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3 years ago

Express 0.1846 as a mixed number

Mathematics

1 answer:

Vinil7 [7]3 years ago

7 0

Answer: I'm not sure about the mixed number but the fraction is 923/5000

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Solve 18 > 12 + 2. Graph the solution.

Whitepunk [10]

Answer:

Step-by-step explanation:

Decimal Form:

3.5

Mixed Number Form:

7 0

3 years ago

Let z=3+i, then find a. Z² b. |Z| c.<img src="https://tex.z-dn.net/?f=%5Csqrt%7BZ%7D" id="TexFormula1" title="\sq

zysi [14]

Given z = 3 + i, right away we can find

(a) square

z ² = (3 + i )² = 3² + 6i + i ² = 9 + 6i - 1 = 8 + 6i

(b) modulus

|z| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(z) = arctan(1/3)

Then

z = |z| exp(i arg(z))

z = √10 exp(i arctan(1/3))

z = √10 (cos(arctan(1/3)) + i sin(arctan(1/3))

Any complex number has 2 square roots. Using the polar form from part (d), we have

√z = √(√10) exp(i arctan(1/3) / 2)

and

√z = √(√10) exp(i (arctan(1/3) + 2π) / 2)

Then in standard rectangular form, we have

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)$

and

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)$

We can simplify this further. We know that z lies in the first quadrant, so

0 < arg(z) = arctan(1/3) < π/2

which means

0 < 1/2 arctan(1/3) < π/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

and since cos(x + π) = -cos(x) and sin(x + π) = -sin(x),

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

Now, arctan(1/3) is an angle y such that tan(y) = 1/3. In a right triangle satisfying this relation, we would see that cos(y) = 3/√10 and sin(y) = 1/√10. Then

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

So the two square roots of z are

$\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

and

$\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

3 0

3 years ago

Read 2 more answers

Hello Can Someone Please Answer This Math Question

Brrunno [24]

Answer:

200 in^2

Step-by-step explanation:

5•4+10•4+10•5=

200 in^2

i hope this helped you

3 0

3 years ago

Yesterday noah ran 2 1/2 miles in 3/5 hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/2 miles in 3/4 hour how fast in mile

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

To calculate the speed of each one we proceed as follows:

speed=distance/time

a] Noah's speed:

distance=2.5 miles

time=3/5 hours

speed=(2 1/2)/(3/5)

=(5/2)/(3/5)

=5/2×5/3

=25/6

=4 1/6 mi/hr

Emily's speed

distance=3 3/4 miles

time=5/6 hour

thus

speed=(3 3/4)/(5/6)

=15/4)/(5/6)

=15/4×6/5

=4 1/2 mi/hr

Anna's speed:

distance=3 1/3 miles

time=3/5

speed=(3 1/3)/(3/5

=(10/3)/(3/5)

=10/3×5/3

=5 5/9 mi/hr

Anna was the fastest

6 0

3 years ago

Read 2 more answers

Please Help I'm not really good at math

UkoKoshka [18]

The true statements about the triangles RST and DEF are: (a), (d) and (e)

<h3>How to determine the true statements?</h3>

The statement ΔRST ≅ ΔDEF means that the triangles RST and DEF are congruent.

This above implies that:

The triangles can be mapped onto each other by rigid transformations such as reflection, translation and rotation
The transformation does not include dilation
Corresponding sides are congruent

The above means that the possible true statements are: (a), (d) and (e)