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Yuki888 [10]
3 years ago
6

Determine the number of ways a computer can randomly generate one or more such integers from 1 through 30. Two distinct integers

whose sum is 27.
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

Answer:

There are 26 possible way to determine two  distinct integers whose sum is 27.

Step-by-step explanation:

To find : The number of ways a computer can randomly generate one or more such integers from 1 through 30. Two distinct integers whose sum is 27.

Solution :

We have given the numbers from  1,2,3,4......,29,30.

In order to get two distinct numbers having the sum 27,

There are the possibilities :

1+26=27

2+25=27

3+24=27

......

24+3=27

25+2=27

26+1=27

The maximum number taken is 26.

So, There are 26 possible way to determine two  distinct integers whose sum is 27.

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dalvyx [7]

Answer:

B^\prime(6) \approx -28.17

Step-by-step explanation:

We have:

\displaystyle B(t)=24.6\sin(\frac{\pi t}{10})(8-t)

And we want to find B’(6).

So, we will need to find B(t) first. To do so, we will take the derivative of both sides with respect to x. Hence:

\displaystyle B^\prime(t)=\frac{d}{dt}[24.6\sin(\frac{\pi t}{10})(8-t)]

We can move the constant outside:

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Then:

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(The derivative of u was determined using the chain rule.)

Then it follows that:

\displaystyle \begin{aligned} B^\prime(t)&=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)] \\ \\ &=24.6[(\frac{\pi}{10}\cos(\frac{\pi t}{10}))(8-t) - \sin(\frac{\pi t}{10})] \end{aligned}

Therefore:

\displaystyle B^\prime(6) =24.6[(\frac{\pi}{10}\cos(\frac{\pi (6)}{10}))(8-(6))- \sin(\frac{\pi (6)}{10})]

By simplification:

\displaystyle B^\prime(6)=24.6 [\frac{\pi}{10}\cos(\frac{3\pi}{5})(2)-\sin(\frac{3\pi}{5})] \approx -28.17

So, the slope of the tangent line to the point (6, B(6)) is -28.17.

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