(1 point) A curve with polar equation r = 27 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian equation of the form y = mx +b ,where m and b are constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then the answer would be 2 *x+3. Hint: multiply both sides by the denominator on the right hand side and...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
Graph the polar equation r=6 sin 30 OD Convert the Cartesian equation to a polar equation that expresses r in terms of e. (x + 3)² + y² = 9 = (Type an expression in terms of 0.)
Describe the graph of the polar equation. 7r cos 0 + r sin 0 = 5 O A. Line with slope - 7 and y-intercept (0,5) O B. Vertical line passing through (7,0) O C. Line with slope 5 and y-intercept (0,7) OD. Parabola with vertex (7,5) opening upward
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stated 1 V3 1, Determine the polar coordinates of the point (z,y) 2, Determine the line tangent to the polar curve T 1+cos θ when θ Be sure to write your line in the form y mx +b 3. Determine the area enclosed by the polar curve cos(28), 0 θ < 2π r Determine the area of the inner loop of the the polar curve
stated 1 V3 1, Determine the polar coordinates of the point...
Find the equation of the tangent line to the curve y = 2x cos z at the point (TT, - 2). The equation of this tangent line can be written in the form y = mx + b where m = and b=
Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 8 cos 0-6 sin 0 Write the Cartesian equation. Describe the curve. Select the correct choice below and, if necessary, fill in any answer box O A. The curve is a circle centered at the point with radius (Type exact answers, using radicals as needed.) B. The curve is a vertical line with x-intercept at the point (Type exact answers, using radicals as needed.) O C. The...
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...
Replace the polar equation with an equivalent Cartesian equation. r2 + 2r -2 sin e cos 0 = 144 O X + y = $12. O x + y = 12 x² + y² = 144 O x2 + 3y2 = 144
Find the equation of the line that is tangent to the curve y = 4x cos x at the point (π,-4π) The equation of this tangent line can be written in the form y = mx + b where m = _______ and b = _______