A baseball player hits a ball toward the outfield. The height h of the ball in feet is modeled by h(t) = -16t2 + 22t + 3, where t is the time in seconds. If no one catches the ball, how long will it stay in the air? (Round to the nearest tenth of a second and enter only the number.)HINTS:
• When the ball hits the ground, its height is zero, so you are looking for one of the zeros of the quadratic equation.
• Though you could use several different methods, the easiest way to solve this particular equation is the quadratic formula (provided here). Take the a, b, and c values from the function in the question above.
• When you solve the quadratic for the zeros, you will have two answers. One of the answers will not make sense for a baseball hit into the outfield. The one that does make sense will be the correct answer.

Answers

Answer 1

Answer: Solving this equation for the roots, we find that the roots are -1/8 and 3/2. Assuming that at t=0 is when the player hits the ball, t=0 and t=3/2 is the amount of time in the air. Therefore, the ball spent 3/2 seconds in the air, or 1.5 seconds.

Answer 2

Answer:

Final answer:

The time that the baseball stays in the air is determined by setting h(t), the height, to 0 and solving for t (time) using the quadratic formula; the positive answer represents the time in seconds that the ball stays in the air.

Explanation:

In order to find how long the baseball will stay in the air, we need to solve for the value of t (time) when the height h(t) is equal to 0. This is given by the formula h(t) = -16t2 + 22t + 3. We equate this to zero and solve for t using the quadratic formula: t = [-b ± sqrt(b2 - 4ac)] / (2a).

Here, a = -16, b = 22, and c = 3. Substituting these values into the formula gives two solutions for t. However, we reject the negative solution since time cannot be negative. Therefore, the positive solution gives the amount of time (rounded to the nearest tenth of a second) the baseball stays in the air before it hits the ground.

Learn more about Quadratic Formula here:

brainly.com/question/32591097

#SPJ11

Related Questions

Solve the problem by using the counting principle. (: Drapery is sold in 4 different fabrics. Each fabric comes in 13 different patterns. Each pattern is offered in 9 different colors. How many fabric-pattern-color combinations are there?
Bill makes leather shoes. He charges $45 for a pair of women's shoes and $50 for a pair of men's shoes. He sells x pairs of women’s shoes and y pairs of men’s shoes each week and earns a total income of $2,500. This situation can be represented by the equation . If Bill has no female customers during a particular week, he needs to sell pairs of men’s shoes to earn his weekly income of $2,500.
HELP PLEASE!! What are the domain and range of each relation? Drag the answer into the box to match each relation
9 gal/s=______at/min
Solve the equation. q – 29 = –57 (1 point) –28 28 86 –86

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent? Answers:
3 dramas, 5 comedies, and 3 documentaries
2 dramas, 6 comedies, and 3 documentaries
1 dramas, 4 comedies, and 6 documentaries
4 dramas, 3 comedies, and 4 documentaries

Answers

Answer:

Gina rent 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

Let Gina rented x movies of dramas , y movies of comedies and z movies of documentaries then , Gina rented total 11 movies.

$\Rightarrow x+y+z=11$ .........(1)

Also given Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries Gina, thus he rented 2x movies of dramas , 3y movies of comedies and 2z movies of documentaries. also, he rented a total of 27 movies.

$\Rightarrow 2x+3y+2z=27$ ............(2)

Also, Robby rented the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, thus, he rented x movies of dramas , 2y movies of comedies and 2z movies of documentaries also, he rented a total of 19 movies.

$\Rightarrow x+2y+2z=19$ ............(3)

Solving the three equation using matrix form,

$\left[\begin{array}{ccc}1&1&1\n2&3&2\n1&2&2\end{array}\right] \left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c}11\n27\n19\end{array}\right]$

This, system is in form of AX= b,

Where, $A=\left[\begin{array}{ccc}1&1&1\n2&3&2\n1&2&2\end{array}\right]$ , $X=\left[\begin{array}{c}x\ny\nz\end{array}\right]$ , $b=\left[\begin{array}{c}11\n27\n19\end{array}\right]$

Pre-mutiply by A inverse both sides,

$X=A^(-1)b$ ............(P)

First finding inverse,

$\mathrm{Augment\:with\:a}\:3x3\:\mathrm{identity\:matrix}$

$=\begin{bmatrix}1&1&1&\mid \:&1&0&0\n 2&3&2&\mid \:&0&1&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}$

$\mathrm{Swap\:matrix\:rows:}\:R_1\:\leftrightarrow \:R_2$

$=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 1&1&1&\mid \:&1&0&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}$

$\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_2\:\mathrm{\:by\:performing}\:R_2\:\leftarrow \:R_2-(1)/(2)\cdot \:R_1$

$=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}$

$\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_3\:\mathrm{\:by\:performing}\:R_3\:\leftarrow \:R_3-(1)/(2)\cdot \:R_1$

$=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&(1)/(2)&1&\mid \:&0&-(1)/(2)&1\end{bmatrix}$

$\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_3\:\mathrm{\:by\:performing}\:R_3\:\leftarrow \:R_3+1\cdot \:R_2$

$=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}$

$\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_1\:\mathrm{\:by\:performing}\:R_1\:\leftarrow \:R_1-2\cdot \:R_3$

$=\begin{bmatrix}2&3&0&\mid \:&-2&3&-2\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}$

$\mathrm{Multiply\:matrix\:row\:by\:constant:}\:R_2\:\leftarrow \:-2\cdot \:R_2$

$=\begin{bmatrix}2&3&0&\mid \:&-2&3&-2\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}$

$\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_1\:\mathrm{\:by\:performing}\:R_1\:\leftarrow \:R_1-3\cdot \:R_2$

$=\begin{bmatrix}2&0&0&\mid \:&4&0&-2\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}$

$\mathrm{Multiply\:matrix\:row\:by\:constant:}\:R_1\:\leftarrow (1)/(2)\cdot \:R_1$

$=\begin{bmatrix}1&0&0&\mid \:&2&0&-1\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}$

Thus, $A^(-1)=\begin{pmatrix}2&0&-1\n -2&1&0\n 1&-1&1\end{pmatrix}$

Put values in equation (P),

$X=A^(-1)b$

$\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c,c,c}2&0&-1\n -2&1&0\n 1&-1&1\end{array}\right]\left[\begin{array}{c}11\n27\n19\end{array}\right]$

$\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c,c,c}2\cdot \:11+0\cdot \:27+\left(-1\right)\cdot \:19\n \left(-2\right)\cdot \:11+1\cdot \:27+0\cdot \:19\n 1\cdot \:11+\left(-1\right)\cdot \:27+1\cdot \:19\end{array}\right]$

$\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c}3\n5\n3\end{array}\right]$

Thus, Gina rent 3 dramas, 5 comedies, and 3 documentaries.

3 dramas, 5 comedies, and 3 documentaries

What is (f+g) (x)???

Answers

Answer:

Step-by-step explanation:

To get to the answer, add both f(x) and g(x) together. This would be (2x^2 +3x -4) + (-4x^2 + 5x - 8). Remember that adding a negative number is the same as subtracting the positive of that number, for example, 3 + (-4) is the same as 3 - 4.

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 8, four divided by three, two divided by nine, ...

Answers

The sequence is decreasing so it is r<1, therefore it is converging

This is the formula for how to find the sum/limit of the convergence (or how to find a infinite geometric sequence): a1/(1-r)

a1=48

r=8/48=.167

Verifying r:

a1/r=48*.167=8.016=8

a1/r^2=48*.167^2=1.338672=1.34

4/3=1.33

(close enough)

Putting it into equation:

a1/(1-r)=48/(1-.167)=48/.833=57.62304922

Answer Choices:

A. Converges; 288/5

B. Converges; 0

C. Diverges

D. Converges; -12432

288/5=57.6

ANSWER IS A. Converges; 288/5

48, 8 , 4/3,2/9

note that each term after the first one is calculated by multiplying the previous on by 1/6. The sequence converges

Limit = a1 / (1 -r) = 48 / ( 1- 1/6) = 57.6 or 57 3/5

Anthony, who is 2 meters tall, is standing on top of a skyscraper that is 1 km tall. How many meters is it from the top of Anthony's head to the bottom of the skyscraper?

Answers

1002 meters. 1km= 1000 meters then add 2 meters. Hope this helped.

Please solve this 3 variable system of equations2g + 3h - 8j= 10
g - 4h =1
-2g - 3h+ 8j= 5

Answers

Not solvable. If you take the first and last equations together, then multiply the last by -1 you get
2g+3h-8j=10
2g+3h-8j=-5
Resulting in
10=-5, which is false, so there is no solution

Please help asap its due in one minuteLarry’s Landscaping charges $235 for spring cleanups and $30 for weekly lawn maintenance. Joe’s Landscaping charges $185 for spring cleanups and $35 for weekly lawn maintenance. The system that models this situation is given, where c is the cost of lawn maintenance and w is the number of weeks.
c = 235 + 30w
c = 185 + 35w
The solution to the system is (10, 535).
Which interpretation correctly describes the solution to the system of equations?
a. Larry’s Landscaping will charge more money on the tenth week by charging $535.
b. Joe’s Landscaping will charge more money on the tenth week by charging $535.
c. The cost for lawn maintenance is the same, $535, for both landscaping companies after 10 wk.
d. A customer can have his or her lawn maintained for a maximum of 10 wk. The customer will pay a total of $535.

Answers

The first thing you would do is substitute the 10 in for 'w' and 535 in for 'c'.
535 = 235 + 30(10)
535 = 185 + 35(10)
Then, you would just solve the equations.
535 = 235 + 30(10)
30(10) = 300
300 + 235 = 535
So the first equation is true, and we know for a fact that Larry's Landscaping charges $535 for a spring cleaning and weekly yard maintenance for 10 weeks.
On to the next equation.
535 = 185 + 35(10)
35(10) = 350
185 + 350 = 535
So, the second equation is true also. And we also know for a fact that Joe's Landscaping charges $535 for a spring cleaning and weekly yard maintenance for 10 weeks.
So, now that we know that they will end up charging the same amount of money for a spring cleaning and weekly yard maintenance, the only answer that fits that is C. The cost for lawn maintenance is the same, $535, for both landscaping companies after 10 weeks.
Hope this helps!

535 for both in ten weeks sorry if I am lake took a while to think.

Other Questions

2 1/3 divided by 3/4

Given the parent functions f(x) = log10 x and g(x) = 3x − 1, what is f(x) • g(x)?

Length and breadth of a rectangular field is 5 : 3. If the breadth of rectangle is 60m, find the length of the rectangle.

Find the difference. Do not round. 12.39 - 1.504 =