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TEA [102]
3 years ago
11

Use De Moivre’s Theorem to compute the following:

29%2B8isin%284%5Cpi%2F5%29%29%7D%20" id="TexFormula1" title="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " alt="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " align="absmiddle" class="latex-formula">

Mathematics
1 answer:
Kipish [7]3 years ago
6 0
Hello here is a solution : 

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I need to know if it’s A B C OR D
Liula [17]

SOLUTION

Consider the property, opposite angle of a cyclic quadrilateral are supplementary

hence

\angle NMP+\angle NOP=180^0

Recall that

\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}

Hnece, we have that

\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}

Then

\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}

Hence

x=17

Since

\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}

Therefore

The measure of angle NOP is 68⁰

Answer; 68⁰ (The fourth Option )

5 0
1 year ago
Write and solve a real world word problem to fit the expression -50 ÷ 5.
MissTica

Answer: THe person who rented a apartment had been in debt for 50 dollars, but she didnt have a lot of money so the land lord would divide the rent by 5

Step-by-step explanation:

6 0
2 years ago
What is a common factor for the two fractional terms StartFraction 5 over 8 EndFraction x andStartFraction 11 over 8 EndFraction
Dafna1 [17]

Answer:

\frac{1}{8x}

Step-by-step explanation:

Given two fractional terms \frac{5}{8x}\ and\ \frac{11}{8xy}. Their common factor is a value or function that can go in both fractional terms. The terms can be written as shown.

\frac{5}{8x} = 5 *\frac{1}{8x}

\frac{11}{8xy} = 11 * \frac{1}{8x} * \frac{1}{y}

It can be seen from the both equations that they both have \frac{1}{8x} as one of their factors i.e <em>1/8x is common to both fractional terms</em>. This gives the common factor for the two fractional terms as \frac{1}{8x}

4 0
3 years ago
Read 2 more answers
Find L when P= 24 and W = 6.<br> P = 2L+ 2W (perimeter of a rectangle)<br> L =
Anon25 [30]

Answer:

6

Step-by-step explanation:

24 = 2L + 2(6), multiply...

24 = 2L + 12, subtract 12 to both sides...

12 = 2L, divide 2 to both sides to isolate the varibale L

6 = L

Therefroe, L = 6

8 0
3 years ago
Thaddeus wants to attend a sports camp this spring that costs $170.00 for the week. He rakes leaves during the fall and earns $5
AnnyKZ [126]
The answer to this question is 25.85

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3 years ago
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