CPhill

how many acres are in 225586 sq. ft.

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There are 43,560 sq. ft. in one acre

So just divide 225586 by 43560 to find the answer.......

y=7x-9 y=x+3

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I assume you want to solve this system....let's do this........so we have

y=7x-9

y=x+3

We can just subtract the second equation from the first     this gives

0 = 6x -12      add 12 to both sides

12 = 6x    divide both sides by 6

2 = x    Now, to find y, just substitute "2" for "x" in one of the equations

Using the second one, we have

y = 2 + 3 

y = 5

To check this, substitute both values back into the first equation.........

If f(x) = 3x + 3/x, then [f(x + h) - f(x)]/h =

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I'm making a broad assumption here, but in my experience,  I believe you're trying to ultimately find the "difference quotient" ⇒  (the derivative of f(x) )

Let's simplify f(x)   so we have

f(x) = [(3x² + 3)/ x ] ......  then [f(x + h) - f(x)]/h =

([(3(x+h)² + 3) / (x+h)] - [(3x² + 3)/ x ]) / h   =

([3x² + 6xh + 3h² + 3] / (x + h)] - [(3x² + 3)/ x ]) / h  =

[3x³ + 6x²h + 3xh² + 3x - 3x³ - 3x²h -3x - 3h) / [(x)(x+h)(h)] =

 [ 3x²h + 3xh² - 3h) / [(x)(x+h)(h)] =

(3x² ) / (x² + xh)    + 3h / (x+h) - 3 / [(x+h) (x)]

Now, let's take the limit of everything by letting h ⇒ 0      We get

3 - 3x^-2

Note that this is just the derivative of f(x)      (Which is what we were hoping for!!!)  

the amplitude of the function y=3/4 sin x + 1/2 is equal to?

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The general form of this is  ⇒    y = Asin(x) + B

The amplitude is given by  ⇒  l A l

So we have  l 3/4 l  = 3/4

Which shape is able to have the greatest area?

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Not possible.....no matter what shape we have, we can always enclose it with some larger one.

If a^b equals (a^x)/10, will b equal x/10?

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Let's suppose that it's true    multiply both sides by 10    we have

10a^b = a^x    take the log of both sides

log 10a^b = log a^x       by a property of logs, we have

b log 10a = x log a      and using another log property, we have

b [log 10 + log a] = x log a        and because log10 = 1    we have

b [1 + log a] = x log a        solving for b, we have

b = [x log a] / [1 + log a]   which is definitely    ≠   x/10

32(15)=x(x+14)

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So we have

480 = x² + 14x  subtract 480 from both sides

0 = x² + 14x - 480   This factors as

(x+30) (x-16) = 0

And setting each factor = 0   we get that

x = -30  and x = 16

Actually, I believe the answer that Anonymous gave makes perfect sense. If the question refers to the horizontal distance (distance along the ground) that the plane traveled, then the angle is relevant. We can obviously see that the plane traveled 3000 ft. "along" the hypoteneuse. Thus, "distance traveled" depends upon which "distance" we're talking about......

Re: Area of hexagon

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Let's think about this for just a second. A hexagon is just composed of 6 equilateral triangles. Then the area of one of these triangles is just (1/2)s²sin(60°) = (1/2)s²(√(3)/2) = (1/4)s²(√(3), where s is the side length of the hexagon. And since we have 6 of these triangles, then the total area is just 6* (1/4)s²(√(3)=

(3√(3))/2*s²  

find the 54th term of the sequence -8, -5, -2, . .

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The n^th term is given by:  

a_n = -8 + 3(n-1)

See if you can take it from there........