Question 3 Near a buoy, the depth of a lake at the point with the coordinates (z, y) is z = 200 +0.02æ² – 0.0001y, where z, y and z are measured in meters. A fisherman in a small boat starts at the point (80, 60) and moves toward the buoy, which is located at (0,0). Is the water under the boat getting deeper or shallower? Explain. PREVIEW a

Q: A helical trajectory An object moves on the helix ⟨cos t, sin t, t⟩, for t ≥ 0.a. Find a position…

A: Given Data The function of the helical trajectory is x=<cost, sint, t>.  (a) Let, The…

Q: The function r(1) = 4i + 13 cos(t) j+ 13 sin(t) k traces a circle. Determine the radius, center, and…

A: Given:   To find: (i) The equation of plane containing the circle. (ii) The center and radius of…

Q: Question 25 etermine the coordinates of the foci given the standard equation - 3) (y+2) = 1 %3D 169…

A: follow next step

Q: center of the motion is the origin, the motion is counterclockwise and that t 0 corresponds to a…

A:

Q: A ball is thrown at an initial height of 65 feet at an initial velocity of 75 feet/second at an…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: A point moves along a right-circular helix C, which is the curve of the path 7 :R → R³ given by,…

A:

Q: Auastion 7) det 4 and u= Campute the distance d from y to the lir

A: To find: Compute the distance d from y to the line through u and the origin. Given information:…

Q: ariants/512235/take/13/ SKETCHPAD Question 13 A plane takes off from an airport at an angle of…

A:

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each…

A:

Q: 3- The equations X= a -a sind, Y=a- a cosd,(0<0<2n Represent one arch of a cycloid .show that the…

A: To calculate the surface area of revolution about the x-axis, use the following formula:…

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each…

A:

Q: Question 9. A circular helix in ryz-space has the following parametric equations, where 0 ER. r(0) =…

A: Here,  xθ=4cosθyθ=4sinθzθ=3θ

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 E R. 4 cos…

A:

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: Question 3 Find the tangent plane to the equation z 3r - 5y + 5y at the point (- 5, 2, 65). Submit…

A:

Q: Question (1): The arc of the parabola y = x2 from (1,1) to (2,4) is rotated about y-axis. Find the…

A:

Q: Question #2) Find the absolute extrema when f(x,y) = xe – x² – e :R is the rectangular regioi with…

A: Both questions are independent to each other so according to the guidelines , I am solving first…

Q: 3- The equations X= að -a sinð, Y= a- a cosº,(0<< 2n Represent one arch of a cycloid .show that the…

A:

Q: Question 1 > Eliminate the parameter t to find a simplified Cartesian equation of the form Y S¤(t) =…

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

Q: Question 22 An engineer is looking to find the fluid force exerted on this plate submerged in water.…

A: The solution is given below:

Q: Question 006A: Complete the following questions involving the amount of Force that is exerted on a…

A:

Q: Question 9. A circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ)…

A: 9. The given parametric equations are,x(θ)=4cosθy(θ)=4sinθz(θ)=3θ

Q: 4. Proposal #4: “The Gentle Wave" The equation: y = 10(0.9)ª - sin (x) %3D a. My graph: b. My…

A: Given equation: y=10(0.9)·sinx Graph of the equation is:

Q: Assume the center of the motion is the origin, the motion is counterclockwise and that t = 0…

A: This is basic equation of motion problem

Q: Question 1 The area of the surface generated by revolving the line x =y from x=0 to x=2 about the…

A:

Q: I. y 8. The solutions to the equation cos(x – y) + sin y = v2 form a tilted ellipse. Find the…

A:

Q: consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle…

A: Given, the position of the particle is  r(t) =b(ωt-sinωt)i^+b(1-cosωt)j^ The velocity vector is…

Q: A cyclist is travelling in a straight path at a constant speed along a dirt oad with a button stuck…

A: Given that:x=rt-sinty=r1-cost

Q: Find oveslapping Over of two equations also give ts alea geometoical representation. 2. (v-fr)-1…

A:

Q: Question 3. (2,) are the coordinates of the Centre of Mass for the lamina with mass per unit area 2…

A:

Q: Figure I. Figure I shows a solid sphere, centre ) and radius 2r, which is fixcd on a horizontal…

A:

Q: Question 3 A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the…

A: Solution :-

Q: Solve parts these 2 parts of the question. Image attached.

A: Convert the parametric equation to Cartesian equation as follows.

Q: ind an equation of the tangent plane at P = ( 2,3, - 3 |to the given surface. 10x? + z?e"-* = 49…

A:

Q: In the figure, block A (mass 1.8 kg) slides into block B (mass 2.4 kg), along a frictionless…

A:

Q: A mass weighing 8 pounds stretches a spring 3 in. The mass is initially released from a point 6…

A: To find the equation of motion for the given spring-mass system.

Q: Question 20 Find the length of the curve. Hint: Use the Arclength formula for parametric equations…

A: Find the length of the given curve

Q: Identify the surface whose equation is given. p = sin(8) sin(4) O a sphere of radius - centered at…

A:

Q: Describe the graph of the equation. r = 7 cos ti - 9 sin t j + k major axis of length 7 parallel to…

A: We need to describe graph of given function.

Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: as engineer design a cooling tower in the shape of hyperboloid of one sheet. The horizontal cross…

A:

Q: A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck…

A: Given: The equations of a cycloid x=rt-sin t, y=r1-cos t.

Q: Describe the graph of the equation. r = 6 cos ti - 10 sin tj + k major axis of length 6 parallel to…

A: The graph of the given parametric curve is:

Q: no. Find equation of L with focus ot (0,~) and divectrix y=q the paraloola form i

A:

Q: Part 3). Consider the right triangle shown below. Verify that y =h by using calculus principles to…

A:

Q: QUESTION 13 A curve Cis defined by the parametric equations x = 3 sin t, y = t. Find the points on C…

A: Given:       xt=3sin t        yt=t The first derivative of the function given in parametric form is:…

Q: (a) Circle: x = h +r cos 0, y = k + r sin 0 (b) Ellipise: x = h + a cos 0, y = k + b sin 0 (c)…

A: We have to find out in rectangular form

Q: Find an equation in cylindrical coordinates for the rectangular equation = x² + y² – 6 Entry Tip #1:…

A:

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.