Answer:
m = - 8 ± 6
Step-by-step explanation:
Given
m² + 16m - 8 = 0 ( add 8 to both sides )
m² + 16m = 8
To complete the square
add ( half the coefficient of the m- term )² to both sides
m² + 2(8)m + 64 = 8 + 64
(m + 8)² = 72 ( take the square root of both sides )
m + 8 = ± = ±
= ± 6
Subtract 8 from both sides
m = - 8 ± 6
Answer: Aproximately 2,525 balloons
Step-by-step explanation:
1. Find the volume of a balloon with the formula given in the problem, where is the radius (
), then:
2. Convert the volume from m³ to lliters by multiplying it by 1,000:
3. You know that that 1 liter of helium can lift 1 gram and that Ryan weighs 5 stone and 5 pounds. So you must make the following conversions:
1 g=0.0022 lb
From 5 stones to pounds
4. Then Ryan's weigh is:
5lb+70lb=75lb
5. Then, if 1 liter of helium can lift 0.0022 lb, to lift 75 lb (which is the weight of Ryan) they need:
6. Then, to calculate the aproximated number of balloons they need to make him float (which can call ), you must divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:
≈2,525 balloons.