Answer:
![D(t)=50(0.8)^t](https://tex.z-dn.net/?f=D%28t%29%3D50%280.8%29%5Et)
Step-by-step explanation:
We are given that
Initially the difference between the cake's and the cooler's temperature ,a=50 degree Celsius
![r=\frac{1}{5}/min](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B5%7D%2Fmin)
We have to find the function that gives the temperature difference in degrees Celsius D(t).
We know that
![D(t)=a(1-r)^t](https://tex.z-dn.net/?f=D%28t%29%3Da%281-r%29%5Et)
Substitute the values
![D(t)=50(1-\frac{1}{5})^t=50(1-0.2)^t](https://tex.z-dn.net/?f=D%28t%29%3D50%281-%5Cfrac%7B1%7D%7B5%7D%29%5Et%3D50%281-0.2%29%5Et)
![D(t)=50(0.8)^t](https://tex.z-dn.net/?f=D%28t%29%3D50%280.8%29%5Et)
This is required function that gives the temperature difference in degrees Celsius.
Answer:
![6](https://tex.z-dn.net/?f=6)
Step-by-step explanation:
GIVEN: The weight, in pounds, of a newborn baby
months after birth can be modeled by the function
.
TO FIND: What is the y-intercept of the function and what is its interpretation in the context of the problem.
SOLUTION:
in ![W(t)=1.25t+6](https://tex.z-dn.net/?f=W%28t%29%3D1.25t%2B6)
if ![t=0](https://tex.z-dn.net/?f=t%3D0)
![W(0)=6](https://tex.z-dn.net/?f=W%280%29%3D6)
Hence y-intercept is ![6](https://tex.z-dn.net/?f=6)
the y-intercept in this represents the weight of baby just after he is born.
1 7/10 is equivalent to the improper fraction 17/10
Step-by-step explanation:
Geometry is one of the oldest branches of math. Geometry is mostly about distance, shape, size, and relative position of figures. It is related to measurement, relationships of points, lines, angles, surfaces, and solids. There are 8 types of Geometry and the basic concepts of Geometry are point, line and plane. It isn't possible to exactly define the terms, however, we know it is refers to the mark of the position and has an accurate location.
Hope this helps :)
![x^2+bx+c = (x-r)(x-s)\\ x^2+bx+c = x^2-(r+s)x+rs\\\\ b = -(r+s)\\ c = rs](https://tex.z-dn.net/?f=x%5E2%2Bbx%2Bc%20%3D%20%28x-r%29%28x-s%29%5C%5C%0Ax%5E2%2Bbx%2Bc%20%3D%20x%5E2-%28r%2Bs%29x%2Brs%5C%5C%5C%5C%0Ab%20%3D%20-%28r%2Bs%29%5C%5C%20c%20%3D%20rs)
Say r is rational. Suppose for a second, that s is not. Then, r+s is irrational. But this contradicts the fact that b is rational.
So, if one root is rational, then the other root is also rational