Answer:
The model for the temperature of the drink can be written as
Step-by-step explanation:
For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.
We can model that in this way
If we rearrange and integrate
We know that at time 0, the temperature of the drink was 52°F. Then we have:
We also know that at t=2, T=55°F
The model for the temperature of the drink can be written as
Answer:
5.44 cm³
Step-by-step explanation:
The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.
The area of a hexagon with side length s is given by ...
A = (3/2)√3·s²
For s=1 cm, the area is ...
A = (3/2)√3(1 cm)² = (3/2)√3 cm²
__
The area of a circle is given by ...
A = πr²
The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...
A = π(0.5 cm)² = 0.25π cm²
__
The volume is the face area multiplied by the length, so is ...
V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³
V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³
The volume of the metal is about 5.44 cm³.
Answer:
9.75 hours
Step-by-step explanation:
If Rob drove 35% of the time and Mark drove the remainder of the time, the total is 100 %
100-35 = 65
so Mark drove 65% of the time
The total time driven was 15 hours, so we multiply the total time driven by the percentage of time that Mark drove to find the number of hours that Mark drove.
15 * 65%
15*.65
9.75 hours
The answer of f(-2) is 42
