Answer:
Rational numbers' decimal representations either finish or repeat a pattern. Divide the top by the bottom, the numerator by the denominator to convert fractions to decimals, and if the division doesn't come out evenly, round off after a specific number of decimal places.
Step-by-step explanation:
Answer: 51 uinits
The three numbers are x , x + 21 and x + 27.
The greatest of the 3 numbers is x + 27, so x + 27 has to be the hypotenuse.
----------------------------------------------
Pythagoras Theorem
----------------------------------------------
a² + b² = c²
x² + (x+21)² = (x+27)²
x² + x² + 42x + 441 = x² + 54x + 729
x² - 12x -288 = 0
(x - 24)(x + 12) = 0
x = 24 or x = -12 (rejected, length cannot be negative)
----------------------------------------------
Find hypotenuse
----------------------------------------------
Hypotenuse = x + 27 = 24 + 27 = 51 units
-----------------------------------------------
Answer: 51 units
----------------------------------------------
Y = ln {[sin(x)]^2}
use the chain rule
y' = 1 /[sin(x)]^2 * 2sin(x)*cos(x) = 2cos(x) / sin(x) = 2 cot(x)
Answer: 2 cot(x)
(15p⁺⁴.q⁻⁶) /(-20p⁻¹².q⁻³).
Remember that a⁻ⁿ = 1/aⁿ and 1/a⁻ⁿ = aⁿ
(-15/4).(p⁻⁴.q⁻⁶)(p⁺¹².q⁺³).
(-15/20).(p⁻⁴.p¹².q⁻⁶.q³)
Remember aⁿ.aˣ = aⁿ⁺ˣ
(-15/20).(p⁸.q⁻³)
-3/5(p⁸.q⁻³)
