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koban [17]
3 years ago
12

3. A soccer player heads a ball from a height of 6 feet with an initial vertical velocity of 20 feet per second. The height h in

feet of the ball is given by h= –16t + 20t +6,
where t is the time elapsed in seconds. How long will it take the ball to hit the
ground if no other players touch it? State the method you used to solve this
quadratic equation and why you chose that method.
Mathematics
1 answer:
kherson [118]3 years ago
6 0

Answer:

Part A

1.5 seconds

Part B

By substitution and factorization because h = 0 at ground level

Step-by-step explanation:

Part A

The height from which the soccer player heads the ball, h = 6 feet

The initial velocity of the ball, v = 20 ft./s

The height of the ball in feet, h = -16·t² + 20·t + 6

From the given equation of the ball, we have;

At the initial height, t = 0, from the given equation, h = 6

At the  ground level,  the height, h = 0, therefore, we get;

0 = -16·t² + 20·t + 6

Factorizing using a graphing calculator gives;

0 = 2 × (-8·t² + 10·t + 3) = -2 × (8·t² - 10·t - 3) = -2 × (2·t -3)·(4·t + 1)

∴ (2·t -3)·(4·t + 1) = 0

t = 1.5 or t = -1/4 = -0.25

Therefore;

The time it takes the ball to hit the ground, t = 1.5 seconds.

Part B

The method used in solving the given quadratic equation is by plugging in the value of 'h' as h = 0 in the given equation and factorizing the result because at ground level, the height, h = 0.

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Step-by-step explanation:

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Principal = 5300=5300 rupees
PSYCHO15rus [73]

Answer:

Using the formula:

A=P+I

where

A is the total amount

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Principal(P) = 5300 rupees.

rate of interest(r) = 6.5% = 0.065

Total amount(A) = 6678 rupees.

Then using above formula we have;

6678 = 5300+I

Subtract 5300 both sides we get;

1378 = I

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I = \$1378

We have to find the time period.

Using formula of Simple interest:

I = Prt

where r is the rate of interest (in decimal)

here, r = 6.5% = 0.065

Substitute the given values top find t:

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If S is countable and nonempty, prove their exist a surjection g: N --> S
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Answer with Step-by-step explanation:

We are given S be any set which is countable and nonempty.

We have to prove that their exist a surjection g:N\rightarrow S

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Cardinality of natural numbers set =\chi_0( Aleph naught)

There are two cases

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2.S is countably infinite set

1.When S is finite set and nonempty set

Then cardinality of set S is any constant number which is less than the cardinality of set of natura number

Therefore, their exist a surjection from N to S.

2.When S is countably infinite set and cardinality with aleph naught

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Hence, proved

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