One quarter of a certain number added to one eighth of the same number is 12. What is the number
1 answer:
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<h2>Range of x </h2><h3>
and x>6</h3><h3>Step-by-step explanation:</h3>
Given AB = 4x + 5, BC = 3x - 2 and AC 9x -5
The sum of the length of any two sides of a triangle is greater than the length of third side.
Case I
AB + BC > AC
⇔4x +5 +3x -2 > 9x -5
⇔7x + 3 >9x - 5
⇔ 7x -9x > -5 -3
⇔-2x > -8
⇔x <4
Case II
if AB+AC > BC
4x +5 +9x -5> 3x -2
⇔13x >3x -2
⇔ 13x -3x> -2
⇔10x > -2
⇔x >
Case III
AC+BC > AB
⇔9x - 5 +3x - 2 > 4x +5
⇔6x -7 > 4x +5
⇔6x -4x >5+7
⇔2x > 12
⇔x > 6
The candle has the shape of a cylinder with height H=6 in, and radius of the circular base R= (2.8)/2 =1.4 (in).
The volume of the cylinder is Area(base)*height =
(in cubed)
According to Cavalieri's principle, the volume of the candle is equal to the volume of the cylinder we described.
Answer: 37 in cubed
The volume of the cylinder is Area(base)*height =
According to Cavalieri's principle, the volume of the candle is equal to the volume of the cylinder we described.
Answer: 37 in cubed