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2 years ago

Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.

Mathematics

1 answer:

Tanzania [10]2 years ago

5 0

Answer:

$a_{n}$ = - 3 $a_{n-1}$

Step-by-step explanation:

There is a common ratio between consecutive terms of the sequence, that is

r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 243 ÷ 81 = - 3

The recursive formula is of the form

$a_{n}$ = r $a_{n-1}$ = - 3 $a_{n-1}$

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an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of

-BARSIC- [3]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Center = (0, 0)

Vertex = (13, 0)

Focus = (12, 0)

Process

From the data we know that it is a horizontal ellipse.

1.- Calculate "a", the distance from the center to the vertex.

a = 13

2.- Calculate "c", the distance from the center to the focus

c = 12

3.- Calculate b

Use the Pythagorean theorem to find it

a² = b² + c²

-Solve for b

b² = a² - c²

-Substitution

b² = 13² - 12²

-Simplification

b² = 169 - 144

b² = 25

b = 5

4.- Find the equation of the ellipse

$\frac{x^{2} }{13^{2}} + \frac{y^{2}}{5^{2}} = 1$ or $\frac{x^{2} }{169} + \frac{y^{2}}{25} = 1$

7 0

3 years ago

Please help this is due after 30 minutes!

Tanzania [10]

Step-by-step explanation:

I entered it in and it was .9993319736

6 0

2 years ago

Read 2 more answers

2ᵃ = 5ᵇ = 10ⁿ. Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl

11Alexandr11 [23.1K]

There are two ways you can go about this: I'll explain both ways.

Solution 1: Using logarithmic properties
The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = $\frac{c}{a}$
c = bln5; ln5 = $\frac{c}{b}$

Hence, c = n(ln2 + ln5) = n( $\frac{c}{a}$ + $\frac{c}{b}$ )
Factorise c outside on the right hand side.

c = cn( $\frac{1}{a}$ + $\frac{1}{b}$ )
1 = n( $\frac{1}{a}$ + $\frac{1}{b}$ )
$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$

$\frac{1}{n}$ = $\frac{a + b}{ab}$
and thus, n = $\frac{ab}{a + b}$

Solution 2: Using exponent rules
In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = $\sqrt[a]{c}$ = $c^{\frac{1}{a}}$

Then, 5 = $c^{\frac{1}{b}}$
and 10 = $c^{\frac{1}{n}}$

But, 10 = 5·2, so 10 = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$
∴ $c^{\frac{1}{n}}$ = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$

$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$
and n = $\frac{ab}{a + b}$

4 0

3 years ago

Let f(x)=8x+8 find and simply f(x+1)

shusha [124]

Answer:

Step-by-step explanation:

f(x) = 8x + 8

f(x+1) = 8(x+1) + 8

= 8x + 8 + 8

= 8x + 16

8 0

2 years ago

Read 2 more answers

Barry read for 15 more minutes than Robert.

Greeley [361]

Hi!

C. v + 15

Barry read for 15 MORE minutes than Robert.

6 0

3 years ago