Answer:
Step-by-step explanation:
the coordinate of D is (3,-3) because it is 3 units right from the x axis and -3 units down in y axis.
Answer:
V =2160 pi units^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2h
We know the radius is 12 and the height is 15
V = pi (12)^2 (15)
V = pi 144*15
V =2160 pi units^3
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that ![A(0) = 910](https://tex.z-dn.net/?f=A%280%29%20%3D%20910)
So
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
How long would it be until the mass of the sample reached 400 grams?
This is t for which ![A(t) = 400](https://tex.z-dn.net/?f=A%28t%29%20%3D%20400)
So
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![400 = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=400%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![(0.5)^{\frac{t}{25}} = \frac{400}{910}](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%20%5Cfrac%7B400%7D%7B910%7D)
![(0.5)^{\frac{t}{25}} = 0.43956](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%200.43956)
![\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}](https://tex.z-dn.net/?f=%5Clog%7B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%7D%20%3D%20%5Clog%7B0.43956%7D)
![\frac{t}{25}\log{0.5} = \log{0.43956}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B25%7D%5Clog%7B0.5%7D%20%3D%20%5Clog%7B0.43956%7D)
![t = \frac{25\log{0.43956}}{\log{0.5}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B25%5Clog%7B0.43956%7D%7D%7B%5Clog%7B0.5%7D%7D)
![t = 25.6](https://tex.z-dn.net/?f=t%20%3D%2025.6)
It will take 25.6 years for the mass of the sample to reach 400 grams.
2y^2 (3x+5z)
6xy^2 + 10zy^2