How many solutions does tan^-1 3 have?

1 answer:

6 0

y = arctan(3) 

Since the inverse tangent is a function, there is only one y-value. However, there are infinitely many solutions to tan(y) = 3 (they are arctan(3) + kπ where k is an integer). The approximate value of y here is y = arctan(3) ≈ 1.24905 (in radians).

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Solve the inequality for x 3^(6x+18)<27^(3x)

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Answer:

$\displaystyle x > 6$

General Formulas and Concepts:

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Order of Operations: BPEMDAS

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Parenthesis
Exponents
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Division
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Multiplication Property of Equality
Division Property of Equality
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Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$
Set: $\displaystyle 6x + 18 < 3(3x)$
Factor: $\displaystyle 3(2x + 6) < 3(3x)$
[Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$
[Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$
[Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$
[Division Property of Equality] Divide -1 on both sides: $\displaystyle x > 6$