Answer:
look at the picture ..........
What is the volume of the rectangular prism?
2 answers:
Rectangular prism is also called <u>cuboid</u>.
<h3><u>G</u><u>i</u><u>v</u><u>e</u><u>n</u><u> </u><u>:</u></h3>- Length = 3 feet
- Breadth = 6 feet
- Height = 2 feet
- Volume of the rectangular prism.
Formula :
Volume = (3 × 6 × 2) feet
Volume = (18 × 2) feet
Volume = 36 feet
Therefore,
- Volume of the rectangular prism is <u>36 feet
</u>.
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The dimensions for this rectangle are b= 30 ft and h=20 ft.
<h3>Perimeter</h3>The perimeter of a geometric figure is the sum of its sides.
The question gives:
- the geometric figure - rectangle
- the total perimeter - 120 ft
Therefore for the perimeter, you have
P= + h+ h +h
P=2b+3h
2b+3h=120 (1)
From equation 1, you can write:
2b=120-3h
b=
b= 60 - (2)
The area for the rectangle is given by A= bh. Therefore, by replacing (2) in the formula for rectangle area, you have:
The maximum area will be calculated from the derivation of the previous equation of area.
The maximum area can be found when the first derivative is equal to zero. Thus,
60-3h=0
-3h=-60 *(-1)
3h=60
h=20
Now, you know the height and from equation 2 (b= 60 - ) you can find the base.
b= 60 -
b=60 - 3*10
b=60-30
b=30
Read more about the First Derivative Test here:
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Let us suppose it will take t hours for the temperature to drop at least 36°F.
We have been given that temperature in Antarctica will decrease 8°F each hour for the next 6 hours.
And we have to find the time to drop the temperature to at least 36°F. At least means greater than equal to.
Therefore, we have the below inequality
Now, we solve the inequality.
Divide both sides by 8, we get
Hence, it will take atleast 4.5 hours to drop the temperature to 36°F.