8.4.17-GO Use a graphing calculator to generate the curve over the interval for the parameter t. Then find the equivalent rectangular equation. x- 2t, y=t+4 for t in [-3,2] ES Select the correct graph from those shown on the right. cents

Q: 12: A tangent to the circle x² + y? = 5 at the point (1,2) and th circle x? + y² – 8x + 6y + 20 - A)…

A: Given that  A tangent to the circe x^2+y^2=5 at the point (1, 2)

Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

A:

Q: 7) Find the exact length of the curve. x= e' +e', y =5-2t; 0<t<3

A: Solution:Givenx=et+e-t     y=5-2t     0≤t≤3To find the length of the curveFormula:Length of the…

Q: (11) At what point do the curves ri(t) = (t, 2-t, t²) and r3(s) = (1-s, s+1, s²+1) intersect? Find…

A:

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: メ=1 45 the right of the line , y= what is the of the unbounded regron between the grea Curve Ond the…

A:

Q: 4. a) Find the entire are length of the curve r = 2a cos³ (0/3).

A: 4a Given curve is r=2acos3θ3. We have to the entire arc length of the given curve. The entire arc…

Q: 1 Find the exact length of the curve: r(t) = , 6.

A:

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: II. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 <t <

A: Given:    x = 2t    y = cos4t    0 ≤ t ≤ π/2

Q: Consider the following. x = et − 4,    y = e2t   Eliminate the parameter to find a Cartesian…

A:

Q: 32. The centre of symmetry of the curve y = * + 2 is at the point A. (0,0) В. (-2,0) с. (2,0) D.…

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: o the circle of radius 2 centered at co.2.0) and lying in the (b) plane y=2 - the line through the…

A: Given that

Q: Eliminate the parameter t from the following. x = 4 sin t, y = 4 cos(t) Sketch the graph of the…

A: The given question has been solved in detail

Q: If the distance from P(1, 0) to the point T(1 ) is x, determine the coordinates P(1,0) of the point…

A:

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: 6.3.4 Find the length of the following curve. 21 2 from y = 3 to y = 11

A:

Q: 1. Consider the implicitly defined curve Py- 2r = 25. (a) Verify that the point (1,3) is on the…

A: Given,          x2y3-2x4=25

Q: III. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 < t <

A:

Q: Зу — 4у 3D —х — 2 The curve above can be parameterized as which of the following pairs of equations?

A:

Q: 8) Wihat is the length of the pot Df the curve y2=(x-1)between the points (4,0) ond (2,4) ?

A: Let f(x) be a smooth function over the interval [a,b]. Then the arc length of the portion of the…

Q: 32. The centre of symmetry of the curve y = * + 2 is at the point A. (0,0) В. (-2,0) С. (2,0) D.…

A:

Q: (8.4) Find a rectangular-coordinate equation for the curve x 2cos(t) and y = 3sin(t), 0<t< 2n. %3D

A: The given x = 2cost y = 3 sint

Q: Let m be a positive real number and C be the curve given by: r(t) = m(cost – 2)ỉ – msintj + (mt –…

A:

Q: Consider the following. et – 6, y = e2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given that

Q: 6- Which of the following is the shortest distance from the point (15, 0) to the curve y = a)3 c)9…

A: we have given a curve y=6x  and a point (15,0)let (a,b) be any point on the curve y=6xtherefore this…

Q: Consider the following.x = et - 6y = e2t(a) Eliminate the parameter to find a Cartesian equation of…

A: From the equation for x, write t in terms of x.

Q: 12 1 If the curve shown in the figure is rotated about the y-axis, this creates the shape of a

A:

Q: Find the indreated equations over beund od by the grephs of the graphs of Hhe Crea He given interval…

A:

Q: 12) Find the exact length of the curve [4,16] on 3

A: We can find the exact length of the curve as below,

Q: 9 Find the length of the curve x = on 3sys5. %3D 27' 4y The length of the curve x = 9 - on 3sys 5 is…

A: We have to find arc length of give curve.

Q: 1 x = + 6 2y What is the length br of the portion of the graph of the between the points with y = 1,…

A:

Q: Consider the following. X = 7 cos(0), y = 8 sin(0), - T/2 < 0 S TT/2 (a) Eliminate the parameter to…

A:

Q: f(z) = 3 cot (4) Which ot the halowing mpresents the graph ot

A: Topic- trigonometry

Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

A:

Q: Find the length of one branch of the curve 9y^2=4(1+x^2)^3 from x=0 to x=2

A: Given curve is 9y2=4(1+x2)3

Q: 6. Which of the following is true if OF dr 0 on all closed curves? (a) V×F = 0. (b) div F = V·F = 0.

A:

Q: Any help will be useful.

A:

Q: /1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0<t <1.

A: Use the parameterization of curve for finding the length of curve .

Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: 6. The curve C: 3*-1 + xy - y? +5 = 0. show that at points (1,3) can be writien in the form -In(ue)…

A: Solve the following

Q: 5. Given X = 50.1, µ = 48.2, and o = 2.2, indicate on the curve where the given X %3D %3D value…

A:

Q: 6- Which of the following is the shortest distance from the point (15, 0) to the curve y = V6x ? a)3…

A: Solution: The objective is to find the shortest distance from the point (15,0) to the curve y=6x

Q: 3. Plot both the following curves on the same set of axes. r = 5 - 4 cos e and the parabola y = r.

A: Given

Q: 2. Compare the OC curves of the plans n = 5 and c= 0, 1, at Pa = .95, .50, .10. Plot the AOQ and ATI…

A: Given problem is :

Q: 1- Fit a least-square geometric curve y = ax to the following data 2 3 4 5 y 27.8 62.1 110 161

A: We have to find Geometric Curve using least square method.

Q: Which graph is the one described by the set of parametric equa Sz = t ly = t³ %3D for -0<t < o∞ ?…

A: Given:  x = t , y = t3

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.