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3 years ago

If a_1=2a 1 =2 and a_n=(a_{n-1})^2-2a n =(a n−1 ) 2 −2 then find the value of a_4a 4 .

Mathematics

1 answer:

Aleks04 [339]3 years ago

6 0

9514 1404 393

Answer:

Step-by-step explanation:

We assume your recursive formula is ...

$a_1=2\\a_n=a_{n-1}^2-2$

Using this to find a4, we get ...

$a_2=a_1^2-2=2^2-2=2\\a_3=a_2^2-2=2^2-2=2\\a_4=a_3^2-2=2^2-2=2\\\\\boxed{a_4=2}$

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Will give branlist The sum of two numbers is 107, the difference is 51. Find the numbers.

UNO [17]

Answer:

Answer is 79 and 28

Step-by-step explanation:

Let two numbers be x and y.

x + y = 107. --> 1

x - y = 51 -->2

solving above equations,

2x = 158

x =79

y = 28

3 0

3 years ago

the length of a rectangle is 3 times its width. the perimeter is 55. find the length and width of the rectangle

Shkiper50 [21]

Answer:

Step-by-step explanation: L= length w= width p= perimeter

L=3W p=55CM

P. of rectangle= 2(l+w)=55cm

L+w= 55/2= 27.5 cm

3w+w=27.5cm

4w=27.5cm

w=27.5/4=6.875cm w=6.875cm L= 3w=6.875*3=20.625cm

4 0

3 years ago

17.The diameter of a circle has endpoints P(–7, –10) and Q(3, 2).

ser-zykov [4K]

A.) (-2,-4)
(7+3)/2=5, (10+2)/2=6
(-7+5,-10+6)
(-2,-4)
b.)r^2=244
10^2+12^2=244
r=2(61)^(1/2)
c.)(x+2)^2+(y+4)^2=244

7 0

4 years ago

If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

Solution:

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

Use the following log rules

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

3 years ago

If the Ramirez family deposits $5000 in a savings account at 7.5% interest compounded continuously, how much will be in the acco

GenaCL600 [577]

Answer: The amount is $14794.39 and the interest is $9794.39

Step-by-step explanation: If you deposit $5000 into an account paying 7.5% annual interest compounded yearly , how much money will be in the account after 15 years?

To find amount we use formula:

A-P(1+r/n) n*t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

P=$5000, r=7.5, n=1 and, t=15 years

After plugging the given information we have

A= $5000 (1+0.075/1)^1.15

A= 5000 *1.075^15

A=14794.39

To find interest we use formula A=P+I'

since A= 14794.39 and P=5000

we have: A=P+I 14794.39=5000+I

I= 14794.39 -5000

I=9794.39

8 0

3 years ago

Read 2 more answers

If a_1=2a 1 ​ =2 and a_n=(a_{n-1})^2-2a n ​ =(a n−1 ​ ) 2 −2 then find the value of a_4a 4 ​ .

If a_1=2a 1 =2 and a_n=(a_{n-1})^2-2a n =(a n−1 ) 2 −2 then find the value of a_4a 4 .