A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inc
hes. Use π = 3.14. What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
1 answer:
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Answer:
a) In the first season, there were 25.450 million viewers.
b) In the fourth season, the number of viewers was 11.950 million.
Step-by-step explanation:
Hi there!
The average number of viewers in season t is given by the following function:
a) To obtain the average number of viewers in season 1, we have to evaluate the function at t = 1:
In the first season, there were 25.450 million viewers.
b) Now we have to evaluate the function at t = 4:
In the fourth season, the number of viewers was 11.950 million.
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This would be one way to write the expresion/equation; in which "x" represents the unknown number.
Now, to solve for "x" ;
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Given:
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Add "5" to EACH SIDE of the equation:
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to get:
x = (-2 * 3) ;
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x = - 6 .
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Answers:
- D ' at (9, -9)
- E ' at (5, -9)
- F ' at (5, -2)
- G ' at (9, -2)
Refer to the diagram below
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Explanation:
For points D,E,F,G we will follow these steps
- Shift everything 3 units to the left so that the vertical line x = 3 will move on top of the y axis (which is the vertical line x = 0).
- Reflect across the y axis using the rule
. Here we have the x coordinate flip in sign from positive to negative, or vice versa. The y coordinate stays the same.
- Shift everything 3 units to the right so we effectively undo the first step. This places the points in the proper final position.
Let's go through an example:
Point D is located at (-3, -9). Apply the three steps mentioned above.
- Shift point D three units to the left to arrive at (-6, -9)
- Reflect over the y axis to go from (-6, -9) to (6, -9)
- Lastly, shift 3 units to the right to move to (9, -9) which is the location of D'
In short, D(-3,-9) reflects over the line x = 3 to land on D ' (9, -9)
The other points E, F, G will follow the same steps to get the answers you see at the top.
The diagram below visually summarizes everything.
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Side notes:
- The distance from D to the line of reflection is the same as the distance from D' to the line of reflection. Put another way, the line of reflection bisects segment DD'. Points E,F,G follow the same property.
- Going from D to E to F to G has us go counterclockwise. Going from D' to E' to F' to G' has us go clockwise. Any reflection transformation will flip the orientation.
