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3 years ago

Divide 4860 in the ratio of 5:4:3

Mathematics

1 answer:

tigry1 [53]3 years ago

7 0

Total portions are
5+4+3
12
One portion,
4860 / 12
405 So
5 : 4 : 3
5*405 : 4*405 : 3:405
2025 : 1620 : 1215

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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

2 years ago

PRACTICE 1

kari74 [83]

Answer:

ones

Step-by-step explanation:

8 0

2 years ago

Xin Used 20 yards of fencing to build the walls of a square a chicken coop. Used 20 yards of fencing to build the walls of a squ

Gnoma [55]

Answer:

Equation: $20=4x$ or $x=\frac{20}{4}$

Solution: $x=5$

Step-by-step explanation:

The formula that is used to calculate the perimeter of a square is:

$P=4s$

Where "s" is the side lenght the square.

Knowing that Xin used 20 yards of fencing to build the walls of a square chicken coop (in which the lenght in yards of each wall is represented with "x"), you can identify that:

$P=20\\\\s=x$

Then, you can susbtitute values into the formula $P=4s$ :

$20=4x$

Finally, you must solve for "x" in order to find its value.

This is:

$\frac{20}{4}=x\\\\x=5$

6 0

3 years ago

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected resi

mihalych1998 [28]

Answer:

Mean = 910.2

Standard deviation = 12.8

Step-by-step explanation:

82% over the age of 25 are high school graduates.

A survey randomly selected students of certain country included 1110 who were over the age of 25 and 871 of them were high school.

n = 1110

p = 82% = 0.82

q = 1 - 0. 82

q = 0.18

Mean = np

= 1110*0.82

= 910.2

Standard deviation = √npq

= √ 1110*0.82*0.18

=√163.836

= 12.8

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3 years ago

Plz help me<br>also good morning

lilavasa [31]

Answer:

x=-24

Step-by-step explanation:

8 0

2 years ago

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