Answer:
-19,531,250
Step-by-step explanation:
multiply the last term by -5
9514 1404 393
Answer:
- no, √2 is irrational
- 7/5, 99/70, 19601/13860, any truncation of the decimal value
Step-by-step explanation:
1.√2 is not the square root of a perfect square integer, so is irrational. There is no rational number that is exactly √2.
The proof usually looks something like this. Let p/q represent the reduced square root. Then 2 = p²/q², or 2q² = p², which means p must be even. If p is even, then p² will have at least 2 factors of 2. This requires that q² be even, hence q must be even. This contradicts our assumption that p/q is a reduced fraction, so there cannot be any p/q that is equal to 2.
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2. Any truncation or rounding of the decimal representation of √2 will be a rational number: 1.4, 1.41, 1.414, and so on. In addition, there are some fractions that represent √2 fairly well. A couple are 99/70 and 19601/13860.
Additional fractions can be found by evaluating the continued fraction ...
1 +1/(2 +1/(2 +1/(2+ ...)))
at some level of truncation. A few of these values are 7/5, 17/12, 41/29, 99/70, 239/169, 577/408.
The Babylonian method can also be used to find rational approximations. If you start with <em>any</em> rational approximation p/q, then a <em>better</em> approximation will be (2q² +p²)/(2pq). This formulation can be iterated as many times as you like. It very rapidly converges to very good approximations.
Answer:
Step-by-step explanation:
The 20% discount amounted to ...
0.20 × $42.00 = $8.40
so the price before tax was ...
$42.00 -8.40 = $33.60
The tax amount is 3% of this value, so is ...
0.03 × $33.60 = $1.008 ≈ $1.01
So the total price paid for the shirt was ...
$33.60 +1.01 = $34.61
Randy paid $34.61 for the shirt after discount and tax.
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<em>Alternate solution</em>
You can realize that the 20% discount means that Randy will pay 80% of the original price of the shirt. Similarly, the 3% added tax means Randy will finally pay 103% of the discounted price. Then the total price Randy pays is ...
$42.00×0.80×1.03 = $34.608 ≈ $34.61
B: -3.5,-2.7,-2.69,-2.66,-1.49
Answer:
The output of y = 1
Step-by-step explanation:
