Answer:
120 grams will be left after 180 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
![N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}](https://tex.z-dn.net/?f=N%28t%29%3DN_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%7D)
where,
= quantity of the substance remaining
= initial quantity of the substance
= time elapsed
= half life of the substance
From the information given we know that:
- The initial quantity is 480 g,
- The half-life is 90 years,
- 180 years is the time elapsed.
And we want to find how much will be left. For this we use the above formula.
![N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120](https://tex.z-dn.net/?f=N%28t%29%3D480%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cfrac%7B180%7D%7B90%7D%7D%5C%5C%5C%5CN%28t%29%3D480%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E2%5C%5C%5C%5CN%28t%29%3D480%5Ccdot%20%5Cfrac%7B1%7D%7B2%5E2%7D%3D120)
120 grams will be left after 180 years.
I= $75
500 x 5% x 3 years = 75
Answer:
9 or B
Step-by-step explanation:
3^4=81
3^2=9
81/9=9
With these transversals across parallel lines the angles are either congruent or supplementary (adding to 180) and its pretty easy to figure out which is which, obtuse verse acute in the figure.
Each yellow circle indicates x and the path to the next square. So for example the Start has alternate interior angles, which are congruent, so x is 141 degrees.
The given equation is:
![y= \sqrt{x+3}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%7Bx%2B3%7D%20)
We have to find, which of the given set of parametric equations given in the options, result in the above equation:
The correct answer would be option A.
The equations in option A are:
![x(t) = 5t \\ y(t)= \sqrt{5t+3}](https://tex.z-dn.net/?f=x%28t%29%20%3D%205t%20%5C%5C%20%0Ay%28t%29%3D%20%5Csqrt%7B5t%2B3%7D%20)
From first equation we can see that 5t is equal to x. Using the value of 5th in second equation, we get the equation as:
Therefore, the correct answer is option A