Josephine wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability tha
1 answer:
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Answer:
Hence, option: B is correct (11.02 seconds)
Step-by-step explanation:
Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.
Now we are asked:
How long does it take for the ball to reach the ground?
i.e. we have to find the value of t such that height is zero i.e. h(t)=0.
or
i.e. we need to find the roots of the above quadratic equation.
on solving the equation we get two roots as:
t≈ -3.02377 and t≈11.0238
As time can't be negative; hence we will consider the value of t as t≈11.0238.
Hence it takes 11.02 seconds for the ball to reach the ground.
Hence option B is correct (11.02 seconds).
So I'm going to assume that this question is asking for <u>non extraneous solutions</u>, or solutions that are found in the equation <em>and</em> are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:
Next, square both sides:
Next, subtract x and add 2 to both sides of the equation:
Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:
Next, factor x^2 - 2x and -3x + 6 separately. Make sure that they have the same quantity on the inside of the parentheses:
Now you can rewrite the equation as
Now, apply the Zero Product Property and solve for x as such:
Now, it may appear that the answer is C, however we need to plug the numbers back into the original equation to see if they are true as such:
Since both solutions hold true when x = 2 and x = 3, <u>your answer is C. x = 2 or x = 3.</u>
