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Rashid [163]
3 years ago
11

If x = (10 − 3i) and y = (3 − 10i), then xy = -109i and x/y =

Mathematics
2 answers:
Yuliya22 [10]3 years ago
7 0
Xy = -109i
We could find the value of i by substitute the algebraic form of x and y to the equation above

xy = -109i
(10 - 3i)(3 - 10i) = -109i
(10)(3) -3i(3) + 10(-10i) - 3i(-10i) = -109i
30 - 9i - 100i -30i² = -109i

multiply both side by -1
-30 + 9i + 100i + 30i² = 109i
30i² + 9i + 100i - 109i - 30 = 0
30i² - 30 = 0
30i² = 30
i² = 1
i = -1 or i = 1

Then find the value of x and y if i = -1
If i = -1, therefore
x = 10 - 3(-1)
x = 10 + 3
x = 13

y = (3 - 10i)
y = 3 - 10(-1)
y = 3 + 10
y = 13

x/y = 13/13 = 1

Then find the value of x and y if i = 1
x = 10 - 3(1)
x = 10 - 3
x = 7

y = (3 - 10i)
y = 3 - 10(1)
y = 3 - 10
y = -7

x/y = 7/-7 = -1

The value of x/y is either 1 or -1
Serggg [28]3 years ago
6 0

Answer:

x/y is either 1 or -1.

Step-by-step explanation:

Given :  x = (10 − 3i) and y = (3 − 10i), Then xy = -109 i

To find  : x/y

Solution : We have x = (10 − 3i) and y = (3 − 10i),

We need to find x/y

Given xy = -109i

(10 - 3i)(3 - 10i) = -109i .

Distributes 10 over (3 -10i) and -3i over (3 -10i).

(10)(3) -3i(3) + 10(-10i) - 3i(-10i) = -109i

30 - 9i - 100i -30i² = -109i

multiply both side by -1

-30 + 9i + 100i + 30i² = 109i

30i² + 9i + 100i - 109i - 30 = 0

30i² - 30 = 0

30i² = 30

i² = 1

Taking square root both sides

i = -1 or i = 1

Then find the value of x and y if i = -1

If i = -1, therefore

x = 10 - 3(-1)

x = 10 + 3

x = 13

y = (3 - 10i)

y = 3 - 10(-1)

y = 3 + 10

y = 13

x/y = 13/13 = 1

Then find the value of x and y if i = 1

x = 10 - 3(1)

x = 10 - 3

x = 7

y = (3 - 10i)

y = 3 - 10(1)

y = 3 - 10

y = -7

x/y = 7/-7 = -1

The value of x/y is either 1 or -1

Therefore,  x/y is either 1 or -1.

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In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.
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Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse           Soh

<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse          Cah

<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent                Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = d*\frac{41ft}{d}     Multiply both sides by "d"

dcos77° = 41 ft                          

dcos77° / cos77° = 41 ft / cos77°        Divide both sides by cos77°

d = 41 ft / cos77°                      Input into calculator

d = 182.261874....... ft           Unrounded answer

d ≈ 182 ft                       Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

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Answer:

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