Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
1 answer:
Answer:
The equation of the ellipse is
Step-by-step explanation:
Let the equation of the ellipse is {As the center of the ellipse is at the origin}
Therefore, the vertices of the ellipse are (± a,0) and foci are (± ae,0)
Now, given that a = 3 and ae = 2
Now, eccentricity of a ellipse is given by b² = a² - a²e² = 3² - 2² = 5
Therefore, the equation of the ellipse is (Answer)
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Options:
A.) square root
B.) exponential
C.) absolute value
D.) cube root
Answer : A) square root
We know area of square having side 's' = s* s =
For example
Area of square =
To find side we take square root
Area =
16 =
Take square root on both sides
4= side
Betsy knows that the area of the rug is A square feet.
Area A =
So answer is square root.
Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is . Thus, there are only 35 ways to distribute the blackboards in this case.