8/9
Let's reverse the question - Is a over b less than a squared over b squared? Answer - Only when a is less than b example 1: a is less than b a = 2 a squared = 4 b = 3 b squared = 9 2 / 3 = .6666 4 / 9 = .444444 2 / 3 is greater than 4 / 9 example 2: a is equal to b a = 2 a squared = 4 b = 2 b squared = 4 2 / 4 = .5 2 / 4 = .5 2 / 4 is equal to 2 / 4 example 3: a is greater than b a = 3 a squared = 9 b = 2 b squared = 4 3 / 2 = 1.5 9 / 4 = 2.25 3 / 2 is less than 9 / 4 - wjs1632 -
answer: b over a for ur question: if, a/b = 3/4 then, 4/3 = ? when u switch the place holders like that, it is called the 'inverse'. and since 4/3 is the inverse of 3/4, then the inverse of a/b is b/a.
It is: a/3 times b/4 = ab/12
b^2 - 7b + 12 = b^2 - 4b - 3b + 12 = b(b -4) -3(b - 4) = (b - 3)(b - 4)
b/6
Let's reverse the question - Is a over b less than a squared over b squared? Answer - Only when a is less than b example 1: a is less than b a = 2 a squared = 4 b = 3 b squared = 9 2 / 3 = .6666 4 / 9 = .444444 2 / 3 is greater than 4 / 9 example 2: a is equal to b a = 2 a squared = 4 b = 2 b squared = 4 2 / 4 = .5 2 / 4 = .5 2 / 4 is equal to 2 / 4 example 3: a is greater than b a = 3 a squared = 9 b = 2 b squared = 4 3 / 2 = 1.5 9 / 4 = 2.25 3 / 2 is less than 9 / 4 - wjs1632 -
answer: b over a for ur question: if, a/b = 3/4 then, 4/3 = ? when u switch the place holders like that, it is called the 'inverse'. and since 4/3 is the inverse of 3/4, then the inverse of a/b is b/a.
It is difficult to answer the question because it is still ambiguous. Putting brackets in helps. So: (3 over 4) x b = 3/4*b = 3*b / 4 YES but 3 over (4 x b) = 3/(4*b) is not 3/4*b
It is: a/3 times b/4 = ab/12
a.
(b/12)=(2/3) b=(2/3)*12 b=8 so, (8/12)=(2/3) 0.6667=0.6667
(2, -4)
8/12 is 4/6 or 2/3 in its reduced terms
b^2 - 7b + 12 = b^2 - 4b - 3b + 12 = b(b -4) -3(b - 4) = (b - 3)(b - 4)
b/6
8/12 = 4/3b8/12 = 4 x b/33x8/12 = 4xb24/12 = 4b2 = 4b2/4 = 4b/4b = 2/4b = 1/2
All you need is knowledge of the sine and cosine ratios in a right angle triangle, and Pythagoras. Using Pythagoras you can work out the third side of the triangle which means you now know the value of cos B and so can substitute that into 3 cos B - 4 cos³ B and simplify it to see what the result is; if the result is 0, you have shown the required value. Try working it out before reading any further. -------------------------------------------------------------------------------- If you can't work it out by your self, read on: The sine ratio is opposite/hypotenuse The cosine ratio is adjacent/hypotenuse In a right angled triangle Pythagoras holds: hypotenuse² = adjacent² + opposite² → adjacent = √(hypotenuse² - opposite²) If sin B = 1/2 → opposite = 1, hypotenuse = 2 → adjacent = √(2² -1²) = √(4 - 1) = √3 → cos B = adjacent/hypotenuse = (√3)/2 → 3 cos B - 4 cos³ B = 3 × (√3)/2 - 4 × ((√3)/2)³ = 3(√3)/2 - 4((√3)²/2³) = 3(√3)/2 - 4(3(√3)/8) = 3(√3)/2 - 3(√3) × 4/8 = 3(√3)/2 - 3(√3)/2 = 0