Simplify (9 + 7i)/(-10 + 8i)

1 answer:

3 0

Multiply numerator and denominator by the conjugate of the denominator

Denominator: -10 + 8i
Conjugate of the denominator: -10 - 8i

Operation:

[9 +7i] / [-10 + 8i] * [-10 -8i] / [-10 - 8i] = [-90 - 72i - 70i +56] / [100 + 64] =

[-34 -142i] / 164 = [-17 -71i] / 82

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Find d/dx(e^3ln(x)). a. e^3lnx b.e^3ln(x)/x c.3e^3lnx d.3x^2

kow [346]

Answer:

D. 3x²

General Formulas and Concepts:

Algebra II

If you raise e to the natural log, they cancel out and vice versa

Calculus

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$f(x)=e^{3lnx}$

Step 2: Rewrite

$f(x) = x^3$

Step 3: Take Derivative

Basic Power Rule: f'(x) = 3x³⁻¹
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Divide x^3-3x^2-10x+24 by x-2

melisa1 [442]

You can do this using synthetic division, which is the easiest way. If x - 2 = 0, then x = 2. That 2 will go outside the "box" and the leading coefficients of the terms in the polynomial will go inside the "box". 2 (1 -3 -10 24). Bring down the first number, the 1. Multiply that 1 by the 2 to get 2. Put that 2 up under the -3 and add to get -1. Multiply that -1 by the 2 to get -2. Put that =-2 up under the -10 and add to get -12. Multiply that -12 by the 2 to get -24. Put the -24 up under the 24 and add to get 0. That means that x - 2 is a factor of the polynomial. What's left, the bolded numbers, are the coefficients of a new polynomial that is one degree less than the polynomial you started with. In other words, when we divide your polynomial by x-2, you get $x^2-x-12$ .