10 / 1 is a rational and which is equal to 10 so 10 is also a rational number
Answer:
1680 ways
Step-by-step explanation:
We have to select 6 different integers from 1 to 10. It is given that second smallest integer is 3. This means, for the smallest most integer we have only two options i.e. it can be either 1 or 2.
So, the selection of 6 numbers would be like:
{1 or 2, 3, a, b, c ,d}
There are 2 ways to select the smallest digit. Only 1 way to select the second smallest digit. For the rest four digits which are represented by a,b,c,d we have 7 options. This means we can chose 4 digits from 7. Number of ways to chose 4 digits from 7 is calculated as 7P4 i.e. by using permutations.
According to the fundamental rule of counting, the total number of ways would be the product of the individual number of ways we calculated above. So,
Total number of ways to pick 6 different integers according to the said criteria would be = 2 x 1 x 840 = 1680 ways
The height that a ball reaches at a certain time t is given by the equation,
h = 2 - 15t + 5t²
We are asked to compute for the values of t that would allow the ball to reach a height of 7 meters.
Substitute the 7 to the equation,
7 = 2 - 15t + 5t²
Transposing,
5t² - 15t - 7 + 2 = 0
Simplifying,
5t² - 15t - 5 = 0
Divide the equation by 5,
t² - 3t - 1 = 0
The values of t can be calculated through the quadratic formula,
t = (-b +/- sqrt(b² - 4ac))/2a
Substituting,
t = (3 +/-sqrt (9 - 4(-1)) / 2(1)
t = 3.3 or t = -0.30
Since, we cannot have t as a negative number hence, our final answer is:
<em> t = 3.3 s</em>
If you are asking what this is the definition of, i think it's the domain, although i couldn't say this is all the way correct,because that's in relation tho input-output function