The cube root of 2 is irrational. The proof that the square root of 2 is irrational may be used, with only slight modification. Assume the cube root of 2 is rational. Then, it may be written as a/b, where a and b are integers with no common factors. (This is possible for all nonzero rational numbers). Since a/b is the cube root of 2, its cube must equal 2. That is, (a/b)3 = 2 a3/b3 = 2 a3 = 2b3. The right side is even, so the left side must be even also, thatis, a3 is even. Since a3 is even, a is also even (because the cube of an odd number is always odd). Since a is even, there exists an integer c such that a = 2c. Now, (2c)3 = 2b3 8c3 = 2b3 4c3 = b3. The left side is now even, so the right side must be even too. The product of two odd numbers is always odd, so b3 cannot be odd; it must be even. Therefore b is even as well. Since a and b are both even, the fraction a/b is not in lowest terms, thus contradicting our initial assumption. Since the initial assumption cannot have been true, it must <span>be false, and the cube root of 2 is irrational.
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The boat travels 20m in 18 sec. it has an average velocity of 20/18 m/s = +1.11 m/s
5.00 x 13 hours = 65
$65 + $14.50 = $79.50
Given :
- CD is the altitude to AB.
A = 65°.
To find :
- the angles in △CBD and △CAD if m∠A = 65°
Solution :
In Right angle △ABC,
we have,
=> ACB = 90°
=> CAB = 65°.
So,
=> ACB + CAB+ZCBA = 180° (By angle sum Property.)
=> 90° + 65° + CBA = 180°
=> 155° +CBA = 180°
=> CBA = 180° - 155°
=> CBA = 25°.
In △CDB,
=> CD is the altitude to AB.
So,
=> CDB = 90°
=> CBD = CBA = 25°.
So,
=> CBD + DCB = 180° (Angle sum Property.)
=> 90° +25° + DCB = 180°
=> 115° + DCB = 180°
=> DCB = 180° - 115°
=> DCB = 65°.
Now, in △ADC,
=> CD is the altitude to AB.
So,
=> ADC = 90°
=> CAD = CAB = 65°.
So,
=> ADC + CAD +DCA = 180° (Angle sum Property.)
=> 90° + 65° + DCA = 180°
=> 155° +DCA = 180°
=> DCA = 180° - 155°
=> DCA = 25°
Hence, we get,
- DCA = 25°
- DCB = 65°
- CDB = 90°
- ACD = 25°
- ADC = 90°.
