I switched the x and y so it’s easier to see. The answer is (x-1)/(23).
Answer:
It depends what the problem requests
Step-by-step explanation:
0/1 , 1/1
Multiply there denominators with any number...
0/1×60=0/60
1/1××60=60/60
Now,
You have many choices...
1/60,10/60,30/60,2/60,5/60........so on....
Answer: 0.9649
Step-by-step explanation:
Let A denote the event that the days are cloudy and B denotes the event that the days are rainy.
Given : For the month of March in a certain city, the probability that days are cloudy :![P(A)=0.57](https://tex.z-dn.net/?f=P%28A%29%3D0.57)
Also in the month of March in the same city,, the probability that the days are cloudy and rainy :![P(A\cap B)=0.55](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D0.55)
Now by using the conditional probability, the probability that a randomly selected day in March will be rainy if it is cloudy will be :-
![P(B|A)=\dfrac{P(A\cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%3D%5Cdfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28A%29%7D)
![\Rightarrow\ P(B|A)=\dfrac{0.55}{0.57}\\\\=0.964912280702\approx0.9649\ \ \text{[Rounded to four decimal places.]}](https://tex.z-dn.net/?f=%5CRightarrow%5C%20P%28B%7CA%29%3D%5Cdfrac%7B0.55%7D%7B0.57%7D%5C%5C%5C%5C%3D0.964912280702%5Capprox0.9649%5C%20%5C%20%5Ctext%7B%5BRounded%20to%20four%20decimal%20places.%5D%7D)
Hence, the probability that a randomly selected day in March will be rainy if it is cloudy = 0.9649
Answer:
The area is growing at a rate of ![\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D226.2%20%5C%2C%5Cfrac%7Bcm%5E2%7D%7Bmin%7D)
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3
and we identify such as the following differential rate:
![\frac{dr}{dt} = 3\,\frac{cm}{min}](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%203%5C%2C%5Cfrac%7Bcm%7D%7Bmin%7D)
Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find
.
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):
![A=\pi\,r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%5C%2Cr%5E2)
We now apply the derivative operator with respect to time (
) to this equation, and use chain rule as we find the quadratic form of the radius:
![\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5BA%3D%5Cpi%5C%2Cr%5E2%5D%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2Ar%2A%5Cfrac%7Bdr%7D%7Bdt%7D)
Now we replace the known values of the rate at which the radius is growing (
), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :
![\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}\\\frac{dA}{dt} =\pi\,*2*(12\,cm)*(3\,\frac{cm}{min}) \\\frac{dA}{dt} =226.19467 \,\frac{cm^2}{min}\\](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2Ar%2A%5Cfrac%7Bdr%7D%7Bdt%7D%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2A%2812%5C%2Ccm%29%2A%283%5C%2C%5Cfrac%7Bcm%7D%7Bmin%7D%29%20%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D226.19467%20%5C%2C%5Cfrac%7Bcm%5E2%7D%7Bmin%7D%5C%5C)
which we can round to one decimal place as:
![\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D226.2%20%5C%2C%5Cfrac%7Bcm%5E2%7D%7Bmin%7D)