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cluponka [151]
3 years ago
14

Example 15

Mathematics
1 answer:
koban [17]3 years ago
8 0

cos

(

x

)

+

sin

(

x

)

tan

(

x

)

=

sec

(

x

)

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As long as x is not zero, x to the power of 0 is defined to be equal to 1. Using this definition, 5 to the power of 0=? , ( 6 to
Volgvan
If you ever times a number by 0 then the answer will be 0 no matter what

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Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360
Natasha2012 [34]

\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]

\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]

5 0
3 years ago
Boris invest $2200 at a rate of 3% per year simple intrest how much intrest did boris earn in 10 years
ankoles [38]
Here you go, hope it helps:)

7 0
3 years ago
Which choice shows the graph of a linear function?
ExtremeBDS [4]

Answer:

4th one

Step-by-step explanation:

because its a line (linear)

6 0
3 years ago
Read 2 more answers
The second side of a triangular deck is 4 feet longer than the shortest side. The third side that is 4 feet shorter than twice t
Svetlanka [38]

The second side of a triangular deck is 4 feet longer than the shortest side

(s+4) = the 2nd side

and a third side that is 4 feet shorter than twice the length of the shortest side.

(2s-4) = the 3rd side

If the perimeter of the deck is 48 ​feet, what are the lengths of the three​ sides?

s + (s+4) + (2s-4) = 48

Combine like terms

s + s + 2s + 4 - 4 = 48

4s = 48

s = 48/4

s = 12 ft is the shortest side

I'll let you find the 2nd and 3rd sides, ensure they add up to 48

Hope this helps!

5 0
3 years ago
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