9514 1404 393
Answer:
149.04°
Step-by-step explanation:
You must consider the signs of the components of the vector. The value -5+3i will be in the 2nd quadrant of the complex plane.
When you use the single-argument arctan function, it will tell you the angle is -30.96°, a 4th-quadrant angle. (arctan( ) is only capable of giving you 1st- or 4th-quadrant angles.)
You find the 2nd-quadrant angle by adding 180° to this value:
-30.96° +180° = 149.04° = arg(-5+3i)
__
The attachments show the calculation using a suitable calculator (1st) and a spreadsheet (2nd). The spreadsheet function ATAN2(x,y) gives the 4-quadrant angle in radians, considering the signs of the two arguments. Here, we converted it to degrees. The calculator can be set to either degrees or radians.
To answer your question: Rewrite <span>81<span>x2</span></span> as <span><span>(<span>9x</span>)</span>2</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−49</span></span>Rewrite 49 as <span>72</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−<span>72</span></span></span> Both terms are perfect squares, factor using the difference of squares formula, <span><span><span>a2</span><span>−<span>b2</span></span></span>=<span><span>(<span>a+b</span>)</span><span>(<span>a<span>−b</span></span>)</span></span></span> where <span>a=<span>9x</span></span> and <span>b=7</span>.<span><span>(<span><span>9x</span>+7</span>)</span><span>(<span><span>9x</span><span>−7</span></span><span>)</span></span></span>
Answer:
c)30%
Step-by-step explanation:
Step one:
given data
The shopkeeper said each pair of earrings cost Rs. 12
if he offered 12 pairs for Rs. 100.
let us find the cost per pair
= 100/12
=Rs. 8.3 per pair
Required
The percent discount
Step two:
%percent discount= 12-8.3/12*100
%percent discount= 3.66/12*100
%percent discount= 0.305*100
%percent discount= 30.5%
