Answer:
Step-by-step explanation:
We want to write the conjugate of the complex number:
Recall that the conjugate of a complex number in the form <em>a</em> + <em>b</em>i is <em>a</em> - <em>b</em>i, and vice versa.
We can rewrite our complex number as:
Hence, <em>a</em> = 0 and <em>b</em> = 6.
Then its conjugate will be:
Answer:
Step-by-step explanation:
<u>Assume a solution</u>
Assume that 60 is the length. The width is then 1/4 less, or 60 -60/4 = 45.
The diagonal of this rectangle is found using the Pythagorean theorem:
d = √(60² +45²) = √5625 = 75
<u>Make the adjustment</u>
This is a factor of 75/40 larger than the actual diagonal, so the actual dimensions must be 40/75 = 8/15 times those we assumed.
length = (8/15)×60 = 32
width = (8/15)×45 = 24
The length and width of the rectangle are 32 and 24, respectively.
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<em>Comment on this solution method</em>
This method is suitable for problems where variables are linearly related. If we were concerned with the area, for example, instead of the diagonal, we would have to adjust the linear dimensions by the <em>square root</em> of the ratio of desired area to "false" area.
This is true because the denominator is greater than 3 so the fraction is smaller and 8 is greater than 6 so 1/8 is smaller
To calculate the value of x, you can apply:
Tan(α)=Opposite leg/Adjacent leg
In this case, the opposite leg is "x", and the adjacent leg is 15. The angle α is 30° (α=30°)
When we substitute this values, we obtain:
Tan(α)=Opposite leg/Adjacent leg
Tan(30°)=x/15
x=(15)(Tan(30°))
x=5√3
<span>What is the value of x?
</span>
The answer is: The value of x is 5√3
