Answer:
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Step-by-step explanation:
Answer:
Hence, the sphere has a radius of 
and is centered at the point (1,-1,1)
Step-by-step explanation:
We have the equation
We have to take into account the relation between coordinates
by substituting we have:
![\rho=2[\frac{x}{\rho}-\frac{y}{\rho}+\frac{z}{\rho}]\\\\\rho^2=2x-2y+2z\\\\x^2+y^2+z^2=2x-2y+2z](https://tex.z-dn.net/?f=%5Crho%3D2%5B%5Cfrac%7Bx%7D%7B%5Crho%7D-%5Cfrac%7By%7D%7B%5Crho%7D%2B%5Cfrac%7Bz%7D%7B%5Crho%7D%5D%5C%5C%5C%5C%5Crho%5E2%3D2x-2y%2B2z%5C%5C%5C%5Cx%5E2%2By%5E2%2Bz%5E2%3D2x-2y%2B2z)
We have to complete squares:
Hence, the sphere has a radius of and is centered at the point (1,-1,1)
hope this helps!!
Answer:
It will take 4 minutes and 30 seconds for hot coffee to cool to a temperature of 25 ° C
Step-by-step explanation:
This problem can be modeled by a first order equation
T(t) = TA + kt
In which TA is the temperature at instant zero and r is the rate of warming(g>0) or cooling(k<0). t is the time in minutes.
The initial temperature of the cup of coffee is 70ºC. So TA = 70. The temperature cools at the rate of 10ºC per minute, so k = -10. So, the equation of the model is:
T(t) = 70 - 10t
We want to know the instant of time when T = 25, so:
25 = 70 - 10t
10t = 70 - 25
10t = 45
t = 4.5 minutes
It will take 4 minutes and 30 seconds for hot coffee to cool to a temperature of 25 ° C
