Answer:
The required co-ordinate is (-2, -5).
Step-by-step explanation:
For a given point, reflection of a point (x, y) across a horizontal line y = k, the reflected co-ordinates will be:
.
Here, (x, y) = (-2, 7) then reflection along the line y = 1, we get:
![$ R_{y = 1} (-2, 7) = (-2, 2(1) - 7) $](https://tex.z-dn.net/?f=%24%20R_%7By%20%3D%201%7D%20%28-2%2C%207%29%20%3D%20%28-2%2C%202%281%29%20-%207%29%20%24)
= (-2, -5)
The reflected point is (-2, -5).
Thank you for posting your question here at brianly. I hope the answer will help you. Below is the solution:
or segment from (4,0) to (-4,0), y is always zero because straight segment.
<span>in that case x*y=x*0=0 </span>
<span>and x+y=x+0=x </span>
<span>if you choose x=4-t where t goes from 0 to 8 you should get </span>
<span>r(t)=0i+(4-t)j </span>
Answer:
He pays to the cab driver for 25 miles.
Step-by-step explanation:
Consider the provided information.
Let us consider he walks x miles at the rate of 4 miles per hour.
As we know ![Time=\frac{Distance}{Speed}](https://tex.z-dn.net/?f=Time%3D%5Cfrac%7BDistance%7D%7BSpeed%7D)
Therefore, time taken is: ![Time=\frac{x}{4}](https://tex.z-dn.net/?f=Time%3D%5Cfrac%7Bx%7D%7B4%7D)
He get a taxi for (31-x) miles at the rate of 50 miles per hour.
Therefore, time taken is: ![Time=\frac{31-x}{50}](https://tex.z-dn.net/?f=Time%3D%5Cfrac%7B31-x%7D%7B50%7D)
It took 2 hours after he started.
That means the sum of time take is 2 hours.
![\frac{x}{4}+\frac{31-x}{50}=2](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D%2B%5Cfrac%7B31-x%7D%7B50%7D%3D2)
![\frac{25x+62-2x}{100}= 2](https://tex.z-dn.net/?f=%5Cfrac%7B25x%2B62-2x%7D%7B100%7D%3D%202)
![23x+62= 200](https://tex.z-dn.net/?f=23x%2B62%3D%20200)
![23x= 138](https://tex.z-dn.net/?f=23x%3D%20138)
![x= 6](https://tex.z-dn.net/?f=x%3D%206)
Hence he walk 6 miles and he get a taxi for 31-6=25 miles.
He pays to the cab driver for 25 miles.
Answer:
Proof in explanation.
Step-by-step explanation:
I'm going to attempt this by squeeze theorem.
We know that
is a variable number between -1 and 1 (inclusive).
This means that
.
for all value
. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.
![-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4](https://tex.z-dn.net/?f=-x%5E4%20%5Cle%20x%5E4%20%5Ccos%28%5Cfrac%7B2%7D%7Bx%7D%29%20%5Cle%20x%5E4)
By squeeze theorem, if ![-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4](https://tex.z-dn.net/?f=-x%5E4%20%5Cle%20x%5E4%20%5Ccos%28%5Cfrac%7B2%7D%7Bx%7D%29%20%5Cle%20x%5E4)
and
, then we can also conclude that
.
So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at
.
![\lim_{x \rightarrow 0}x^4=0^4=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%200%7Dx%5E4%3D0%5E4%3D0)
.
We can finally conclude that
by squeeze theorem.
Some people call this sandwich theorem.