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spin [16.1K]
3 years ago
14

The height in feet of the projectile seconds after lunch is modeled by the equation h=32t - 16t2 how long after launch does the

projectile return to the ground
Mathematics
1 answer:
Gekata [30.6K]3 years ago
6 0
When h=0 is when it returns to the ground
solve

0=32t-16t^2
factor
0=16t(2-t)
set equal to zero

0=16t
0=t

0=2-t
t=2

at t=0 and 2
it returns after 2 seconds
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Answer the questions below about the quadratic function.f(x) = -2x² - 4x
Juli2301 [7.4K]

We are given the function below;

f(x)=-2x^2-4x

PART A

We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.

ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum

PART B and C

To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.

From the graph, the black point helps answer part A and part B.

ANSWER: The function's maximum value is f(x)=2.

This is the point where the slope of the graph is equal to zero

ANSWER: The maximum value then occurs at x= -1

We can also solve this by differentiating the function.

\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}

5 0
1 year ago
22% of all resumes received by a corporation for a management position are from females. 18 resumes will be received tomorrow.
Vladimir79 [104]

Answer:

5.80% probability that exactly 1 resume will be from females.

Step-by-step explanation:

For each resume received by the corporation, there are only two possible outcomes. Either they are from a female, or they are not. The probability of a resume received being from a female is independent from other resumes. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

22% of all resumes received by a corporation for a management position are from females.

This means that p = 0.22

18 resumes will be received tomorrow.

This means that n = 18

What is the probability that exactly 1 resume will be from females?

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{18,1}.(0.22)^{1}.(0.78)^{17} = 0.0580

5.80% probability that exactly 1 resume will be from females.

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3 years ago
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No; a range value has two domain values.
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