Answer:
75 cubic units
Step-by-step explanation:
Bottom layer of a rectangular prism is made up of 15 unit cubes.
Therefore, area of the 15 unit cubes = 15(area of the base of one unit cube)
= 15(1)²
= 15 unit²
Number of layers of unit cubes in the rectangular prism = 5
So the height of the prism = 5 units
Volume of the prism = (Area of the base) × Height
= 15 × 5
= 75 cubic unit
Answer:$7.56 because 72 times 0.105 is 7.56
Step-by-step explanation:
A=1/10, b=1/12, c=1/15 (these are the rates for each worker...)
1.)
2(1/10)+4(1/12)+t/15=1
1/5+1/3+t/15=1
(3+5+t)/15=1
3+5+t=15
8+t=15
t=7
So it would take c 7 hours to finish the job.
2.)
1/40-1/60
(3-2)/120
1/120
The drain rate is 1/60. So you will need to find t when the tank is empty, while starting at 2/3 capacity...
2/3-t/60=0
(40-t)/60=0
40-t=0
t=40
It would take 40 minutes to empty the tank when it is 2/3 full.
C. f(x) = – 2 cos 6x + 1
Start by determining the amplitude. Since we've deduced the amplitude is 2, the equation can include either a positive or negative 2 (since amplitude measures absolute value).
Next is the period. The equation for period P is P = (2pi)/b. If P is pi/3, then
pi/3 = (2pi)/b. Thus your b value should be 6.
Finally, the midline would be given by + 1 since adding a unit shifts the function upwards. This means that instead of the highest y value being 2 and the lowest -2, instead you'd have values of 3 and -1.
(3 – 1)/2 = 1 (midpoint theory).
