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inna [77]
3 years ago
13

What is the answer 5i/(2+3i)^2

Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0
Simplify the following:5 i/(3 i + 2)^2
(3 i + 2)^2 = 4 + 6 i + 6 i - 9 = -5 + 12 i:(5 i)/12 i - 5
Multiply numerator and denominator of (5 i)/(12 i - 5) by 5 + 12 i:(5 i (12 i + 5))/((12 i - 5) (12 i + 5))
(12 i - 5) (12 i + 5) = -5×5 - 5×12 i + 12 i×5 + 12 i×12 i = -25 - 60 i + 60 i - 144 = -169:(5 i (12 i + 5))/-169
i (12 i + 5) = -12 + 5 i:(5 5 i - 12)/(-169)
Multiply numerator and denominator of (5 (5 i - 12))/(-169) by -1:Answer: (-5 (5 i - 12))/169
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Question 6 of 15
umka2103 [35]

Answer:

LE=5\ units

Step-by-step explanation:

we know that

In a rectangle, the two diagonals are congruent and each diagonal bisects the other

so

LN=2KE ----> equation A

KE=LE -----> equation B

step 1

Find the value of x

solve equation A

LN=2KE

substitute the given values

(2x+2)=2(3x-7)

solve for x

2x+2=6x-14\\6x-2x=2+14\\4x=16\\x=4

step 2

Find the value of KE

KE=3x-7

substitute the value of x

KE=3(4)-7=5\ units

Remember that

KE=LE  -----> by each diagonal bisects the other

therefore

LE=5\ units

8 0
3 years ago
A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate he
Solnce55 [7]

Answer:

<h2>The height is 3.43 centimeters, approximately.</h2>

Step-by-step explanation:

Notice that there are 16 pieces from the circle, which means each sector has an angle of

\theta = \frac{360\°}{16}=22.5\°

Where all sectors have equal area.

Now, the area of the whole circle is 12.25 \pi \ cm^{2}, if we use the formula of its area, we'll find the radius of the circle

A= \pi r^{2}\\ 12.25\pi = \pi r^{2}\\ r=\sqrt{12.25} \approx  3.5

Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.

To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.

cos(11.25\°)=\frac{h}{3.5}\\ h=3.5 \times cos(11.25 \°)\\h \approx 3.43

Therefore, the height is 3.43 centimeters, approximately.

6 0
3 years ago
Combining like terms with negative coefficients &amp; distribution
Leno4ka [110]

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6 0
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The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region? 2x2 4x2 6x2 8x2
notka56 [123]
The picture in the attached figure

we know that
area of the <span>the shaded region=area of rectangle -area of a kite

area of rectangle=(3x+x)*(x+x)----> 4x*2x---> 8x</span>²

area of a kite=(1/2)*[d1*d2]
where d1 and d2 are the diagonals
d1=4x
d2=2x
so
area of a kite=(1/2)*[4x*2x]----> 4x²

area of the the shaded region=8x²-4x²-----> 4x²

the answer is 
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