
4. Convert the equation y - 7 to parametric form L(t) = +tu. Hint: find two...
convert the rectangular equation y = 3x - 6 into parametric form.
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Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
Let L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for a line that passes through the point P=(-3, 10, 10) and intersects L at a point that is distance 5 from the point Q=(-5, -6, 9). Note that there are two possible correct answers. Use the square root symbol 'V' where needed to give an exact value for your answer. 8 N
Find a vector parametric equation F(t) for the line through the points P= (1,1, 4) and Q = (-2,-2,8) for each of the given conditions on the parameter t. (a) If 7(0) = (1,1, 4) and 7(5) = (-2,-2,8), then F(t) = HI (b) lf F(7) = P and 7(11) = Q, then F(t) = HI -2, respectively, then (C) If the points P and Q correspond to the parameter values t = 0 and t F(t) =
4. (10 points) (a) Find a parametric equation and symmetric equation of the line that pases through the point (2, -1, 3) and is parallel to the vector 7 +27 -37. (b) At what points does this line intersect the yz-plane?
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Determine the system response y(t) for h(t)=u(t)tu(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: C[x(t) *h(t)) = X(s)H(s). y(t) = tu(t)-(t +2)u(t + 2) y(t) = tu(t) + (t - 2)u(t + 2) y(t) = tu(t) + (t - 2)u(t - 2) y(t) = tu(t)-(t - 2)u(t - 2) Question 8 (10 points) What is the Fourier Transform of f(t) = 55(t - 1)? ew 5e-sw 5e-510 را که م
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t? - <t<«. C2: x = 3t, y=t?, - <t<mo. These two trajectories are known to *intersect* at exactly two points. The origin (0,0) is one of them. And there is another one, which we'll call P. Find Pand select the choice below which gives the slope of the tangent line to the first curve at the point P. Note that only ONE of the...
2. a) Find the solutions (t) and y(t) of the system of differential equations: 10y, y10 by converting the system into a single second order differential equation, then solve it. The initial conditions are given by r(0) 3 and y(0)-4. Show your full work. [7 marks] b) For t = [0, 2n/5]: identify the parametric curve r(t) (t),(t)), find its cartesian equation, then sketch it. Hint: You can use parametric plots in Matlab or just sketch the curve by hand....
1. (3) Find parametric equations for the tangent line to the curve x(t) y(t) = 7+3 when t = 1. 5 3+212
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...