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3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Mathematics

1 answer:

valkas [14]3 years ago

4 0

Answer:

7, 12, 17...172 (34th term)

Step-by-step explanation:

You might be interested in

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.

slava [35]

Answer:

After solving the power:

$\bold{2(cos60^\circ+isin60^\circ)}$

Rectangular form:

$\bold{1+i\sqrt3}$

Step-by-step explanation:

Given the complex number:

$2(cos20^\circ+isin20^\circ)^3$

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as $a+ib$ where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

$(cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )$

First of all, let us solve:

$(cos20^\circ+isin20^\circ)^3$

Let us apply the De Moivre's Theorem:

Here, n = 3

$(cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ$

Now, the given complex number becomes:

$2(cos60^\circ+isin60^\circ)$

Let us put the values of $cos60^\circ = \frac{1}{2}$ and $sin60^\circ = \frac{\sqrt3}{2}$

$2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }$

So, the rectangular form of the given complex number is:

$\bold{1+i\sqrt3}$

3 0

3 years ago

1/8 of pizza costs 2 dollars. In an hour, 6 1/4 pizzas were sold. How much money was made at the food booth in that hour

12345 [234]

Answer:

$12.50

Step-by-step explanation:

1) Mutliply 6 with 2

6*2= 12

2) multiply 1/4 with 2

1/4 * 2 =1/2

3) add 12 and 1/2

12+1/2 = 12.50

7 0

4 years ago

How do you solve: 21 11/12 plus 17 5/12

GarryVolchara [31]

The problem is $21 \frac{11}{12} + 17 \frac{5}{12}$

Add the whole numbers

$21 + 17 = 38$

Match up the fractions and make sure the denominators are the same (they are)

$\frac{11}{12} + \frac{5}{12}$ $= \frac{16}{12}$

Break down the fraction

$16$ ÷ $12 = 1 \frac{4}{12}$

Reduce-You need to find a common factor for both the numerator and denominator

$4$ ÷ $4$ $= 1$

$12$ ÷ $4 = 3$

Combine everything

$38 + 1\frac{1}{3} =39 \frac{1}{3}$

Answer: $39 \frac{1}{3}$

6 0

4 years ago

Read 2 more answers

Which graph represents the solution set of y = x2 − 4 and x + y + 2 = 0?

statuscvo [17]

Answer:

Graph of solutions of:

y = x^2 -4 (red)

x + y + 2 = 0 (purple)

Step-by-step explanation: