A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g. 3 in 23 = 2 × 2 × 2)

8 0

3 years ago

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If x+y = 1, and x^2 + y^2 = -1, what is x^7 + y^13? 1) 0 2) 1 3) -2 4) 2 5) -1

damaskus [11]

Solve for x and y :

x + y = 1 → y = 1 - x

x ² + y ² = -1

x ² + (1 - x)² = -1

x ² + (1 - 2x + x ²) = -1

2x ² - 2x + 1 = -1

2x ² - 2x + 2 = 0

x ² - x + 1 = 0

x ² - x + 1/4 = -3/4

(x - 1/2)² = -3/4

x - 1/2 = ±√(-3/4)

x - 1/2 = ±√3/2 i

x = 1/2 ± √3/2 i → x = exp(± iπ/3)

y = 1 - (1/2 ± √3/2 i ) → y = -1/2 ± √3/2 i → y = exp(± 2iπ/3)

Then

x ⁷ + y ¹³ = exp(± 7iπ/3) + exp(± 26iπ/3)

… = exp(± iπ/3) + exp(± 2iπ/3)

since 7π/3 is equivalent to π/3, and 26π/3 is equivalent to 2π/3 (both modulo 2π).

In either case, we get

x ⁷ + y ¹³ = x + y = 1

so the answer is (2) 1.

8 0

3 years ago

Mike and Joe are both plumbers. Mike chargers initial fee of $100 plus an hourly fee of $60. Joe charges an initial fee of $50 p

S_A_V [24]

Mike earns the most by $5 dollars

3 0

3 years ago

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Shari drew several lines. Which lines are perpendicular to ←→ Select all that apply.

goldfiish [28.3K]

Answer:

Options B, D and E

Step-by-step explanation:

From the picture attached,

AB and CE are the parallel lines and three lines AD, AC and BE are intersecting these parallel lines.

m∠A = m∠C = 90°

Therefore, AC is perpendicular to the lines AB, CD and CE.

Options B, D and E are the correct options.

5 0

3 years ago