The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1 + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390
Pemdas, so exponent before multiply
so do a^-1/2 then multiply it by 2
remember that
![x^ \frac{m}{n}= \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%20%5Cfrac%7Bm%7D%7Bn%7D%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%20)
and
therefor,
the we multiply by 2
Answer:
A=556
Step-by-step explanation:
lxwxh
Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.
Consider this: (2)^a negative power = (1/2)^the same power but positive.
So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.
What I just said in that paragraph was: log₂ of(N) = <em>- </em>log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.
Now let's look at the problem:
log₂(x-1) + log(base 1/2) (x-2) = log₂(x)
Subtract log₂(x) from each side:
log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0
Subtract log(base 1/2) (x-2) from each side:
log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.
The left side is the same as log₂[ (x-1)/x ]
==> The right side is the same as +log₂(x-2)
Now you have: log₂[ (x-1)/x ] = +log₂(x-2)
And that ugly [ log to the base of 1/2 ] is gone.
Take the antilog of each side:
(x-1)/x = x-2
Multiply each side by 'x' : x - 1 = x² - 2x
Subtract (x-1) from each side:
x² - 2x - (x-1) = 0
x² - 3x + 1 = 0
Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .
I think you have to say that <em>x=2.618</em> is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.
There,now. Doesn't that feel better.
Total length of the kitchen wall = 24 2/3 feet.
Let us convert 24 2/3 feet into improper fracion.
24 2/3 = (24*3+2)/3 = 74/3 feet.
Length of each strip = 1 3/4 feet.
Let us convert 1/3/4 feet in improper fracion.
1 3/4 feet = (1*4+3)/4 = 7/4 feet.
Total number of strips required = (Total length of the kitchen wall) ÷ (Length of each strip)
= 74/3 feet ÷ 7/4 feet.
Let us convert division sign into multiplication, we get
74/3 × 4/7.
Multiplying across, we get
296/21.
On dividing 296 by 21, we get 14.09 approximately.
14.09 represents more than 14.
So, we can round it to the next whole number, that is 15.
Therefore, 15 strips of border are needed.
