Answer:
Step-by-step explanation:
The usual equation used for the vertical component of ballistic motion is ...
h(t) = -16t² +v₀t +h₀
where v₀ is the initial upward velocity, and h₀ is the initial height. Units of distance are feet, and units of time are seconds.
Your problem statement gives ...
v₀ = 64 ft/s
h₀ = 8 ft
so the equation of height is ...
h(t) = -16t² +64t +8
__
For quadratic ax² +bx +c, the axis of symmetry is x=-b/(2a). Then the axis of symmetry of the height equation is ...
t = -64/(2(-16)) = 2
The object will reach its maximum height after 2 seconds.
The height at that time will be ...
h(2) = -16(2²) +64(2) +8 = 72
The maximum height will be 72 feet.
Answer:
$60
Step-by-step explanation:
75% divided by 100 x 80 = 60
OR
$80 divided by 100 x 75 = 60
The answer is __ because the directions that the truck traveled are basically in the shape of a right triangle. From the warehouse to the airport, that's the slanted line, and from the warehouse to the factory, and the factory to the airport, those are the other lines.
To find the slant line of a right triangle, you want to use the Pythagorean theorem:
a^(2) * b^(2) = c^(2)
c being the slant line
In this case, we want to count how many boxes the other two lines are, then later factor in what units it's in. (meaning later we convert the boxes into miles)
The distance from the warehouse to the factory is 8, and the distance from the factory to the airport is 6. Now, we want to multiply 8 squared by 6 squared to equal c squared.
64+36 = 100
c squared = 100
Next, we have to find the square root of both sides of the equation.
c = 10
This means that there are 10 boxes in between the airport and the warehouse. Since one box = 44 miles, then we multiply our answer by 44 to find the real amount of miles that the truck traveled.
The distance from the warehouse to the airport = 440 miles
The distance from the warehouse to the factory = 352 miles (44*8)
The distance from the factory to the airport = 264 miles (44*6)
Now just add all the values together to find out how many miles in total the truck traveled.
440 + 352 + 264 = 1056
