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vladimir2022 [97]
3 years ago
14

Find the shaded region of the figure below​

Mathematics
1 answer:
lilavasa [31]3 years ago
4 0

Answer:

-x³ + 3x² - 14x + 12

Step-by-step explanation:

Area of outer rectangle = (x² + 3x - 4) * (2x - 3)

      = (x² + 3x - 4) * 2x  + (x² + 3x - 4) * (-3)

     =x²*2x + 3x *2x - 4*2x  + x² *(-3) + 3x *(-3)  - 4*(-3)

     =2x³ + 6x² - 8x - 3x² - 9x + 12

    = 2x³ + <u>6x² - 3x²</u>   <u>- 8x - 9x</u> + 12     {Combine like terms}

    = 2x³ + 3x² - 17x + 12

Area of inner rectangle = (x² - 1)* 3x

                                       = x² *3x - 1*3x

                                       = 3x³ - 3x

Area of shaded region = area of outer rectangle - area of inner rectangle

         = 2x³ + 3x² - 17x + 12 - (3x³ - 3x)

         = 2x³ + 3x² - 17x + 12 -3x³ + 3x

        = 2x³ - 3x³ + 3x² - 17x + 3x + 12

        = -x³ + 3x² - 14x + 12

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The scheduled arrival time for a daily flight from Boston to New York is 9:35 am. Historical data show that the arrival time fol
Lady_Fox [76]

Answer:

The mean is 11.5 minutes and the standard deviation is of 6.64 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean is:

M = \frac{a+b}{2}

The standard deviation is:

S = \sqrt{\frac{(b-a)^{2}}{12}}

Arrival time of 9:18 am and a late arrival time of 9:41 am.

9:41 is 23 minutes from 9:18. So the time is uniformily distributed between 0 and 23 minutes, so a = 0, b = 23.

Mean:

M = \frac{a+b}{2} = \frac{0+23}{2} = 11.5

Standard deviation:

S = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(23 - 0)^{2}}{12}} = 6.64

The mean is 11.5 minutes and the standard deviation is of 6.64 minutes

8 0
3 years ago
2,10,18,26 find the 61st term
saw5 [17]

Answer:

482

Step-by-step explanation:

We can see that the numbers shown resemble an arithmetic sequence because they have a common difference. The formula for the nth term of an arithmetic sequence is:

a_{n} =a_{1} +(n-1)d

Where a_{1} is the first term, a_{n} is the nth term, and d is the common difference. To find the 61st term, all we need is the first term and the common difference. By looking at what given, we can say the first term is 2. Now, to find the common difference, we find the difference of a term from the term before it. In this case we can do 10-2, which is 8 , or the common difference. Since we have everything we need, it can be plugged into the equation:

a_{61} =2 + (61 - 1)*8\\a_{61} = 2 + 60*8\\a_{61} = 2 + 480\\a_{61} = 482

So, the 61st term is 482.

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Answer:

800 m

Step-by-step explanation:

6 0
3 years ago
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5 0
3 years ago
What is the base for the expression -6 to the power of 4
natima [27]

For this case we have that by definition it is fulfilled:

a ^ b

Where:

a: It is the base

b: It is the exponent

So, if we have the following expression:

-6 to the power of 4, is equivalent to: (-6) ^ 4

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-6: It is the base

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8 0
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