Answer:
1) Multiplying powers with the same base would be product rule. It where you just add the exponents. Dividing powers with the same base would be the quotient rule. Its where you subtract the exponents.
2)Where you multiply the two exponents together
3)The negative law is where for example, if it were in the numerator, then it would be placed at the denominator with a positive exponent whereas if it were in the denominator it would be on the numerator with the positive exponent. The zero law just states the anything to the power to zero is one.
Step-by-step explanation:
1) 3^3 x 3^4 = 3 ^3+4 = 3^7
3^9 ÷3² = 3^9-2 = 3^7
2) (3^2)^2 = 3^2×2 =3^4
3) 1/3^-5 = 3^5 \
3^-7 =1/3^7
2^0 = 1
Given:
5 bonds of face value of 1,000 that paid 5% annual interest rate.
5 bonds x 1,000 = 5,000
5,000 x 5% x 1 year = 250
The total annual interest income of James is 250. Each bond earns 50 per annum.
<span>25 x 10^6 = 25,000,000
</span>standard form: 25,000,000
<span>scientific notation: 2.5 x 10^7
hope it helps</span>
We have that O(n²) is the theta notation for 7n² + 4n + 2.
Let's give big-Oh a formal definition:
O(g(n)) = {the set of all f such that 0 f(n) cg(n) for any n >= n₀ fulfilling positive constants c and n₀}
To show this
We need to find c and n₀ such that:
7n² + 4n + 2 <= cn² for all n >= n₀ .
Divide both sides by n², getting:
7 + 4/n + 2/(n²) <= c for all n >= n₀ .
If we choose n₀ equal to 1, then we need a value of c such that:
7 + 4 + 2 <= c
We can set c equal to 13. Now we have:
7n² + 4n + 2 <= 13n² for all n >= 1 .
Hence, 7n² + 4n + 2=O(n²)
Learn more about Big-Oh notation here-
brainly.com/question/14438669
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