CPhill

If you keep reading, I'm not claiming I know WHAT it is......I was just giving some examples....whatver it is, since we don't have (pi) involved, it's probably not a curved surface......

x and y are similar shapes. the total surface area of x is 900cm squared. the total surface area of y is 1600cm squared. the volume of x is 540cm squared. calculate the volume of y

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(I'm going to assume that you meant the volume of x to be 540cm.³ )

Let's assume that we could take all the "surfaces" of x and lay them flat on a table.

Note that, if x's surface area is 900cm², and it volume is 540cm³, the other dimension must be .6cm.

And the "scaling" factor  between the larger object y and the smaller similar object x is given by SQRT(y's surface area/ x's surface area) = SQRT(1600/900) = 40/30 = 4/3

To see that this is true, let's suppose that the surface area of x is just a square with a side = 30cm - it may not be a square, but let's suppose that it is !!  Again, let's suppose that the surface area of y is a square, too, with a side of 40cm. Then, the scaling factor is 4/3....for each dimension of x, the same dimension in y is 4/3 as long......since they're "similar" objects.

Well, if that's true, the other dimension of our hypothetical y must be = (4/3) * .6cm = .8cm.

So , if we could take y's "surfaces" and lay them flat, too, it's total volume would be !600cm * .8cm. = 1280cm³

Finally, no matter what the dimensions of x, each dimension of y is (4/3) as much. So, if the width (w) * length (l) * height (h) of x = volume = 540cm³, then the dimensions of y = (w*4/3) (l*4/3) (h*4/3) = (w* l * h)  * (4/3)^{3 ₌}

(volume of x) * (scaling factor)³ = (540cm³) * (4/3)³ = 1280cm³.......which is just what we thought!!!

2b-8=-1b+7

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OK....let's get the "b's" to the left and everything else to the right.

Add 1b to each side

3b - 8 = 7

Add 8 to each side

3b = 15

Divide by 3 on each side

b = 5

Don't forget to "check" your answer !!

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Here's a pretty simple way to do this. Let Tommy's cards =x. Then Pete's cards = 3x. And Andy's cards = 3x - 35.

So.....

[x] + [3x] + [3x - 35] = 259    simplify

7x - 35 = 259         add 35 to both sides

7x = 294       divide by 7 on both sides

x = 42

So Andy's cards = [3(42) - 35] = 91

......For extra-virgin olive oil the density is about 0.8000g/cc (@ 20C) –(This comes from olives that don’t even think about “it”)........

LOL !!!!

Shame on that "regular" olive oil !!!!

where do you put the brackets for 69-4+9+15

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No brackets are necessary!!!........we perform addition and subtraction as we encounter them from left to right..............

p=1-r^1-y where y is a constant, find y for p=0.55 and r=7.5

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OK...so I assume we have

.55 =1 -7.5^(1-y)                 subtract 1 from both sides

-.45 =- 7.5^(1-y)                 multiply both sides by  -1

.45 = 7.5^(1-y)                    take the log of both sides

log .45 =log 7.5^(1-y)          and by a log property we can bring the (1-y) "out front" on the right

log .45 = (1-y)log 7.5            divide both sides by log 7.5

(log .45 / log 7.5) = 1 - y      add y to both sides and subtract (log .45 / log 7.5) from both sides

y = 1 - (log .45 / log 7.5)

y ≈ -1.3963

Check this for yourself to see that it "works" !! ........

The first one, for sure. The second is the fifth root of the fourth root of 7.

Glad to see Anonymous involved, too!!

Good to see another method presented........and a "rebel" spirit

He/She does NOT follow the motto, "Eliminate the substitution and substitute the elimination !!"

Re: 1-(x-2)=6+2x

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Simplifying on the left, we have

1- x + 2 = 6 + 2x    combining like terms gives us

3 - x = 6 + 2x        add x to both sides

3 = 6  + 3x            subtract 6 from both sides

-3 = 3x                  divide both sides by 2

- 1 = x

Don't just take my word for it !! Check it for yourself in the original equation to see that it's correct!!