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:
Answer:
(1 ) Inner curved surface area of the well is 109.9 sq. meters.
(2) The cost of plastering the total curved surface area is 4396.
Step-by-step explanation:
The inner diameter = 3.5 m
Depth of the well = 10 m
Now, Diameter = 2 x Radius
⇒R = D/ 2 = 3.5/2 = 1.75
or, the inner radius of the well = 1.75 m
CURVED SURFACE AREA of cylinder = 2πr h
⇒The inner curved surface area = 2πr h = 2 ( 3.14) (1.75)(10)
= 109 sq. meters
Hence, the inner curved surface area of the well is 109.9 sq. meters.
Now, the cost of plastering the curved area is 40 per sq meters
So, the cost of total plastering total area = 109.9 x(Cost per meter sq.)
= 109.9 x (40)
= 4396
Hence, the cost of plastering the total curved surface area is 4396.
Answer:
6%
Step-by-step explanation:
Estimated distance = 80 miles
Actual distance covered = 75.5 miles
We need to find the percent error of the cyclist's estimate. Its formula is given by :
Put all the values,
or
= 6%
So, the percentage error is 6%.
Answer:
Answer D is correct
Step-by-step explanation:
hope this helps
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Answer:
The number of ways are 210.
Step-by-step explanation:
Consider the provided information.
Brett has ten distinct T-shirts. He is planning on going on a short weekend trip to visit his brother in college. He has enough room in his bag to pack four T-shirts.
Since order doesn't matter so we will use combination.
Use the formula for combination 
Substitute n=10 and r=4 in above formula.
Hence, the number of ways are 210.
