In the past, professional baseball was played at the Astrodome in Houston, Texas. The Astrodome has a maximum height of 63.4 m. The height in meters of a baseball t seconds after it is hit straight up in the air with a velocity of 45 m/s is given by h= -9.8^2 + 45t + 1. Will a baseball hit straight up with this velocity hit the roof of the Astrodome? Find the value and use it to determine the answer. Discriminant: Will the baseball hit the roof? Why?:

Please show all work and not just the answers.

The correct value of the h function is; h= -9.8t² + 45t + 1

Using the discriminant, no real solution exists and the baseball will not hit the roof

.Step-by-step explanation:

h= -9.8t² + 45t + 1

Astrodome has a maximum height of 63.4 m

find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.

Thus;

63.4 = -9.8t² + 45t + 1

Subtract 63.4 from both sides to give;

-9.8t² + 45t + 1 - 63.4 = 0

-9.8t² + 45t - 62.4 = 0

Using quadratic formula, we have;

t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}

t = -45 ± √(2025 - 2446.08)

t = -45 ± √(-421.08)

The discriminant is -421.08

This value is less than 0.

Thus, no real solution exists and the baseball will not hit the roof.

1. 34

2. 268

3. x=14.4

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.