The expression 35 - m is used to determine the number of gallons left in the tank after m minutes.
<u>Solution:</u>
Given that a tank containing 35 gallons of water is leaking at a rate of gallon per minute.
Let "m" represent the number of minutes spent
Number of gallons left in the tank = initial amount of water present – leaked amount of water
Number of gallons of water left = 35 gallons – number of minutes spent
rate of leakage.
Number of gallons of water left = 35 gallons – m minutes
1 gallons per minute
![= 35 - m \times 1 = 35 - m](https://tex.z-dn.net/?f=%3D%2035%20-%20m%20%5Ctimes%201%20%3D%2035%20-%20m)
Hence, the required expression is 35 – m
I'll assume you're supposed to compute the line integral of
over the given path
. By the fundamental theorem of calculus,
![\displaystyle\int_C\nabla f(x,y)\cdot\mathrm d\vec r=f(4,48)-f(1,3)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cnabla%20f%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cvec%20r%3Df%284%2C48%29-f%281%2C3%29)
so evaluating the integral is as simple as evaluting
at the endpoints of
. But first we need to determine
given its gradient.
We have
![\dfrac{\partial f}{\partial x}=3y\sin(xy)\implies f(x,y)=-3\cos(xy)+g(y)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D3y%5Csin%28xy%29%5Cimplies%20f%28x%2Cy%29%3D-3%5Ccos%28xy%29%2Bg%28y%29)
Differentiating with respect to
gives
![\dfrac{\partial f}{\partial y}=3x\sin(xy)=3x\sin(xy)+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D3x%5Csin%28xy%29%3D3x%5Csin%28xy%29%2B%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%5Cimplies%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%3D0%5Cimplies%20g%28y%29%3DC)
and we end up with
![f(x,y)=-3\cos(xy)+C](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D-3%5Ccos%28xy%29%2BC)
for some constant
. Then the value of the line integral is
.
Answer:
No. If you multiply 138 x 7 you will get 966. Which isn't a very close estimate at all.
Answer:
1 x 31 OR 15.5 x 2
Step-by-step explanation:
As 31 is a prime number, the only whole numbers that do it are 1 × 31. There is another method using decimals. Ex: 15.5 x 2=31
The probability is 0.0334.
We will first find the probability that none of the 30 people sampled are infected. Since the probability of one person being infected is 0.00114, the probability that someone is not infected is 1-0.00114 = 0.99886. The probability that none of the 30 people are infected would be (0.99886)^30 = 0.966359. We subtract this from one to find the probability that at least one person is infected:
1 - 0.966359 = 0.0334.