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3 years ago

Helppppppppppppppppppppp

Mathematics

1 answer:

Sedaia [141]3 years ago

6 0

Answer:

Step-by-step explanation:

The square root of 64 is 8.

The cube root of 64 is 4.

So, your answer would be 12.

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BRAINLIST TO FIRST ANSWER

olga nikolaevna [1]

<span>Hermione’s Bikes rents bikes for $10 plus $4per hour. Janice paid $30 to rent a bike. For how many hours did she rent the bike?</span>

6 0

4 years ago

Read 2 more answers

Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

4 0

3 years ago

What makes 5,459,176,320 unique

Lisa [10]

Answer:

There is every digit (0-9( except for 8

Step-by-step explanation:

6 0

3 years ago

HELPPPPPPP!!!!!!!!!!!!!

Sonbull [250]

14.23 is your answer!!!!!!!

4 0

4 years ago

Read 2 more answers

Tina is saving to buy a notebook computer. She has two options. The first option is to put S200 away initially and save $10 ever

BigorU [14]

The equation for the first option is Y=10x + 200
The equation for the second option is Y=30x + 100

X = one month
To find when they would be the same about you have to set the equations equal to each other

10x + 200 = 30x + 100
-10x -100 -10x -100

100= 20x

5 = x

After five months she would save the same amount. To find how much is saved you have to plug in 5 for x in one of the equations. You can always double-check 5 by plugging it in both equations and making sure you get the same answer

Y= 10(5) + 200 = 250

Y= 30(5) + 100 = 250

She would have saved $250 after five months by using either method

6 0

3 years ago