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4 years ago

Simplify the expression to a+bi form

Mathematics

1 answer:

Wewaii [24]4 years ago

6 0

$-\sqrt{100}-\sqrt{-192}+\sqrt4-\sqrt{-27}=(*)\\\\\sqrt{100}=10\ because\ 10^2=100\\\\\sqrt{-192}=\sqrt{-1}\cdot\sqrt{192}=i\sqrt{64\cdot3}=i\sqrt{64}\cdot\sqrt3=8i\sqrt3\\_{\sqrt{64}=8\ because\ 8^2=64,\ use\ \sqrt{-1}=i\ and\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}}\\\\\sqrt4=2\ because\ 2^2=4\\\\\sqrt{-27}=\sqrt{-1}\cdot\sqrt{27}=i\sqrt{9\cdot3}=i\sqrt9\cdot\sqrt3=3i\sqrt3\\_{\sqrt9=3\ because\ 3^2=9}\\\\(*)=-10-8i\sqrt3+2-3i\sqrt3=(-10+2)+(-8i\sqrt3-3i\sqrt3)\\\\=-8+(-11\sqrt3)i=-8-11\sqrt3i$

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Ms. Anguiano is enjoying a bicycle ride on a country road

GalinKa [24]

Answer:

The rate is 13 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- Jim lives three miles east of State College

- At noon, he leaves his house and begins to walk due east at a

constant speed of 2 miles per hour

- Annie lives four miles north of State College

- At noon, she leaves her house and begins to bicycle due north at a

constant speed of 8 miles per hour

- The east is perpendicular to the north

* Lets solve the problem

∵ At noon means 12 p.m

∵ They moved till 1 p.m

∵ Jim walked for 1 hour and Annie bicycled for 1 hour

∵ The rate of Jim is 2 miles per hour

∵ The rate of Annie is 8 miles per hour

- The distance = rate × time

∴ Jim walked = 2 × 1 = 2 miles

∴ Annie bicycled = 8 × 1 = 8 miles

- Lets calculate the distance of Jim from the State College till his

position at 1 p.m

∵ Jim lives three miles east of State College

∴ His distance at 1 p.m = 3 + 2 = 5 miles east

- Lats calculate the distance of Annie from the State College till her

position at 1 p.m

∵ Annie lives four miles north of State College

∴ Her distance at 1 p.m = 4 + 8 = 12 miles North

- Lets find the distance between them at 1 p.m

∵ The north ⊥ east

- Use Pythagoras Theorem to find the distance

∴ The distance = √(5² + 12)² = √(25 + 144) = √169 = 13 miles

- The rate = distance/time

∵ The distance between them is 13 miles in 1 hour

∴ The rate = 13/1 = 13 miles per hour

* The rate is 13 miles per hour

6 0

4 years ago

Maya wants to buy a piano. The piano measures 19/4 feet long. She has a space 5 feet long for the piano in her house. Does she h

Sophie [7]

Yes, 19/4 is only 4/3/4 so you still have 1/4 ft left to fill

8 0

4 years ago

If a tellemarketer made 200 phone calls and 35 customers signed up what is the relative frequency of getting a customer and not

Snezhnost [94]

Answer:

82.5% and 17.5%

Step-by-step explanation:

The telemarketer made 200 phone calls and only 35 people signed up. Therefore, we need to find the amount of people who didnt.

200 - 35 = 165

165 people did not sign up.

This meants that the frequency of getting a customer is 35/200 and not is 165/200. In percentages,

The relative frequency of not getting a customer is 82.5%

The relative frequency of getting a customer is 17.5%

6 0

3 years ago

A test driver has to drive a car on a 1-mile track for two rounds in a way, that his average speed is 60 mph. On his first round

Darya [45]

(40+x)/2=60

40 +x = 120

x = 80

check :

40+80 = 120

120/2 = 60

so his second round needs to be 80 mph

3 0

3 years ago

What smaller angle is coterminal with 573°

Kobotan [32]

The positive coterminal angle is 213° and negative coterminal angle is -147° and -507°

<u>Explanation:</u>

Coterminal angles are two angles that are drawn in the standard position (so their initial sides are on the positive x-axis) and have the same terminal side

In other words, two angles are coterminal when the angles themselves are different, but their sides and vertices are identical.

Another way to describe coterminal angles is that they are two angles in the standard position and one angle is a multiple of 360 degrees larger or smaller than the other. That is, if angle A has a measure of M degrees, then angle B is co-terminal if it measures M +/- 360n, where n = 0, 1, 2, 3, ...

So,

When angle is 573° then the coterminal angle is

573° - 360 (1) = 213°

573° - 360(2) = -147°

573° - 360 (3) = -507°

Therefore, positive coterminal angle is 213° and negative coterminal angle is -147° and -507°

5 0

3 years ago