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Lady bird [3.3K]
4 years ago
5

Pls pls pls help me real fast​

Mathematics
1 answer:
stellarik [79]4 years ago
5 0
The answer is 60 i believe
You might be interested in
Express z = square root (4 + 3i) in the form p + qi , where p and q and are rational numbers.​
Gwar [14]

Answer:

z = (3/√2) + (1/√2)î = (1/√2) [3 + i] = (2.1213 + 0.7071i)

OR

z = -(3/√2) + i(1/√2) = (1/√2) [-3 + i] = (-2.1213 + 0.7071i)

p = (3/√2) = 2.1213

q = (1/√2) = 0.7071

OR

p = (-3/√2) = -2.1213

q = (1/√2) = 0.7071

Step-by-step explanation:

z = √(4 + 3i)

Let the complex number z be equal to

z = p + qi

So, we can write

z = p + qi = √(4 + 3i)

p + qi = √(4 + 3i)

Square both sides

(p + qi)² = [√(4 + 3i)]²

p² + pqi + pqi + (qi)² = (4 + 3i)

p² + 2pqi + q²i² = 4 + 3i

note that i² = -1

p² + 2pqi - q² = 4 + 3i

(p² - q²) + 2pqi = 4 + 3i

Comparing both sides, and them equating the real parts on both sides to each other and the complex parts to each other

(p² - q²) = 4 (eqn 1)

2pq = 3 (eqn 2)

From eqn 2

p = (3/2q)

p² = (9/4q²)

Substituting this into eqn 1

(9/4q²) - q² = 4

multiplying through by 4q²

9 - 4q⁴ = 16q²

4q⁴ + 16q² - 9 = 0

let q² = x, q⁴ = x²

4x² + 16x - 9 = 0

Solving the quadratic equation

x = 0.5 or -4.5

q² = 4

q² = 0.5 or q² = -4.5

q = √0.5 or √-4.5

q = (1/√2) = (√2)/2 = 0.7071

Or q = i(3/√2) = i(3√2)/2 = 2.1213I

p = (3/2q)

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = p + qi

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

z = (3/√2) + (1/√2)î = (1/√2) [3 + i]

= 2.1213 + 0.7071i

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = i(1/√2) + [i(3/√2) × i]

z = i(1/√2) - (3/√2)

z = -(3/√2) + i(1/√2)

z = (1/√2) [-3 + i]

z = -2.1213 + 0.7071i

Hope this Helps!!!

8 0
4 years ago
A segment is on a number line with endpoints at −5.3 and 8.7.<br> What is the length of the segment?
Kisachek [45]

Answer:

about 6.3✔

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obta
Andru [333]

Answer:

Step-by-step explanation:

According to the given question, a tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 37,000 miles and a standard deviation of 3,887 miles.

Let us define X be the random variable shows that the mileages tires normally distributed with

mean

μ = 37000

standard deviation

σ =3, 887

Therefore

X ~ (μ = 37000, σ =3,887)

The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. Therefore the  guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage is determined as:

P(X < k) = 0.02

\Rightarrow P\left ( \frac{X-\mu }{\sigma }\leq \frac{k-\mu }{\sigma } \right )=0.02&#10;\\\\P\left ( Z \leq \frac{k-37,000 }{3,887 } \right )=0.02

From the standard normal curve 2% area is determined as -2.0537 and hence

\frac{k-37,000}{3,887}=-2.0537\\\\k=37000-7982.7319\\\\k=29017.2681\\\\\Rightarrow k=29018

If we consider z value at two decimal places then

\frac{k-37,000}{3,887} =-2.05\\\\\Rightarrow k=29032&#10;

Therefore the  guaranteed 29032 mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage.

The area under the standard normal curve is determined as:

6 0
4 years ago
Question 7!!!! 12 points
rosijanka [135]

Answer:

35+50x\le 1325

Step-by-step explanation:

So y=mx+b tells us the initial amount is b (also known as the y-intercept).

Anyways you have to pay a one time fee of 35 dollars and then it is 50 dollars per month.

Let x represent the number of months she goes to yoga.

If she goes 1 month it costs her 35+50.

If she goes 2 months it costs her 35+50+50 or just 35+50(2).

If she goes 3 months it costs her 35+50+50+50 or just 35+50(3).

If she goes x months it costs her 35+50x.

Now she only has 1325.

So we want the cost of her x months to be less than or equal to 1325 because she doesn't have more than that.

So we want 35+50x\le 1325

7 0
4 years ago
Read 2 more answers
Can anybody finish the puzzle #14 please??
Pepsi [2]

With each iteration, you're swapping the two coordinates, and then change sign of the first one:

First transformation

  • Start with (3,1)
  • Swap coordinates: (1,3)
  • Change sign of the first coordinate: (-1,3)

Second transformation

  • Start with (-1,3)
  • Swap coordinates: (3,-1)
  • Change sign of the first coordinate: (-3,-1)

Third transformation

  • Start with (-3,-1)
  • Swap coordinates: (-1,-3)
  • Change sign of the first coordinate: (1,-3)
6 0
4 years ago
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