Answer:
![\frac{dy}{dx}=8.5](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D8.5)
Step-by-step explanation:
Let
denotes number of windows and
denotes the number of yards of fabric needed.
Stephen is making curtains for several windows in his aunt's house. He determines that he needs 8.5 yards of fabric for each window.
a. Equation becomes ![y=8.5x](https://tex.z-dn.net/?f=y%3D8.5x)
This answer is already given in question.
b. To find rate of change in this situation, find ![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D)
![y=8.5x](https://tex.z-dn.net/?f=y%3D8.5x)
Differentiate with respect to ![x](https://tex.z-dn.net/?f=x)
![\frac{dy}{dx}=8.5(1)=8.5](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D8.5%281%29%3D8.5)
The POI is (3,-2). The two equations are simply straight lines
<u>Answer:</u>
Two events, A and B, are independent. If P(A) = 0.3 and P(B) = 0.2.The value of P(A and B) is 0.06
<u>Solution:</u>
Given that P(A) and P(B) are two independent events which means the occurrence of one event does not affect the occurrence of another event.
Here we have to find out P(A and B)
When P(A) and P(B) are two independent events, then P(A and B) can be found out by,
P(A and B) = P(A)
P(B)
Given that P(A) = 0.3 and P(B) =0.2
P(A and B) = 0.3
0.2
P(A and B)= 0.06
Thus the value of P(A and B) is 0.06
Answer:
The average velocity is 19.44 m/s.
Step-by-step explanation:
The average velocity between two points can be calculated with the following formula:
![\bar v=\dfrac{\Delta X}{\Delta t}=\dfrac{(120-50)\, km}{(110-50)\, min}=\dfrac{70\,km}{60\,min}\\\\\\\bar v=1.667\dfrac{km}{min}*\dfrac{1\,min}{60\,s}*\dfrac{1000\,m}{1\,km}=19.44\dfrac{m}{s}](https://tex.z-dn.net/?f=%5Cbar%20v%3D%5Cdfrac%7B%5CDelta%20X%7D%7B%5CDelta%20t%7D%3D%5Cdfrac%7B%28120-50%29%5C%2C%20km%7D%7B%28110-50%29%5C%2C%20min%7D%3D%5Cdfrac%7B70%5C%2Ckm%7D%7B60%5C%2Cmin%7D%5C%5C%5C%5C%5C%5C%5Cbar%20v%3D1.667%5Cdfrac%7Bkm%7D%7Bmin%7D%2A%5Cdfrac%7B1%5C%2Cmin%7D%7B60%5C%2Cs%7D%2A%5Cdfrac%7B1000%5C%2Cm%7D%7B1%5C%2Ckm%7D%3D19.44%5Cdfrac%7Bm%7D%7Bs%7D)
The procedure is to calculate the difference for both distance and time, and dividing the two differences, we get the average velocity.