If you make a straight-line projection from Fig. 1.5,what will be the minimum feature size in integrated circuits in the year 2025? The curve can be described by F = 8.00 × 10^(−0.05806(Year−1970))um. Do you think this is possible? Why or why not?

Q: Find the slope of the line tangent to the graph of y= sin3x at x=pie/6

A:

Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the equation of a curve whose tangent line has slope 2x – 5 and the curve passes through the…

A:

Q: Use a linear approximation to estimate V65.

A: 653

Q: Find the orthogonal trajectories of the family of curves.

A:

Q: The Gateway Arch in Saint Louis is modeled by the curve: y = 210 − 20 cosh ( x/30) . At what height…

A: yx = Height of the Gateway archyx = 210 - 20coshx30         Blue curve---------------------formulae…

Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: How can we find the Deltas graphically?

A: suppose y = f(x) be any function. The graph of the function is given. To find the Deltas…

Q: Find the slope and y-intercept of the line through the point (10,9) that cuts off the least area…

A: Equation of line in point slope form : (y - a) = m*(x-b)  Where, slope = m and point = (a,b)

Q: Describe the tangent line at an arbitrary point on the graph of y = 2x + 8

A: we have to describe the tangent line at an arbitrary point on the graph of y=2x+8

Q: How is sinusoidal function used in calculating population growth or decay over a period of time?…

A: Given question:- How is sinusoidal function used in calculating population growth or decay over a…

Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

A:

Q: Can you clarify the first part again, does it mean that the relative maximum, minima, and horizontal…

A:

Q: Estimate solutions of the following equation using a graphical estimation method:

A:

Q: what is the equation of the normal line to the curve 2x3+2y3-9xy=2 at the point (0,1)?    Please…

A: Given: 2x3+2y3-9xy=2 To Determine: Equation of the normal line

Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

A:

Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: nitial value problem is

A:

Q: Find the equations of the tangent line and normal line to the parabola y=2x2 at the point (2,8).

A: We find dy/dx at x=2 to find the slope of the tangent  Then we use the point-slope formula to find…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: Which hyperbolic functions are increasing on their domains?

A: First of all, consider all the six trigonometric hyperbolic functions and their domains.

Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

Q: What does the slope of a secant line through two points on the graph of a distance vs time graph…

A: lets consider

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

A:

Q: Find the equation of the tangent line on the top graph of ... at the point (3,2)

A:

Q: 9 Find the length of the segment 16 between the lines. y- 1-x + arcsinx of the curve -0, x

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Give an equation for the tangent line to = 1 at the y2+1 point (5,2) and sketch it on the graph. -5-…

A:

Q: Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x2y - x =…

A:

Q: Define “hyperbolic” trajectories?

A: we have to define "hyperbolic" trajectories

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: find the equation of a tangent line for y=arcsin(x/8) at the point (4,π/6)

A:

Q: Please provide an example of real life computation and application of slope of a tangent line

A:

Q: As an application of partial derivative of multi-variable functions, provide one page about Lagrange…

A:

Q: A pole 8 meters long is carried horizontally along a corridor 3 meters wide and into a second…

A:

Q: Describe the tangent line at an arbitrary point on the “curve” y = 2x + 8.

A:

Q: The ________ of a sine or cosine curve represents half the distance between the maximum and…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: Find the function whose tangent line slope is 3 and whose graph passes through (1,-1)

A:

Q: Sketch a graph of y = 2x on [-1, 2] and use geometry to find theexact value of function given

A: Let's sketch the graph of the following function:                                       y=2x…

Q: Suppose the slope of the tangent line at any point is vx – 1 . What is the equation of the curve if…

A:

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

A:

Q: Find an equation of the tangent line to the graph of y = arcsin(2x) at the point 2/2 4

A:

Q: Find the differentual equatrion characterizing the family of curves described

A: Given that: ky=x2

Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: Find the length of the arc y =: 8 1 from X = 1 tox = 4. 4x?

A: Graph: Given: y=x48+14x2. So,          y'=x48+14x2' =x32-12x3.

Q: The slope of the line tangent to the curve y=2x- 3 at point (1,-1) is 5

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

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

A:

Q: Please answer number 5 determine the equation of the orthogonal trajectories of the following…

A: Given that        ex + e-y = C1 Here we have to find the equation of the orthogonal trajectories.

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.