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Scrat [10]
3 years ago
6

A ball is thrown vertically upward from the top of a building 160 feet tall with an initial velocity of 48 feet per second. The

distance d (in feet) of the ball from the ground after t seconds is d(t) = 160 + 48t - 16t^2.
After how many seconds does the ball strike the ground? Please explain if you can!
When will the ball reach its maximum height? What is the maximum height of the ball? Please explain if you can!
Mathematics
1 answer:
alina1380 [7]3 years ago
8 0

Answer:

# after 5 seconds, the ball strikes the ground

# The ball reaches maximum height at t = 1.5 seconds

# The max height is 196 feet

Step-by-step explanation:

The equation is:

d(t)=-16t^2+48t+160

t is the time

d(t) is the distance traveled

Initial height is 160 feet and initial velocity is 48 ft/sec

If we want to find the time it takes the ball to hit the ground, we let d(t) equal to 0 and find t. Shown below:

-16t^2+48t+160=0\\t^2-3t-10=0\\(t-5)(t+2)=0\\t=5,-2

We disregard t = -2 since time can't be negative. We take t = 5

Thus, after 5 seconds, the ball strikes the ground.

The equation is a quadratic of the form: ax^2+bx+c

Matching equations, we can say:

a = -16

b = 48

c = 160

The time when ball reaches max height is given as:

t=-\frac{b}{2a}

Substituting, we find:

t=-\frac{b}{2a}\\t=-\frac{48}{2(-16)}\\t=1.5

The ball reaches maximum height at t = 1.5 seconds

The max height can be found by putting t = 1.5 into the original equation. Shown below:

d(t)=-16t^2+48t+160\\d(1.5)=-16(1.5)^2+48(1.5)+160\\=196

The max height is 196 feet

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kirza4 [7]

QUESTION 1

When the plane reaches an altitude of 360,000 feet, the temperature outside the plane is 65 degrees below zero Fahrenheit.

This means that the temperature will be:

0-65=-65

The temperature is -65°F.

QUESTION 2

If the temperature gets warmer by 10 degrees, this means that the new temperature will be the sum of the original temperature and 10 degrees:

\Rightarrow-65+10=-55

The temperature is -55°F.

5 0
1 year ago
If 2a+ 2/a =4, what is the value of 2a^2− 2/a^2 ?
aliina [53]

Answer:

0

Step-by-step explanation:

2a+ 2/a =4

Multiply each side by a to clear the fraction

a( 2a+ 2/a) =4*a

Distribute

2a^2 +2 = 4a

Subtract 4a from each side

2a^2 -4a +2 = 4a-4a

2a^2 -4a +2 =0

Divide by 2

2/2 a^2 -4a/2 +2/2 =0/2

a^2 -2a +1=0

Factor

(a-1) (a-1) =0

Using the zero product property

a=1

2a^2 -2/a^2

2(1)^2 -2/1^2

2-2

0

5 0
3 years ago
In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand contain
aalyn [17]

Answer:

0.00597

Step-by-step explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}

=\frac{^{20}C_5}{^{52}C_5}

=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}

=\frac{15504}{2598960}

= 0.00597  

7 0
3 years ago
what are two practical products you could add to find 990 x 37 ; 297 693 2970 6930 69300 6330 29700
VMariaS [17]
First evaluate 990 x 37.
990 x 37 = 36630

Test the given numbers to find the pair that adds up to 36630.
Test 297.
The missing pair will be
36630 - 297 = 36333
Will not work

Test 693.
36630 - 693 = 35937
Will not work

Test 2970.
36630 - 2970 = 33660
Will not work

Test 6930
36630 - 6930 = 29700
This works, because 6930 + 29700 = 36630.

Answer: 6930 and 29700.


8 0
3 years ago
Hong buys a bag of 11 tangerines for $2.86.
Ghella [55]

Answer:

$0.26

Step-by-step explanation:

To find the unit price, divide the cost by the amount you have.

$2.86/11 = $0.26

The unit price is $0.26.

7 0
3 years ago
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