1 Find the equations of the lines (i) - (x) in the diagrams below. ( (iv) (vi) vii) (vai)

Q: 3. Equation of the line that passes through the points (2, 3) and (4, 1).

A: Given points (2,3) and (4,1) We have to find equation

Q: 22 The line y = 2-2x cuts the curve 3x² - y² = 3 at the points A and B. Find the length of the line…

A: Straight line and hyperbola intersect at two points.

Q: 5. Find a general equation of the line which passes through the point (-1,5) and is parallel to the…

A: We need to find the general equation of line which passes through (-1,5) and is parallel to…

Q: 1. Find the equation of a line that passes through the point (3,5) and is a. parallel to the line…

A:

Q: (a) Find the slope m of the tangent to the curve y = 9 + 4x2 − 2x3 at the point where x = a. m =…

A: Slope = dydx=m   ⇒ m=8x-6x2at x=a ⇒ m=8a-6a2

Q: 5. Find the equation of the line that passes through the point (3,-7) whose graph perpendicular to…

A: 5.  The line passes through the point 3, -7 whose graph is perpendicular to the graph of 5x+9y=-126.…

Q: Find the equation of a line with each of the following characteristics. a) parallel to the line y =…

A: (a) Given Data: The equation of the line parallel to the required line is: y=3x+5 ......1 The…

Q: Find the equations of all tangent lines to the graph of y=x -7 x+ 49 that pass through the origin…

A: Equation does not passing through origin.  Hence there are no tangent line whose passing through…

Q: 51. Find an equation of the line that passes through the point (0.0) and is perpendicular to the…

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

A:

Q: Find the equation of the line tangent to the curve. y= -3x + x^2 +2 at the point (3,2) Include y= in…

A: The given equation of the curve: y=-3x+x2+2

Q: 10. The equation for line A is y =(-2/3)x - 4. Line A and Line B are perpendicular, And the point…

A:

Q: Find the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)

A: Given data:     The expression for the equation of the curve is: (x-2)2=-4(y+3). The given point is:…

Q: 5) Find all points (x, y) on the graph of y = - with tangent lines perpendicular to the (x - 4) line…

A:

Q: 1 Find the x-coordinates of all points on the curve y= 9x* – 48x° – 90x + 9x + 34 where the tangent…

A:

Q: Find the equation of the tangent line to the graph of x2y2+ 2xy = 24 at the point (-3, 2).

A: givenx2y2+ 2xy = 24      and point (-3,2)diffentiate this equation for calculating slope of tangent…

Q: Find the equation of the curve that passes through the point (0, 3) and has a slope of 2 x+1 O y =…

A:

Q: 1. Find an equation of the line perpendicular to - 5y = x+6 that passes through the point (10,- 3).…

A: As per our guidelines I am solving only first question please resubmit other questions.  1. To find…

Q: In Problem ,find an equation of the line L.

A: As the line is passing through points (-2,1) and (0,0), we get the slope of the line as…

Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

A:

Q: Find equations of the tangent lines to the curve y = o mc) at the points (1, 0) and at the point (1,…

A:

Q: 21 at the point (1, 7). Find the equation of the line tangent to the graph of the function w(x) = x2…

A: Solve for the equation

Q: 9 Consider the line y= =2x-2. Find the equation of the line that is parallel to this line and passes…

A:

Q: 8. A curve whose slope at any point is 6x² А. у %3D 2х3 — х? +х+6 - 2x + 1 passes through the point…

A: We need to find equation of curve.

Q: 2. Find a general linear equation (ax+by+c=0) of the straight line that has the indicated…

A:

Q: 5+ 4- -5 -4 -3 -D4 of In the above graph of y = f( x ), find the slope of the secant line through…

A: The slope of line passing through two points (x1, y1) and (x2, y2) is y2-y1x2-x1. Given: We have…

Q: 3. (10) Find the equation of tangent line in slope-intercept form to the curve y-r'y+-3=0 that…

A:

Q: B. Find the slope of the curve at the given point. Ax = 4u(2 – 3u)², y = 3u² – 4u + 4 u =

A:

Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

Q: If x^4+y=-4-2xy then find the equations of all tangent lines to the curve when y=-4

A: Givenx4+y=-4-2xy            ⋯(1)To find:The equation of all tangent lines to the curve when…

Q: 11. Find an equation of the line passing through the point (6, 5) and perpendicular to the line…

A: We know that slopem of line which is perpendicular to lineax+by=c is given by m=ba…

Q: Consider the line with the equation: y = – x – 16 Give the equation of the line parallel to Line 1…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 15. Determine the equations of two lines that pass through the point (-1,-3) and are tangent to the…

A:

Q: What is the equation of the curve that passes through the point (2, 3) and has a slope of ye-2at any…

A:

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: A curve has a slope -X+2 of at each point (X,y) on the curve. Which of the following is an equation…

A:

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

A: The slope intercept form is written as y=mx+c

Q: 1. Find the equation of the family of curves whose slope at any point is 6x. Find also the equation…

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

A:

Q: 4. Find the equation of a curve whose slope at any point is equal to x + + and which passes through…

A:

Q: Find the equations of the tangent line and normal line to the curve y = x3- 2x 1+ at the point (0,…

A:

Q: 1. Find the equation of a line in point slope form, in slope intercept form and in standard form of…

A:

Q: 1. Standard form: 10r- 7y = 3 8. Slope-intercept form:

A:

Q: Slope-intercept equation fro y = x+ 9+ 8. 7+ 6. 5+ 4+ 3+ 2+ 1- -9-8 -7 -6 -5 -4 -3 -2 234 5 6789 -2…

A:

Q: A curve has a slope -X+2 of at each point (X,Y) on the curve. Which of the following is an equation…

A:

Q: 9. Standard form: 10r 12y = -4 Slope-intercept form:

A: We have to write in the form y=mx+c

Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (1,…

A:

Q: 1.8 -1 1,0 -5 Calculate the slope of the secant line through the points on the graph where x = 1 and…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.