Answer:
(0,2)
Step-by-step explanation:
solve by addition/elimination
2x + 3y= 6
–3x + 5y = 10
multiply first equation by 3 and second one by 2 to eliminate x)
6x+9y=18
-6x+10y=20 (add the two equations)
6x+9y-6x+10y=38
19y=38
y=38/19=2
2x+3y=6
2x=6-6
x=0
Answer: The answer to a system of equations is the point(s) of intersection of the equation involved.
When you have more than one equation with more than one variable, you have a system of equation. The solution(s) is the set of values for each variable that satisfy the equations. This means that the inputting values make the equations true.
Answer: 46.90mins
Step-by-step explanation:
The given data:
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet/min.
Solution:
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon
= 4/3 × 3.14 × 55³
= 696556.67 ft³
When the volume 2/3 the maximum volume
= 2/3 × 696556.67 ft³
= 464371.11 ft³
The radius, r₂ at the point is
= 4/3·π·r₂³
= 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4
= 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the
above length
Time taken for the radius to increase the length.
= is 70.369 ft/(1.5 ft/min)
= 46.90 minutes
46.90mins is the time taken to inflate the balloon.
A or c is the correct answer
