Is the following table proportional or non-proportional?
1 answer:
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Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: . The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.
"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.
"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.
Now going back to the expression, the nth-term = , we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes:
. This becomes our expression.
a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term.
b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is , provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.
Answer:
Option b which is
Step-by-step explanation:
We have been given the discriminant 12
We have to choose the equation which will satisfy the given discriminant.
We will consider all the given equation one by one
First we will take option a which is
Discriminant from the equation we will find by the formula
Here, a=-1,b=8 and c=2 on substituting the values we will get
Hence, option a is incorrect.
Now, we will consider option b which is
Here, a=2,b=6 and c=3 on substituting the values we get
Hence, option b is correct
Therefore, option b is the required answer.