Line t from point P is tangent to circle O at T, the point of tangency. Find the length of PT when the radius of the circle is 5cm and that distance between points P and O is 8cm.
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Line t from point P is tangent to circle O at T, the point of tangency....
Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B 8.00 -1.00t2 + 0.800, where B is in teslas, t is in seconds, and R 2.25 cm. xxKxX xxxxXL Bin (a) when t = 2.00 s, calculate the magnitude of the force exerted on an electron located at point P, which is at a distance n 4.50 cm from the center of the circular field region. 136e-19X What is...
Show that the radius of curvature x^(2/3) + y^(2/3) = a^(2/3) at P(x, y) is three times the distance from the origin to the tangent line T.
2.1 Point P in the figure is at the center of the circle that would be made by the arc (Hint: half a circle) with radius Rin the wire to the left. The long straight wire is also a distance R away from Point P. The wire on the right is carrying a current of 3.2 amps up toward the top of the page. What is the magnitude and direction of the current in the wire to the left that...
(1 point) The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P = (0, 2) to the line through the points A = (-1,-1) and B=(3,0) is
Hypocycloid When a circle rolls on the inside of a fixed circle, any point P on the circumference of the rolling circle describes a hypocycloid. Let the fixed circle be x2 + y2 = a", let the radius of the rolling circle be b, and let the initial position of the tracing point P be A(a, 0). Find parametric equations for the hypocycloid, using as the parameter the angle θ from the positive x-axis to the line joining the circles'...
0 intersect only at (0,0) g(r)at z arctan(3z) Show that the graph y f(x) and its tangent line y po Consider the ftunction f(x) Intermediate steps: 1) The lIne tangent to y f(x)atz -0isy g(x) where g(r) 9(a)- 2Let H(x) f(x) - 9(x) The derivative ot H (x)s H'(z) = which is zero only when x = Rolle's theorem to H (x) on the interval [ri, 0]. Get a contradiction. 4) Now assume that we have zp O where f(2)-9(T2)...
Modern Geometry Suppose P is a point on the line l. Justify the following construction for the line perpen- dicular to l through P. 1 • Pick a point O not on l and draw the circle with center 0 and radius OP. Let Q be the second point of intersection of this circle with l. • Draw the line (QO) and let R be the second point of intersection of this line with the circle. • Draw the line...
Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed o. Complete parts (a) through (C) for the given values of r, o, and t. r= 8 in., o = TT 5 radian per min, t = 10 min (a) What is the angle generated by P in time t? o= radians (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers in...
need help 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...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t (1)...