Answer:
1250
Step-by-step explanation:
125
<u>* 37</u>
875
<u>+ 375</u>
1250
Answer:
4492 years (to the nearest year)
Step-by-step explanation:
The quantity of radium left after a time t can be modeled using the equation below:
![Q(t)=Q_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }\\Q_0 =$Initial Amount$\\t_{1/2}=$Half-Life of the Substance$\\t=$Time elapsed$](https://tex.z-dn.net/?f=Q%28t%29%3DQ_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%7D%20%7D%5C%5CQ_0%20%3D%24Initial%20Amount%24%5C%5Ct_%7B1%2F2%7D%3D%24Half-Life%20of%20the%20Substance%24%5C%5Ct%3D%24Time%20elapsed%24)
Given that:
![Q_0 =70mg\\t_{1/2}=1600 years](https://tex.z-dn.net/?f=Q_0%20%3D70mg%5C%5Ct_%7B1%2F2%7D%3D1600%20years)
The amount of radium left after a t years is:
![Q(t)=70(\frac{1}{2})^{\frac{t}{1600} }](https://tex.z-dn.net/?f=Q%28t%29%3D70%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D)
If the quantity left is 10 mg, then:
![10=70(\frac{1}{2})^{\frac{t}{1600} }\\\frac{10}{70} =(\frac{1}{2})^{\frac{t}{1600} }\\](https://tex.z-dn.net/?f=10%3D70%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D%5C%5C%5Cfrac%7B10%7D%7B70%7D%20%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D%5C%5C)
Changing to logarithm form
![Log_{0.5}\frac{10}{70}=\frac{t}{1600} \\\frac{Log(10/70)}{Log 0.5} =\frac{t}{1600}\\t=\frac{Log(10/70)}{Log 0.5} X 1600\\=4491.8 \approx 4492 \:years\text{ (to the nearest year)}](https://tex.z-dn.net/?f=Log_%7B0.5%7D%5Cfrac%7B10%7D%7B70%7D%3D%5Cfrac%7Bt%7D%7B1600%7D%20%20%5C%5C%5Cfrac%7BLog%2810%2F70%29%7D%7BLog%200.5%7D%20%3D%5Cfrac%7Bt%7D%7B1600%7D%5C%5Ct%3D%5Cfrac%7BLog%2810%2F70%29%7D%7BLog%200.5%7D%20X%201600%5C%5C%3D4491.8%20%5Capprox%204492%20%5C%3Ayears%5Ctext%7B%20%28to%20the%20nearest%20year%29%7D)
In 4492 years, 10 mg of Radium will be left.
Answer:
n = 55/8
Step-by-step explanation:
![\frac{11}{n} = \frac{8}{5}\\\\cross \ multiply :\\ 8 \times n = 11 \times 5\\\\n = \frac{11 \times 5}{8} = \frac{55}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B11%7D%7Bn%7D%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5C%5C%5C%5Ccross%20%5C%20multiply%20%3A%5C%5C%208%20%5Ctimes%20n%20%3D%2011%20%5Ctimes%205%5C%5C%5C%5Cn%20%3D%20%5Cfrac%7B11%20%5Ctimes%205%7D%7B8%7D%20%3D%20%5Cfrac%7B55%7D%7B8%7D)
Answer:
f(x)=x-5 is a linear function
Step-by-step explanation:
so there are no restrictions to what x can be. The domain is all real numbers. In interval notation, we show that is can be anything from negative infinity through infinity like this: This says that the lower limit of the domain is negative infinity and the upper limit is positive infinity.
Let "a", "b" and "с" be sides of the triangle ("с" is the longest side). The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
We have a=32.18, b=40 and c=53.02
a² + b² = 32.18² + 40² = 1035.5524 + 1600 = 2635.5524
and
c² = 53.02² = 2811.1204
2635.5524 < 2811.1204 ⇒ obtuse triangle