Area of chalkboard = 4 feet x 6 feet = 24 square feet.
Total cost = 24 square feet x $7.21 per square foot = $173.04
Answer: $173.04
For every cubic yard, it equals to 27 cubic feet.
So, could have this fraction
And we want to convert 3 cubic yards into cubic feet.
We can express 3 cubic yards as
Now multiply the
fraction by the second fraction or the reciprocal of the second fraction to cancel out the yards^3 units.
So, 3 cubic yards to equal to 81 cubic feet.
If x is the distance the base of the ladder is from the wall, and y is the distance to top of the ladder is up the wall, then the Pythagorean theorem tells you
... x² + y² = 10²
Differentiating with respect to time, we have
... 2x·dx/dt + 2y·dy/dt = 0
... dy/dt = (-x/y)·dx/dt
We are given x = 6 ft and dx/dt = 3 ft/s. Using the first equation, we can find y as
... y = √(10² -6²) = 8
Then
... dy/dt =(-6/8)·(3 ft/s)
... dy/dt = -2.25 ft/s
The top of the ladder is sliding down the wall at -2.25 ft/s.
For this case we have the following quadratic equation:
The solutions will be given by:
Where:
Substituting the values we have:
We have two roots:
ANswer: