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stich3 [128]
3 years ago
12

2. Describe how to use the conjugate to divide 2 − i by 3 + 2i, and then find the quotient.

Mathematics
1 answer:
DaniilM [7]3 years ago
7 0

Answer:

\frac{4}{13}-\frac{7}{13}i

Step-by-step explanation:

\frac{2-i}{3+2i}

Multiply and divide by the conjugate.

The conjugate is the denominator with the sign of the complex number the opposite of the denominator.

\frac{2-i}{3+2i}\frac{3-2i}{3-2i}\\ =\frac{2\times (3-2i)-i\times (3-2i)}{3^2-(2i)^2}\\ =\frac{6-4i-3i+2i^2}{9+4}\\ =\frac{4-7i}{13}\\ =\frac{4}{13}-\frac{7}{13}i

Quotient = \frac{4}{13}-\frac{7}{13}i

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The length of a rectangle is 1 ft more than double the width, and the area of the rectangle is 45 ft2 . find the dimensions of t
algol [13]
A = L * W
A = 45
L = 2W + 1

45 = W(2W + 1)
45 = 2W^2 + W
2W^2 + W - 45 = 0
(2W - 9)(W + 5) = 0

W + 5 = 0
W = -5...not this one because it is negative

2W - 9 = 0
2W = 9
W = 9/2
W = 4.5 <=== the width is 4.5 ft

L = 2W + 1
L = 2(4.5) + 1
L = 9 + 1
L = 10 <=== the length is 10 ft
3 0
3 years ago
You go to the ice cream store. The store has 6 different types of ice cream, 3 different types of sauces, and 4 different types
Katena32 [7]

Answer:

72 different sundaes

Step-by-step explanation:

We can find the number of different sundaes by

6 different types of ice cream* 3 different types of sauces *4 different types of toppings

6*3*4 = 72 different sundaes

3 0
3 years ago
In the figure, AB=12, BC=8, DE=6, PD=4, and A is the point of tangency. Find the radius of circle P.
Lelu [443]

Answer:

The radius of the circle P = 2√10 = 6.325

Step-by-step explanation:

∵ AB is a tangent to circle P at A

∴ (AB)² = BC × BE

∵ BC = 8 , AB = 12 , ED = 6

∵ BE = ED + DC + CB

∴ BE = 6 + CD + 8 = 14 + CD

∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14

∴ CD = 4

Join PC and PE (radii)

In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф

Use cos Rule:

∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ

∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)

∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ

∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)

∵ (1) = (2)

∴ 32 - 32 cosФ = 52 + 48cosФ

∴ 32 - 52 = 48cosФ + 32cosФ

∴ -20 = 80cosФ

∴ cosФ = -20/80 = -1/4

∴ r² = 32 - 32(-1/4) = 32 + 8 = 40

∴ r = √40 = 2√10 = 6.325

7 0
2 years ago
Figure TUVW ≅ figure ABCD, AB = 12, CD = 6, and DA = 4.
Olegator [25]
The measure of VW is 6. It's because since the figures are congruent their names are written in correspondence ....so since VW corresponds to CD , the answer must be 6.
6 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope inter
Doss [256]

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

3 0
2 years ago
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