5x+1 can be written as 5x*5, so if this equals 30, you can find what 5x equals.
53x+1 can be written as 53x*5, which can be written as (5x)3*5, so once you know what 5x is you just cube it and multiply by 5.
1012 = 1*22 + 0*21 +1*20 = 4 + 0 + 1 = 510
"A ball thrown up from the top of a building is given ... etc."
I don't see it! As far as I can see the negative terms run from 1 cubed to 999 cubed so this term is as I wrote it.
"sketch a washer and find the volume of the solid generated by revolving the region bounded by y=8x-(x^2) and y=0.5(x^2) around the x axis --> Im not sure how to do this one."
"sketch a washer and find the volume of the solid generated by revolving the region bounded by y=2x^2, y=0 and x=2 around the y-axis --> is 16pi the answer??"
(Yes, 16pi is the resulting volume).
The graph below should help:
Hint:
You can write this as \(1000^3-\sum_{k=1}^{999}k^3\)
Now \(\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}{4}\)
Hope this helps!
Multiply both sides by g, divide both sides by sin(84°), take the square root of the result.
"find log25(8) * log1/2(5)"
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