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Suppose a curve is given by the parametric equations x = f ( t ) , y = g ( t ) , where the range of f is [ ? 1 , 10 ] and the range of g is [ ? 5 , 3 ] . What can you say about the curve? Y

Solve: f(x,y) = 65-x^2-y^2

a. For the curve given parametrically by x=3t^3-5t, y=t^4+1, compute \frac{\mathrm{d} y}{\mathrm{d} x} and \frac{\mathrm{d^2} y}{\mathrm{d} x^2} b. For the graph of the function y=\ln (\cos x), set up

Suppose a curve is given by the parametric equations x=f(t), y=g(t), where the range of f is [2, 5] and the range of g is [2, 5]. What can you say about the curve? You must select all correct choices

The reaction between ammonia and nitrous oxide is given below: 2 NH3(g) + 3 N2O(g) ? 4 N2(g) + 3 H2O(g) We therefore know that which of the following reactions can also occur? a. 4 NH3(g) + 6 N2O(g)

Suppose a curve is given by the parametric equations x=f(t), y=g(t), where the range of f is [-1,7] and the range of g is [1,3]. What can you say about the curve? You must select all correct choices t

Solve y(3) + y'' + \frac{1}{4} y' - \frac{25}{2} completely by determinin the general solution

Express the parametric equations in rectangular (i.e., x-y) form. Graph these equations and indicate the direction of the curve, x(\theta) = 2 + \sin \theta \\ y(\theta) = -1 + 4 \cos \theta

Given the system of linear equations: \begin{align*} -x_1 -7x_2 + 9x_3 &= -1\\ 2x_1 + x_2 - x_3 &= 1 \\ 3x_1 -5x_2 +7x_3 &= -1 \end{align*} (a) Write it in the form of Ax = b: (b) Use Guass eliminat

If A is a positive number, the parametric curve (x(t),y(t)) (t^3 - t, \frac{A}{1 + t^2}) looks like: image. For one value of A, the "self-intersection" of the curve is perpendicular. The picture look

Consider the following line integral, where C is the line segment from (2, 4) to (1, 5). integral_C (9 x - 6 y) dx + (10 y - 6 x) dy. (a) Show that the line integral is path independent by finding a s

1. Lithium are nitrogen react in a combination reaction to produce lithium nitride: 6Li(s) + N_2(g) rightarrow 2Li_3N(s) In a particular experiment, 1 00 g samples of each reagent are reacted. The t

Given that that near (1, 1, 1) the curve of intersection of the surfaces x^3 + y^2 - z^4 - 3xyz = 0 and xy + yz + zx - 3z^8 = 0 has the parametric equations x = f(t), y = g(t), z = t. with f, g differ

Let C be the curve defined by the parametric equation x=t^{3} - t, and y =t^{2}. (a)Show that C has two tangents at the point (0, 1) and find their equations. (b)Find the points on C where the tange

The parametric curve x = \sqrt 3 \sin t + \frac{1}{2} \cos t, \quad y = - \sin t + \frac{\sqrt 3}{2} \cos t is a tilted ellipse. What are the dimensions of the rectangular box containing the elli

Assume that it takes six hours of labor time to paint a room and three hours to sand a floor. If 24 hours were spent painting (a) How many rooms could be painted by one worker? (b) If a decision were

Solve: x^3 - y = In y; (1, 1)

A curve is given by the parametric equation x = 2t^2 - t^4 and y = t^3 where \frac {-3}{2} \leq t \leq \frac {3}{2}. (a) Determine the coordinates of any three points that lie on the curve. (b) Ske

Find the parametric equations that define the curve starting at (5,0) and ending at (6,6), as shown. Let parameter t start at 0 and end at 6. y= [{Blank}] (Complete the equation, with the right side

Could someone explain how to do this? For the next three problems, consider 1.0 L of a solution which is 0.35 M HC_2H_3O_2 and 0.2 M NaC_2H_3CO_2 (K_a for HC_2H_3O_2 = 1.8 times 10^-5). Assume 2 signi

In your lab you are studying aspirin and its acid/base properties. You find that a 1.00 L of a 0.500 M solution of aspirin has a pH of 1.86. You are interested in learning about the % dissociation in

Suppose a curve is given by the parametric equations x = f ( t ) , y = g ( t ) . where the range of f is [ 1 , 7 ] and the range of g is [ ? 2 , 7 ] . What can you say about the curve? You m

1. Find the equation in x and y of the curve defined by the parametric equation \left\{\begin{matrix} x = t\\ y = \sqrt{t^2-2t+1} \end{matrix}\right. ,\;\; 0 \leq t \leq 4 2. Find \frac{dy}{dx} for \

(a) Find a parametrization (functions for x and y , each as a function of parameter t ) for the line segment between the points ( 3 , 3 ) and ( ? 1 , ? 5 ) . Include the domain of t . (b) Wri

Many carnival have a version of the double Ferris wheel . A large central arm rotates clockwise . At the end of the central wheel arm is a ferris wheel that rotates clockwise around the arm. assume th

A particular curve is represented parametrically by x = -2sec3t, \; y=2tan3t, \; t \in (-\frac{\pi}{6}, \frac{\pi}{6}). (1) Where in the Cartesian plane is this curve located? A. the right half-plane

Determine the parametric equations of the path of a particle that travels the circle: (x-5)^2 + (y-3)^2 = 81 on a time interval of 0 t 2: A) if the particle makes one full circle starting at the point

Are inconcistency equations always parallel?

Give parametric equations for the following curves: (a) A circle of radius 3 on the plane y = 1 centered at (2,1,0) oriented clockwise when viewed from the origin. (b) A line perpendicular to z = 2x

A) Find a parametric equation of the circle with radius 3 centered at (2,1) traced counterclockwise. B) Repeat the previous problem in the clockwise three-turn. C) An ellipse \frac{x^2}{a^2} + \frac

Given a set of parametric equations x = 3 \cos 2t, y = 1 + cos^2 2t . (a) What would be the range of values on t that would retrace the path of the curve once? (b) Find the corresponding Cartesian

Determine the parametric equations of the path of a particle that travels the circle: (x - 4)^2 + (y - 2)^2 = 49 on a time interval of 0 \leq t \leq 2\pi: a) if the particle makes one full circle sta

The region A enclosed by the line y=3 and the graph of the curve given parametrically by x(t)=t-\frac{1}{t}, \ \ \ \ \ y(t)=2t+\frac{1}{t} Determine the area of A.

Find a parametric representation for the following surface. Write it as a vector. z^2 = 1 + x^2 + y^2 for 1 less than or equal to z less than or equal to 10

Give a set of parametric equations that describes the following curves. Graph the curve and indicate the positive orientation. If not given, specify the interval over which the parameter varies. The

The parametric equations x = x_{1} + \langle x_{2} - x_{1} \rangle t, y = y_{1} + \langle y_{2} - y_{1} \rangle t where 0 \leq t \leq 1 describe the line segment that joins the points P_{1}(x_{1},

a) Parametrize the given ellipse (x/4)^{2} + (y/2)^{2} = 1 What will the parametrization be if the center of the ellipse is translated to the point (5, 1)? b) Find parametric equations for the seg

Find the unit tangent vector T(t) and find a set of parametric equations for the line of the tangent to the curve at point, P. (a) r(t) = 4 cos(t)\vec{i} + 4 sin(t)\vec{j}, P(2, \sqrt{2}, 2 \sqrt{2})

Solve the linear programming problem. Maximize z = 6x + 2y subject to 5x - y \leq14 2x + y \geq 10 x \geq 3 y\leq 8

Give a set of parametric equations that describes the following curves. Graph the curve and indicate the positive orientation. The piecewise linear path from P(-2, 3) to Q(2, -3) to R(3, 5), using pa

Find parametric equations that describe the curve defined by intersecting the cylinder r = 4 with the paraboloid of revolution 8 z + (x^2 + y^2) = 0. Sketch the two surfaces and the curve of intersect

Find a vector parametric equation \vec{r} (t) for the line through the points P = (-3,-2,-4) and Q = (-6, -1, -2) for each of the given conditions on the parameter t. (a) If \vec{r} (0) = \left \lang

Given the system X' = \begin{bmatrix} -1 & 6\\ 1 & -2 \end{bmatrix}X + \begin{bmatrix} 16t\\ -12 \end{bmatrix} and the solutions for the homogeneous system X_1 = \begin{bmatrix} -2\\ 1 \end{bm

Find parametric equations for the line through the point (2, 3, 5) that is perpendicular to the line x = 1 - t, y = 1 + t, z = 2 t and intersects this line. Use Maple to plot the two lines on the same

Find a set of scalar parametric equations for the line containing the point P(1, -2, 3) perpendicular to the line through Q(2, 4, -1) and R(3, 2, 1). Find the distance between point P and the line thr

Consider the circle C of radius 6, centered at the origin. a) Find a parametrization for C inducing a counterclockwise orientation and starting at (6, 0). b) Find a parametrization for C inducing a

Part (A): In your own words, discuss what is meant by parametric equations. When would we use parametric applications? (provide a real-world example). Part (B): Given a set of parametric equations, h

For these three points: A = (1, 0, 2) ; B = (0, 3, -1) ; C = (0, 0, 4). 1) Find Vector BA 2) Let D be the point closest to A, for D lying between B and C. (That is, D is on the line segment connecting

Find a vector parametric equation r vector (t) for the line through the points P = (-4, 0, -2) and Q = (-9, -1, 1) for each of the given conditions on the parameter t. (a) If r vector (0) =< -4, 0, -2

28. Suppose F(x,y) = (2y, -sin(y) ) and C is the circle of radius 7 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation r(t) for the circle C that starts at the poi

Let a curve be given by x = 2 t^3 - 3 t^2 + 1, y = 2 t^3 - 9 t^2 + 12 t - 2. a) Find the slope of the tangent line to this curve at the point (0, 3). b) Find the values of the t where the tangent lin

Parametric Functions: Use a graph to estimate the coordinates of the highest point and the leftmost point on the curve: x = 6te^t , y = te^{-t}. Then find the exact coordinates. Highest point: L

Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) x + y = 2 -x - y = -2

What volume of a 4.50 M KI stock solution would you use to make 0.455 L of a 1.25 M KI solution?

Write a balanced equation for aluminum and sulfur reacting to produce aluminum sulfide.

Write a formula equation for the following equation: Ammonia reacts with hydrogen chloride to form ammonium chloride.

Calculate the volume of a 9.00 M HNO_3 stock solution that must be used to prepare 450 mL 0f a 1.80 M HNO_3 solution.

Balance the chemical equation: Al(OH)_2 to Al^{2+} + OH^-.

Concentrated HCI is 12 M. What is the molarity of an HCI solution prepared by dilluting 10 ml concentrated HCI to a total volume of 250 ml?

Solve for x: 1. \ x^2+6=15\\ 2. \ (x+4)^2=6

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