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2 years ago

1: 2 + 3a + 9a 2: 7 - 5x + 1

Mathematics

2 answers:

charle [14.2K]2 years ago

8 0

Answer:

1. 2 + 12a

2. -5x + 8

Step-by-step explanation:

ch4aika [34]2 years ago

5 0

1. 2 + 12a
2. -5x + 8

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write about how many rotations does the bike wheel make when the bike travels 1 mile explain or show your reasoning

tatuchka [14]

Answer:

it takes 11,600

Step-by-step explanation:

because a mile is 5,280 feet and both of you feet are moving the wheels and that should be multiplied by 2.

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

3/7+-5/11+-5/14+3/11

Pachacha [2.7K]

Answer:

Hey!

Your answer is $1\frac{5}{8}$ !

Step-by-step explanation:

Also can be written as 41/8!

HOPE THIS HELPED!

3 0

3 years ago

Read 2 more answers

A scientist begins an experiment with a culture of 5 bacteria cells. Every hour, the number of bacteria cells triples. Which equ

Ann [662]

Answer:

y= 3(5)x

Step-by-step explanation:

5 0

2 years ago

Which of the following is the equation of the function below?

puteri [66]

Answer:

The equation of the graph below is y = 0.5 csc[0.5(x + π/2)] - 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the trigonometry transformation

- If the equation is y = A csc(B(x + C)) + D

# Amplitude is A

- The Amplitude is the height from the center line to the peak .

Or we can measure the height from highest to lowest points and

divide that by 2

# period is 2π/B

- The Period goes from one peak to the next

# phase shift is C (positive is to the left)

- The Phase Shift is how far the function is shifted horizontally

from the usual position.

# vertical shift is D

- The Vertical Shift is how far the function is shifted vertically from

the usual position.

- If y = csc(x)

∴ A = 1 , B = 1 , C = 0 , D = 0

- That means the amplitude is 1, the period is 2π, no phase shift

or vertical shift

* Now lets solve the problem

- From the graph

# The amplitude = (-0.5 - -1.5)/2 = 0.5

∴ A = 0.5

# The period is from 2.5π to -1.5π

∴ The period is 4π

∵ The period = 2π/B

∴ 4π = 2π/B ⇒ by cross multiplication

∴ B = 2π/4π = 1/2 = 0.5

* There is only one answer has A = 0.5 and B = 0.5

∴ y = 0.5 csc[0.5(x + π/2)] - 1

* The equation of the graph below is 0.5 csc[0.5(x + π/2)] - 1

* For more understand look to the color graph

- The blue graph is y = csc(x)

- The green graph is y = 0.5 csc[0.5(x + π/2)] - 1

5 0

3 years ago

Read 2 more answers