if x^13 = j and x^12 = 4/9, which of the following is an expression for x in terms of j?
a. 9/4 j
b. 4/9 j
c. 4j
d. 9j
e. 13j
x^13 = j Divide both sides with x
x^13 / x = j / x
( Remark: x^13 / x = x^12 )
x^12 = j / x
x^12 = 4 / 9
j / x = 4 / 9 Multiply both sides with 9
9 j / x = 4 Multiply both sides with x
9 j = 4x Divide both sides with 4
9 j / 4 = x
x = 9 j / 4
x = ( 9 / 4 ) j
x^12 * x=x^13
4/9 * x=j
divide both sides by 4/9
x= 9j/4
This is a very poor question, as the letter j is very often used as the square root on -1, and because of that, it should never be used as a variable.
The same thing applies for i, another symbol for sqrt-1.
Why are i and j both used as symbols for sqrt -1? Because in writing i, it is often confused for 1. See http://en.wikipedia.org/wiki/Imaginary_unit
whts the answer
To find an expression for x in terms of j, we will first solve for x in terms of j using the given equations.
From the equation x^13 = j, we can take the 13th root of both sides to isolate x:
x = ∛(j)
From the equation x^12 = 4/9, we can rewrite it as:
x^12 = (2/3)^2
Now, take the 12th root of both sides:
x = ∛((2/3)^2)
Since ∛(a^b) = (a^(b/3)), we can simplify:
x = (2/3)^(2/3)
Now, let's compare each option to see which one matches the expression we found for x:
a. (9/4)j
b. (4/9)j
c. 4j
d. 9j
e. 13j
Comparing the given expression (∛(j) = (2/3)^(2/3)) with the options, we can see that none of the options exactly match. Therefore, none of the given options is an expression for x in terms of j.