Answer:
1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.
Square the equality √2 + √3 = r − √5 to obtain 5 + 2
√6 = r2 + 5 − 2r
√5. It follows
that 2√6 + 2r
√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r
√30
is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is
irrational can now be applied to show that this is not true. Write √30 = m
n in lowest
terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because
2( m
2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest
terms, a contradiction. We conclude that the initial assumption was false, and therefore
√2 + √3 + √5 is irrational.
Step-by-step explanation:
For the middle square: 20in x 20in= 400in
For ONE flap: 20in x 12in= 240in
Multiply by 4 to get the area of all the flaps: 240in x 4 flaps= 960in^2
Add: 400+960= 1360in^2
Answer:
19 days
Step-by-step explanation:
805 = 7x
x = 115 dollars per day
115x = 2185
divide by 115
x=19
he needs to work 19 days
Answer:
Step-by-step explanation:
one solution.
solve for x and there will only be one solution
5x = 38
x= 7.6
Answer:
To calculate the sales tax that is included in a company's receipts, divide the total amount received (for the items that are subject to sales tax) by "1 + the sales tax rate". In other words, if the sales tax rate is 6%, divide the sales taxable receipts by 1.06.
