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4 years ago

Solve C = AB + D for B.

Mathematics

1 answer:

OLEGan [10]4 years ago

8 0

Answer:

(C-D)/A = B

Step-by-step explanation:

C = AB + D

Subtract D from both side

C-D = AB + D-D

C-D = AB

Divide each side by A

(C-D)/A = AB/A

(C-D)/A = B

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What is the difference between dash and hyphen

UNO [17]

Hyphens and Dashes. A hyphen joins two or more words together while a dash separates words into parenthetical statements. The two are sometimes confused because they look so similar, but their usage is different. Hyphens are not separated by spaces, while a dash has a space on either side.

8 0

3 years ago

Factor the expression using the GCF.<br> 60 – 36 =

Ivanshal [37]

Answer

12 (5 - 3)

Step-by-step explanation:

The greatest common factor is the largest number that will divide both numbers evenly. As an example, 6 is a common factor because it divides both 60 and 36. However, it is not the greatest common factor.

If I break 60 into it's prime factors, I would get 2 * 2 * 3 * 5.

If I break 36 into it's prime factors, I would get 2 * 2 * 3 * 3.

The two number have the factors, 2, 2, and 3 in common.

The greatest common factor is then: 2 * 2 * 3, or 12.

The expression can be factored as: 12 ( 5 - 3)

6 0

4 years ago

Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

3 years ago

What is the volume of a cylinder, in cubic centimeters, with a height of 2 centimeters

harina [27]

Answer:

Step-by-step explanation:

Volume of cylinder: V = π×r² × h

diameter = 20 cm ⇒ r = 10 cm

h = 2 cm

Volume:

V = π×(10)²×2 = 200π cm³ = 628.318.... cm³ ≈ 628.3 cm³

7 0

3 years ago

A small company has 10,000 shares. Stephen owns 500 of these shares. The company decides to split its shares. What is Stephen's

Sergeu [11.5K]

So the company splits there shares now every thing doubles now there are 20,000 shares and you own 1,000 to find the answer you divide a

1,000 by 20,000 which will give you 0.05 then you multiply

0.05 by 100 and you get 5

So after the split you own 5% of the company

7 0

3 years ago