Brandon buys radio for 43.99 in a state where the sales tax is 7% how much does he pay in taxes?
2 answers:
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For this case we must algebraically rewrite the given expression. So:
x: It is the variable that represents an unknown number
"double a number" is represented as:
"6 less than double a number" is represented as:
So, the final expression is:
If we want to rewrite the expression in an equivalent way, we take common factor 2:
Asnwer:
Equivalent expression:
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
