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oreosama
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Hi these are questions from my test review that i am unsure of, i posted question and my answer
if you can tell me if I've gotten right answer that would be much appreciated!
Let C be the curve with the equations x = 2 - t^3, y = 2t - 6, z = \ln(t)
Find the point where C intersects the xz-plane
Find parametric equations of the tangent line at (1,-4,0)
ans:
<br /> (-25,0,ln(3))<br />
<br /> x = 1 - 3t, y = -4 + 2t, z = t<br />
=========================================find an equation of the osculating plane of the curve x = \sin{5t}, y = \sqrt{5}t, z = \cos{5t} at the point (0,\pi \sqrt{5}, -1)
ans:
-\frac{\sqrt{6}}{6} \cos{5t} x + \frac{\sqrt{30}}{6} ( y - \frac{\pi \sqrt{5}}{5}) + \frac{\sqrt{6}}{6} \sin{5t} (z + 1) = 0=========================================Find the curvature of the curve y = 2 \sqrt{x} at the point (3, 2\sqrt{3})
ans:
\kappa(3) = \frac{1}{16}
=========================================
An athlete throws a shot at an angle of 45 degrees to the horizontal at an initial speed of 36 ft/sec. It leaves his hand 4 feet above the ground.
Where is the shot 2 seconds later?
Where does the shot land?
ans:
(36\sqrt{2} ft, 36\sqrt{2} - 15.6 ft)
x = 132ft
=========================================Find the tangential and normal components of the acceleration vector of a particle with position function r(t) = \cos{t} i + \sin{t} j + \sqrt{15}t kans:
at = 0
an = 1==========================================
True/false...
The curve r(t) = <0,t^2, 4t> is a parabola
T
The curve with the vector equation r(t) = t^3 i + 2t^3j + 3t^3 k is a line
T
The binormal vector is B(t) = N(t) x T(t)
F (opposite direction... not sure about this one though)
If curvature \kappa(t) = 0 for all t, the curve is a straight line
T
The curve r(t) = <2t, 3 - t, 0 > is a line that passes through the origin.
F
If |r(t)| = 1 for all t, the r'(t) is orthogonal to r(t) for all t
T
if u(t) and v(t) are differentiable vector functions then \frac{\delta}{\delta t}[u(t) x v(t)] = u'(t) x v'(t)
FI'm pretty sure the majority of these are right. the physics one and oscillating plane are the ones I am kind of unsure of! thanks for any help i have test soon!
if you can tell me if I've gotten right answer that would be much appreciated!
Let C be the curve with the equations x = 2 - t^3, y = 2t - 6, z = \ln(t)
Find the point where C intersects the xz-plane
Find parametric equations of the tangent line at (1,-4,0)
ans:
<br /> (-25,0,ln(3))<br />
<br /> x = 1 - 3t, y = -4 + 2t, z = t<br />
=========================================find an equation of the osculating plane of the curve x = \sin{5t}, y = \sqrt{5}t, z = \cos{5t} at the point (0,\pi \sqrt{5}, -1)
ans:
-\frac{\sqrt{6}}{6} \cos{5t} x + \frac{\sqrt{30}}{6} ( y - \frac{\pi \sqrt{5}}{5}) + \frac{\sqrt{6}}{6} \sin{5t} (z + 1) = 0=========================================Find the curvature of the curve y = 2 \sqrt{x} at the point (3, 2\sqrt{3})
ans:
\kappa(3) = \frac{1}{16}
=========================================
An athlete throws a shot at an angle of 45 degrees to the horizontal at an initial speed of 36 ft/sec. It leaves his hand 4 feet above the ground.
Where is the shot 2 seconds later?
Where does the shot land?
ans:
(36\sqrt{2} ft, 36\sqrt{2} - 15.6 ft)
x = 132ft
=========================================Find the tangential and normal components of the acceleration vector of a particle with position function r(t) = \cos{t} i + \sin{t} j + \sqrt{15}t kans:
at = 0
an = 1==========================================
True/false...
The curve r(t) = <0,t^2, 4t> is a parabola
T
The curve with the vector equation r(t) = t^3 i + 2t^3j + 3t^3 k is a line
T
The binormal vector is B(t) = N(t) x T(t)
F (opposite direction... not sure about this one though)
If curvature \kappa(t) = 0 for all t, the curve is a straight line
T
The curve r(t) = <2t, 3 - t, 0 > is a line that passes through the origin.
F
If |r(t)| = 1 for all t, the r'(t) is orthogonal to r(t) for all t
T
if u(t) and v(t) are differentiable vector functions then \frac{\delta}{\delta t}[u(t) x v(t)] = u'(t) x v'(t)
FI'm pretty sure the majority of these are right. the physics one and oscillating plane are the ones I am kind of unsure of! thanks for any help i have test soon!
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