slope = -1; passes through the point (-4, 10)

Q: A duck's flight is given by the following expression: y = x^2 + x + 4. X and y are coordinates of…

A:

Q: What is the equation of the curve passing through the point (3,-2) and having a slope at any point…

A: We want to find correct option.

Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: Determine an equation of the line tangent to the graph at the point (3,8)

A: We find f'(x) using the quotient rule. And plug x=3 in it to find f'(3)

Q: Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Write your result in…

A: From graph we have g(2)=4 and therefore we compute the tangent of the graph y=g(x) at the point…

Q: Find the value of x. m2 = 11x +9 30° + 2

A:

Q: Find equations of the tangent lines to the curve y²-xy-6=0 at the points (-1,2), and (-1,-3).

A: Given curve: We have to find the equations of the tangent line to the curve  at the points  and

Q: Determine the slope of 3(x² +y´) = 100xy at the point (3,1)

A: The given function is 3x2+y2=100xy. Evaluate the slope dydx by implicit differentiation as follows.…

Q: passes through the points (-2, -9) and (4, -6)

A:

Q: Determine the equation of the curve whose slope at any point is equal to and which passes through…

A:

Q: Section 2.3 For what values of x is the tangent line of the graph of flx) = 6x3+36x?+53x parallel to…

A: The solution of the problem is given in the next step.

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.