Answer:
Step-by-step explanation:
Joint variation has the equation
y = kxz
k is the constant of variation and needs to be solved for using the initial conditions, then filled in later to another equation related to the given info to solve for something else. We are given y = amount of oil used, x = distance traveled, z-squared is the speed. Our equation looks like this, to be exact:
![y=kxz^2](https://tex.z-dn.net/?f=y%3Dkxz%5E2)
Filling in with the initial conditions:
which gives us the
k = .0014166667
Now we need to find the amount of oil used, y, under other circumstances, but this time we have our k.
![y=(.0014166667)(32)(23)^2](https://tex.z-dn.net/?f=y%3D%28.0014166667%29%2832%29%2823%29%5E2)
which gives us that the amount of oil used, when rounded to the tenths,
y = 24.0 barrels
Answer:
9
Step-by-step explanation:
Answer:
-47
Step-by-step explanation:
For this problem, we can use the rule "two negatives make a positive".
-81-(-34)
= -81 + 34
If you subtract 34 from 81, you find the opposite positive/negative answer.
81 - 34 = 47
Change all of the positive/negative signs:
-81 + 34 = -47
Answer:
y = 0 and x = 6
y = 2 and x = 3
y = 4 and x = 0
y = 6 and x = -3
Step-by-step explanation:
2x+3y=12 is the equation of a straight line.
There are infinite number of solutions, but here you're probably looking for solutions where x and y are whole numbers. Trial and error will find you some, although if you examine the equation closely you see that if x is a multiple of 3 and y is a multiple of 2, then they produce terms that are the LCM (least common multiple) of 2 and 3, namely 6. That's the logic in the whole number solutions.
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.