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Let "a" and "b" represent the values of the first and second purchases, respectively.
0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00
At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate
Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00
Julia spent $65 in all at the two stores.
Step-by-step explanation:
let the big cube side be b
small cube side be s
s = 2/3 * b
bv + sv = 118.125
b^3 + 8/9 b^3= 118.125
17 b^3/8 = 118.125
b^3 = 55.58
b = 3.816in
s = 2.544in
Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume 
and prove 
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required
