Given f(x)=x^3+5x+k, and x+2 is a factor of f(x), then what is the value of k?
2 answers:
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Answer:
1. 157 in³
2. 12 in
3. volume of the rice container is 1.5 times the volume of the sugar container
4. 50.24 in³
5. Rice container has the greatest volume
Flour container has the smallest volume
Step-by-step explanation:
By inspection of the diagram, the three containers are all cylinders.
Volume of a cylinder =
(where r is the radius and h is the height)
Given = 3.14
1. volume of sugar container = 3.14 x 2.5² x 8 = 157 in³
2. 235.5 = 3.14 x 2.5² x h
⇒ 235.5 = 19.625h
⇒ h = 235.5 ÷ 19.625 = 12 in
3. height of sugar container = 8 in
height of rice container = 12 in
12 ÷ 8 = 1.5
⇒ height of rice container is 1.5 times the height of the sugar container
volume of sugar container = 157 in³
volume of rice container = 235.5 in³
235.5 ÷ 157 = 1.5
⇒ volume of the rice container is 1.5 times the volume of the sugar container
4. volume of flour container = 12.56 x 4 = 50.24 in³
5. volume of sugar container = 157 in³
volume of rice container = 235.5 in³
volume of flour container = 50.24 in³
Rice container has the greatest volume
Flour container has the smallest volume