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Figure 22-11 ​Refer to Figure 22-11. Assume that the consumer depicted in the figure has an income of $20. The price of Skittles is $2 and the price of M&M’s is $4. The consumer’s optimal choice is point

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).xy = 1

Write the vector v in the form ai + bj, given its magnitude and the angle α it makes with the positive x-axis. = 15, α = 30°

Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.v = -3i – 2j,w = -3i – j

Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.v = -2i – 5j,w = -3i + j

Write the expression in the standard form a + bi.(1 + i)20

Plot the complex number in the complex plane.2i

Test the equation for symmetry with respect to the given axis, line, or pole.r = -4 cos θ; the polar axis

Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.v = i + 7j,w = i + j

Test the equation for symmetry with respect to the given axis, line, or pole.r = 4 + 2 sin θ; the line θ =