Answer:
x = 9.125 and 0.875
Step-by-step explanation:
Given the expression
log (x² + 8) = 1 +log(x)?
This can also be written as;
log (x² + 8) = log 10 +logo(x)
log (x² + 8) = log(10x)
(x² + 8) = (10x)
x² -10x + 8 = 0
Factorize;
x = 10±√(-10)²-4(8)/2
x = 10±√100-32/2
x = 10±√68/2
x = 10±8.25/2
x = 10+8.25/2 and 10-8.25/2
x = 18.25/2 and 1.75/2
x = 9.125 and 0.875
For this case by similarity of triangles we can use the following relationship:
(x) / (9) = (5) / (15)
We clear the value of x:
x = ((5) / (15)) * (9)
Rewriting:
x = (1/3) * (9)
x = 3
Answer:
The value of x for this case is:
x = 3
Explicit Formula
Just in case you don't know what this is, the explicit formula is the formula that solves for any term in the series without necessarily knowing what came before the term you are solving.
<em><u>Givens</u></em>
d = t_(n + 1) - t_n You can take any term and the next term for this part of the formula
d = t_3 - t_2
t_3 = 1
t_2 = -7
d = 1 - - 7 = 8
a = -15
<em><u>Formula</u></em>
t_n = a + (n - 1)*d
t_n = -15 + (n - 1)*8
For example find the 5th term.
t_5 = - 15 + (5 - 1)*8
t_5 = - 15 + 4 *8
t_5 = -15 + 32
t_5 = 17 Which is what you have.
Recursive Formula
Computers really like this formula. They use it in what is called a subroutine and they pass values from one part of the program to a subroutine which evaluates the given and sends the result back. I'm telling you all this so you see why you are doing it. The disadvantage of it for humans is that you must know the preceding term to use the recursive formula.
<em><u>Formula</u></em>
t_n = t_(n - 1) + d
<em><u>Example</u></em>
t_6 = t_(6 - 1) + d
t_6 = t_5 + 8
t_6 = 17 + 8
t_6 = 25
You can check this by using the explicit formula.
Answer:
Hundreds.
Step-by-step explanation:
There are 3 digits. And the decimal is after the value of 110.
You have to use the formule: y2-y1/x2-x1
-2-(-2)/4-(-3)=0/7
