The distance between points a and b with the given coordinates is: 30/8 units.
<h3>How to Find the Distance Between Two Points?</h3>
The distance between two points with each given value of their coordinates is determined by subtracting the values of these coordinates, then finding the absolute value of the difference. That is, if the result after subtraction is negative, the negative sign is ignored.
The distance between two points is the absolute value of the difference of their points, which is the number of units that lies between the two points.
Given the following:
a = 1/8
b = 31/8
The distance between points a and b = |1/8 - 31/8|
ab = |(1 - 31)/8|
ab = |(-30)/8|
ab = 30/8 units
Thus, the distance between points a and b with the given coordinates is: 30/8 units.
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Answer:
(2*2*1.5*1/3)+(2*1.5*4)= 14
Step-by-step explanation:
To find the area of a pyramid, you use the equation of 1/3 *lwh. When we place the values in there, we get 2*2*1.5*1/3, which is equal to 2. Then we solve the bottom part. Since it is a rectangular prism, we use the equation of lwh. When we insert the values, we get 2*1.5*4, which is equal to 12. Now, we take these two values of 2 and 12 and we combine them, giving us our final answer of 14.
Answer: The answer is 3 1/2
I hope this helps
Step-by-step explanation:
![\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20f%28x%2Cy%2Cz%29%3Dy%5C%2C%5Cvec%5Cimath-4yz%5C%2C%5Cvec%5Cjmath%2B3z%5E2%5C%2C%5Cvec%20k)
![\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z](https://tex.z-dn.net/?f=%5Cimplies%5Cnabla%5Ccdot%5Cvec%20f%28x%2Cy%2Cz%29%3D0-4z%2B6z%3D2z)
By the divergence theorem,
![\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cpartial%20W%7D%5Cvec%20f%5Ccdot%5Cmathrm%20d%5Cvec%20S%3D%5Ciiint_W2z%5C%2C%5Cmathrm%20dV)
I'll assume a sphere of radius
centered at the origin, and that
is bounded below by the plane
. Convert to spherical coordinates, taking
![x=\rho\cos\theta\sin\varphi](https://tex.z-dn.net/?f=x%3D%5Crho%5Ccos%5Ctheta%5Csin%5Cvarphi)
![y=\rho\sin\theta\sin\varphi](https://tex.z-dn.net/?f=y%3D%5Crho%5Csin%5Ctheta%5Csin%5Cvarphi)
![z=\rho\cos\varphi](https://tex.z-dn.net/?f=z%3D%5Crho%5Ccos%5Cvarphi)
Then
![\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciiint_W2z%5C%2C%5Cmathrm%20dV%3D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_0%5Er2%5Crho%5E3%5Ccos%5Cvarphi%5Csin%5Cvarphi%5C%2C%5Cmathrm%20d%5Crho%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20d%5Cvarphi%3D%5Cpi%20r%5E4)
Answer:
The number can have no more than 5 digits
Step-by-step explanation: