

A:

Q: 3. Find the points where tangent lines are vertical or horizontal: x³ + y³ = 6xy

A: Given:- x3+y3 = 6xy To find :- Points where tangent horizontal and vertical

Q: Where on the curve y = (361 +x²)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: If the slope of the tangent line to the curve at the point (– 1, 2) is 4, find a. y=ax^2+3

A: The given curve is y=ax2+3. First derivative of y=ax2+3 is dydx=2ax. At -1, 2, dydx=2a-1=-2a Thus,…

Q: 00 with tangent l and mZ1 = 46° mZ2, mZ3, mZ4, m25 Given: Find: A 4, B.

A: Explanation of the Solution is given below...

Q: FIND THE EQUATION OF THE TANGENT AND THE NORMAL TO THE CURYE Y =5X' AT THE POINT (1. 5).

A:

Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

A:

Q: Plot the "astroid" y = (4 - x 2/3) 3/2 for 0 ≤ x ≤8. Show that the first-quadrant segment of each…

A:

Q: Write an equation for the tangent line at the given poi 1) x? +y? = 4, (/2, 2) Ans. %3D 2) xy = -4,…

A:

Q: At what point/s is tangent line to the curve given by ?(?) = ?4 − 8?2 + 3 horizontal?

A: We have to find the points where the tangent line is horizontal for the given curve fx=x4-8x2+3

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A:

Q: [10] At what point on the curve y = e*is the tangent line parallel to the line y = 2x? Give answer…

A: Given curve y=ex   and line y=2x

Q: Find the slope of the tangent line to the graph at the given point. 4xcosy+1=5 at the point…

A: To find the slope of the tangent line we need to find dydx.…

Q: Find an equation of the tangent Iine to the ollowing curve at the point (0, 5). xe' + ye* = 5

A:

Q: For what vatues of y=Coshx will the tangent line Slope be equal to 6

A:

Q: Find the lines that are tangent and normal to the curve y = tan x at the point (, 1)

A:

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=π/2 in the given function  Since both sides are equal so (1, π/2) is on the curve…

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

Q: Assume that lines that appear to be tangent are tangent. What is the value of x? Round to the…

A: Given figure :

Q: 30. Find the points on the curve y = tan x, -7/2 <x< T/2, where the tangent is parallel to the line…

A:

Q: -Assume the lines that appear to be tangent are tangent. Find ZW. Y 12 X 20 ZW =

A:

Q: At what point on the given curve is the tangent line parallel to the line 3x - y = 4? y = 2 + 2ex 3x…

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: 2. Find the slope of the tangent line to the curve x? + y? = 1 at the point ) %3D

A:

Q: Find the eauation of the tangent line at (2,1) of 4+タ-25+4-o? 83- 258

A:

Q: what the cquation of tine to the graph of the tangent is Y (x) = 3 x at X =0 2

A:

Q: Find a point on the curve y=√x, where the tangent makes an angle of 45 degrees with the positive…

A:

Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

A: As asked we can answer the question with out all explanation in the following steps

Q: Assume that lines that appear to be tangent are tangent. What is the value of x? units.

A: Given that:

Q: What are the values of m and c if the equation of the tangent line is given by y = mx+ c?

A:

Q: The slope of the tangent line to the curve C at the point (1, 2) is A) 4 B c) 2 D - 4 2.

A:

Q: Assume that lines that appear tangent are tangent. Find the value of x. Round to the nearest tenth…

A:

Q: What would the slope of the tangent line be at the point 3,3 on the folium of Descartes x^3+y^3=6xy…

A:

Q: At what point of the curve y = cosh x does the tangent line have slope 9? O a. (in(/7), /82) O…

A:

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: At what point on the given curve is the tangent line parallel to the line 3x - y = 3? y = 3 + 2ex –…

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: Find an equation for the line that goes through the point (0,0) so that the tangent of the angle it…

A: Given, (x1,y1)= (0,0) tangent of the angle it makes with the x-axis=0

Q: find the equation of the tangent and thhe to the Pollo wing cunve uhen x = 1 (2x2- Ja)2 normal .

A:

Q: 4. If the slope of the tangent line to the curve at the point (-1, 2) is 4, find a. " y = ax? +3 O…

A:

Q: For what value(s) of x is the line tangent to the curve y = xV6 - x horizontal? Vertical?

A: Given curve is: y=x6-x Differentiating with respect to x we get,…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.