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Find T(t) \enspace and \enspace N(t) for the curve r(t) = 4t^2 i + 6t j .
Alex Bettington
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August 23, 2024
Consider the polar equation r^2 \sin \theta = 5 (1) What is the equation in Cartesian (rectangular) coordinates equivalent to this polar equation? (2) Which of the following curves is associate...
Alex Bettington
•
August 23, 2024
Find the points on the cone z^2 = x^2 + y^2 which are closest to the point (1, 2, 0).
Alex Bettington
•
August 23, 2024
Convert the polar equation r = -4csc(theta) into a Cartesian equation.
Alex Bettington
•
August 23, 2024
Solve the given boundary-value problem. y double prime + 3y = 9x, y(0) = 0, y(1) + y prime (1) = 0.
Alex Bettington
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August 23, 2024
Write the equation 5x + 4y + 7z = 1 in spherical coordinates
Alex Bettington
•
August 23, 2024
Find an equation of the tangent line to the curve y = x^3-3x+1 at the point (1,-1)
Alex Bettington
•
August 23, 2024
Find an equation of the plane consisting of all points that are equidistant from (5, 3, -4) and (3, -5, -2), and having -2 as the coefficient of x.
Alex Bettington
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August 23, 2024
Find all solutions of the equation in the interval [0, 2pi). 10sin^2(x) = 10 + 5cos(x).
Alex Bettington
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August 23, 2024
Eliminate the parameter t to determine a Cartesian equation for: x = t^2, y = 8 + 4t.
Alex Bettington
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August 23, 2024
Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, -2) and (9, 12, 0).
Alex Bettington
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August 23, 2024
Determine the inverse Laplace transform of F(s) = \frac{3s+5}{s^2+4s+13}
Alex Bettington
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August 23, 2024
Find y_c and y_p by solving the differential equation x^2y'' + 10xy' + 8y = 0 using Cauchy Euler's rule.
Alex Bettington
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August 23, 2024
Solve the differential equation 2y'' -5y' -3y =0 with the initial conditions y(0) = 1, y'(0) =10
Alex Bettington
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August 23, 2024
Find an equation of the plane. The plane through the origin and the points (2, -4, 6) and (5, 1, 3).
Alex Bettington
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August 23, 2024
Find an equation of the set of all points equidistant from the points A(-1, 6, 3) and B(5, 3, -3).
Alex Bettington
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August 23, 2024
Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 8, 0).
Alex Bettington
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August 23, 2024
Solve the given differential equation. (6x) dx + dy = 0. (Use C as the arbitrary constant.)
Alex Bettington
•
August 23, 2024
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