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melamori03 [73]
2 years ago
5

The hardest question ever. in SatMath. please help me

SAT
1 answer:
tatuchka [14]2 years ago
4 0

Answer:

750

Explanation:

<em>I'm gonna make my best effort here... (it's been a long hecking time since SAT math last year :P)</em>

Set both equation equal:

5x = -15x + 3000

20x = 3000

x = 150

Plug into any equation because both are equal anyway:

y = 5x

y = 5(150)

y = 750

(a, b) --> (x, y)

The point is (150, 750) and b = 750

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Simplify: 1 + i + i^2 + i^3 +i^4 +i^5 if i^2 =-1.
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1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)

… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))

… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))

… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )

… = 1 + <em>i</em>

<em />

Alternatively, notice that

1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)

so that

1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )

Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so

1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )

… = 2 / (1 - <em>i</em> )

Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :

… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))

… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)

… = 2 (1 + <em>i</em> ) / (1 + 1)

… = 1 + <em>i</em>

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