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2 years ago

Consider the Inequalities X >7 and X < 12 select all the values that satisfy both Inequalities

Mathematics

1 answer:

Maksim231197 [3]2 years ago

7 0

Answer:

9;10

Step-by-step explanation:

What we can first do is make them into one double sided inequality and then interpret it from there.

After combining them we get: 7<x<12

This means that any number between 7 and 12 can be picked.

Keep in mind, this means that 7 and 12 cannot be picked, they have to be in between.

Therefore, we get our aswers of 9 and 10!

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Problem is in the attached image. Thanks in advance!

lutik1710 [3]

Answer: it will take 2.5 hours for both people to meet after person B leaves.

Step-by-step explanation:

The distance between the house of person A and his cousin's house is 234 miles.

At the point where they meet, they would have travelled 234 miles.

Person A travelled at an average speed of 44 miles per hour.

Let t represent the time spent by Person A in travelling from his house to the point where they meet.

Distance = speed × time

Distance covered by person A would be

44 × t = 44t

One and half hours later, person B leaves his house to visit person A, travelling at an average speed of 62 miles per hour. This means that total time spent by person B in travelling to the point where they meet is (t - 0.5) hours. Distance covered would be

62(t - 0.5) = 62t - 31

Since the total distance covered is 234 miles, then

44t + 62t - 31 = 234

106t = 234 + 31 = 265

t = 265/106 = 2.5 hours

3 0

3 years ago

Find derivative problem Find B’(6)

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:

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

Now, we will utilize the product rule. The product rule is:

$(uv)^\prime=u^\prime v+u v^\prime$

We will let:

$\displaystyle u=\sin(\frac{\pi t}{10})\text{ and } \\ \\ v=8-t$

Then:

$\displaystyle u^\prime=\frac{\pi}{10}\cos(\frac{\pi t}{10})\text{ and } \\ \\ v^\prime= -1$

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

Then it follows that:

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