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2 years ago

If a1=4 and an =2an-1 – 1 then find the value of a4.

1 answer:

7 0

1 = 4

a2 = -2(a1) - 1
a2 = -2(4) - 1
a2 = -9

a3 = -2(a2) - 1
a3 = -2(9) - 1
a3 = -19

Can you do a4 and a5 and answer?

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Find the following Euler Totients using Euler’s Theorem, as explained on p.409 of the text (10 points each): a.ϕ(13) b.ϕ(81) c.ϕ

ad-work [718]

(a) $\varphi(13)=12$ since 13 is prime.

(b) $81=3^4$ , and there are 81/3 = 27 multiples of 3 between 1 and 81, which leaves 81 - 27 = 54 numbers between 1 and 81 that are coprime to 81, so $\varphi(81)=54$ .

(c) $100=2^2\cdot5^2$ ; there are 50 multiples of 2, and 20 multiples of 5, between 1 and 100; 10 of these are counted twice (the multiples of 2*5=10), so a total of 50 + 20 - 10 = 60 distinct numbers not coprime to 100, leaving us with $\varphi(100)=100-60=40$ .

(d) $102=2\cdot3\cdot17$ ; there are 51 multiples of 2, 34 multiples of 3, and 6 multiples of 17, between 1 and 102. Among these, we double-count 17 multiples of 2*3=6, 3 multiples of 2*17=34, and 2 multiples of 3*17=51; we also triple-count 1 number, 2*3*17=102. There are then 51 + 34 + 6 - (17 + 3 + 2) + 1 = 70 numbers between 1 and 102 that are not coprime to 102, and so $\varphi(102)=102-70=32$ .

4 0

3 years ago

What is the positive solution to this equation? 4x2 + 12x = 135

Bas_tet [7]

Answer:

127/12

Step-by-step explanation:

4 × 2 + 12x = 135

(1. Simplify 4 x 2 to 8.

8 + 12x = 135

(2. Subtract 88 from both sides.

12x= 135 - 8

(3. Simplify 135 - 8 to 127

12x = 127

(4. Divide both sides by 12

x= 127/12

Decimal Form: 10.583333

I think this is the awnser, but don't quote me on that

4 0

3 years ago

Trying to finsh fast so help please

max2010maxim [7]

Answer:

A-B

Step-by-step explanation:

5 0

3 years ago

Mary's clock uses 3/4 of the batteries in the package. There are 8

Lelu [443]

DONT look at that photo. You have no idea what's in that link!

The answer is d) 6 batteries

7 0

2 years ago

Find the distance between the

Dovator [93]

Answer:

$\displaystyle d = \sqrt{29}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step-by-step explanation:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{5^2 + 2^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{25 + 4}$
[√Radical] Add: $\displaystyle d = \sqrt{29}$

7 0

2 years ago