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andreev551 [17]

2 years ago

13

Phillip is restoring a square tabletop he wants to finish the outside edges with a piece of decorative molding what total length

of molding will he need if the table has an area of 64ft

1 answer:

PilotLPTM [1.2K]2 years ago

3 0

Answer:

8 square feet

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Robert ran 0.5 miles on July 1st. Each day thereafter, he ran 0.3 miles more than the previous day. Find

marissa [1.9K]

the anser is 244.9

hope this helps, you need more help ask me.

4 0

2 years ago

ratelena [41]

C the correct answer is C

4 0

2 years ago

Given the functions, f(x) = 5x2 - 3x + 1 and g(x) = 2x2 + x - 2, perform the indicated operation. When applicable, state the dom

RUDIKE [14]

You plug in 1,2,3 and so on in the X and you graph , i think

3 0

2 years ago

How many oz of walnuts which cost $6/oz must be added to 2 oz of peanuts which cost $12/oz to make mixed nuts which cost $8/oz

Burka [1]

Answer: 4 oz

<u>Step-by-step explanation:</u>

Create a table. Multiply across and add down (the middle column cannot be added). The Mixture line creates the equation that must be solved.

Let x represent the unknown quantity of walnuts.

$\begin{array}{c|c|c||c}&\underline{Quantity}&\underline{Cost}&\underline{Qty \times Cost}\\Walnuts&x&6&6x\\\underline{Peanuts}&\underline{\qquad 2\qquad}&\underline{\qquad 12\qquad}&\underline{\qquad 24\qquad }\\Mixture&x+2&8&6x+24\end{array}$

$.\qquad \qquad \qquad \qquad (x+2)(8) = 6x+24\\.\qquad \qquad \qquad \qquad 8x + 16 = 6x + 24\longrightarrow \text{distributed}\\.\qquad \qquad \qquad \qquad2x+16=24\qquad \longrightarrow \text{subtracted 6x}\\.\qquad \qquad \qquad \qquad 2x=8\qquad \qquad \ \longrightarrow \text{subtracted 16}\\.\qquad \qquad \qquad \qquad x=4\qquad \qquad \quad \longrightarrow \text{divided by 2}$

4 0

2 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

2 years ago