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olga_2 [115]
3 years ago
13

Due to gravity, an object falls 16t^2 feet in t seconds. You drop a backpack from a window that is 20 feet above the ground. Wil

l the backpack hit the ground in 1 second?
Mathematics
1 answer:
sukhopar [10]3 years ago
3 0

Answer:

NO

Step-by-step explanation:

Let h(t) represent the distance the pack is located above the ground at time t.  Then h(t) = 20 ft - 16t^2 ft.  Notice how h = 20 ft (the initial height) and that it decreases as t increases.

How long does it take for the pack tohit the ground?  Set h(t) = 0 and solve for t:

0 ft = 20 ft - 16t^2 ft yields 16t^2 ft = 20, or t^2 ft = 20/16, which is greater than 1.  So the question "Will the backpack hit the ground in 1 second" is answered by NO.

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Circumference = π * d

π=3.14
diameter = 6

3.14 * 6 = 18.84.
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7 0
3 years ago
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Which of the following expressions can be factored by grouping? (Select all that apply.)
Greeley [361]

Answer:

Options (3), (4) and (5)

Step-by-step explanation:

1). a² - 9a + 7ab + 63b

  = a(a - 9) + 7b(a + 9)

  Now we can not solve this problem further.

  Therefore, can't be factored by grouping.

2). 3a + 4ab - b - 12

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   We can't solve it further.

   Therefore, can't be factored by grouping.

3). ab + 6b - 2a - 12

   = b(a + 6) - 2(a + 6)

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  We can be factored this expression by grouping.

4). x³ + 9x²+ 7x + 63

   = x²(x + 9) + 7(x + 9)

   = (x² + 7)(x + 9)

   Therefore, the given expression can be factored by grouping.

5). ay² + a - y² - 1

  = a(y² + 1) - 1(y² + 1)

  = (a - 1)(y² + 1)

  This expression can be factored by the grouping method.

Options (3), (4) and (5) are the correct answers.

3 0
3 years ago
Easy question and it's a warm up question. Noah has to do 8 homework and he did 7 homework. How many homework left does noah hav
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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2 years ago
The PSTAT Department at UCSB has developed a Markov model to simulate graduation rates in their programs. Students might drop ou
goldfiish [28.3K]

Answer:

State space

S=\{F,So,J,Sr,G,D\}

Transition probability matrix

\begin{bmatrix} & F & So&J&Sr&G&D\,\\ F &0.03&0.91&0&0&0&0.06\,\\So&0&0.03&0.91&0&0&0.06\\J&0&0&0.03&0.93&0&0.04\\ Sr&0&0&0&0.03&0.93&0.04\\G&0&0&0&0&1&0\\D&0&0&0&0&0&1\end{bmatrix}

The transition graph is attached.

Step-by-step explanation:

The state space for this Markov chain is all the possible states that the variable can take.

In this case the student can be: Freshman, Sophomore, Junior, Senior, Graduate and Drop out

S=\{F,So,J,Sr,G,D\}

The transition probability matrix for this state space is:

\begin{bmatrix} & F & So&J&Sr&G&D\,\\ F &0.03&0.91&0&0&0&0.06\,\\So&0&0.03&0.91&0&0&0.06\\J&0&0&0.03&0.93&0&0.04\\ Sr&0&0&0&0.03&0.93&0.04\\G&0&0&0&0&1&0\\D&0&0&0&0&0&1\end{bmatrix}

The transition graph is attached.

7 0
3 years ago
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