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Solve the equation by expressing each side as a power of the same base and then equating exponents.2(1 + 2x) = 8

Parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.x = 4 + 5 cos t, y = 6 + 4 sin t; t = 

Find the unit vector that has the same direction as the vector v.v = -5i – 12j

Solve the equation by expressing each side as a power of the same base and then equating exponents.3(1 + 2x) = 243

Polar coordinates of a point are given. Find the rectangular coordinates of the point.(-3, 120°)

Use synthetic division and the Remainder Theorem to find the indicated function value.f(x) = 2×3 – 5×2 – 4x + 21; f(-2)

Solve the problem.Let A =  and B = . Find 

Find the term indicated in the expansion.(x + 2y)12; 11th term

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers.f(x) = -4×3 – 7×2 + 4x + 6; between -1 and 0

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.log2(x + 3) + log2(x – 3) = 4