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(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Write the parametric equations x=2siny=4cos0 in the given Cartesian form. y^2/16= with x0. Write the parametric...
Write the parametric equations
x=2siny=4cos0
in the given Cartesian form.
y^2/16= with x0.
Write the parametric equations
x=2sin2y=5cos2
in the given Catesian form.
y= with 0x2.
Write the parametric equations
x=4ety=8e−t
as a function of x in Cartesian form.
y= with x0.
Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16 Write the parametric equations x = 2 sin’e, y = 5 cos?...
Question 11 Find the length of the curve with parametric equations x = 2t, y =...
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
Which of the following integrals represents the length of the parametric curve x = 1+e', y=t,...
Which of the following integrals represents the length of the parametric curve x = 1+e', y=t, -3 <t< 3, about the X-axis? A. Vet? + 4t2 dt 3 B. V2et + 4t2 dt Ve2t + 4t dt D. Vet + 4t2 dt U V2e + 4t dt 3 F. . Vet + 4t dt
Question 15 < > Find the length of the curve for the following parametric equations for...
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
Find the integral that represents the length of the parametric curve defined by x = e'...
Find the integral that represents the length of the parametric curve defined by x = e' –t, y = 2e2, 0 <t < 1. Select one: o al. Vre! – 1° +1 dt ObſVe4 – 2e + 2 de o af Vibe' + e² - 2te + 1² de O d. ſ' vroeken? + e= nº di o of Vie + 1 di O !!! Vet – e' + 1 de o ' viel + 1) di on I' v2e...
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t?...
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...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts)...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 +...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Consider the parametric equations below. x = 2 + 4t y = 1-t2
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Write the parametric equations
x=2siny=4cos0
in the given Cartesian form.
y^2/16= with x0.
Write the parametric equations
x=2sin2y=5cos2
in the given Catesian form.
y= with 0x2.
Write the parametric equations
x=4ety=8e−t
as a function of x in Cartesian form.
y= with x0.
Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16 Write the parametric equations x = 2 sin’e, y = 5 cos?...
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
Which of the following integrals represents the length of the parametric curve x = 1+e', y=t, -3 <t< 3, about the X-axis? A. Vet? + 4t2 dt 3 B. V2et + 4t2 dt Ve2t + 4t dt D. Vet + 4t2 dt U V2e + 4t dt 3 F. . Vet + 4t dt
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
Find the integral that represents the length of the parametric curve defined by x = e' –t, y = 2e2, 0 <t < 1. Select one: o al. Vre! – 1° +1 dt ObſVe4 – 2e + 2 de o af Vibe' + e² - 2te + 1² de O d. ſ' vroeken? + e= nº di o of Vie + 1 di O !!! Vet – e' + 1 de o ' viel + 1) di on I' v2e...
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...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
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