Answer:
-2/3
Step-by-step explanation:
n - the larger of two i ntegers
m - the smaller of two integers
n + m = 74 → n = 74 - m
n = 2m + 26
Therefore we have:
2m + 26 = 74 - m |subtract 26 from both sides
2m = 48 - m |add m to both sides
3m = 48 |divide both sides by 3
m = 16
n = 74 - 16 = 58
Answer: 16 and 58.
Answer: the quotient of the given expression is, h5
Step-by-step explanation:
Use the exponent rule:
Given the expression:
⇒
Apply the exponent rules we have;
Simplify:
therefore, the quotient of the given expression is,
Answer:
Half-life of the goo is 49.5 minutes
![G(t)= 300e^{-0.014t}](https://tex.z-dn.net/?f=G%28t%29%3D%20300e%5E%7B-0.014t%7D)
191.7 grams of goo will remain after 32 minutes
Step-by-step explanation:
Let
denotes initial and final mass.
![M_0=300\,\,grams\,,\,M_f=37.5\,\,grams](https://tex.z-dn.net/?f=M_0%3D300%5C%2C%5C%2Cgrams%5C%2C%2C%5C%2CM_f%3D37.5%5C%2C%5C%2Cgrams)
According to exponential decay,
![\ln \left ( \frac{M_f}{M_0} \right )=-kt](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%20%28%20%5Cfrac%7BM_f%7D%7BM_0%7D%20%5Cright%20%29%3D-kt)
Here, t denotes time and k denotes decay constant.
![\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%20%28%20%5Cfrac%7BM_f%7D%7BM_0%7D%20%5Cright%20%29%3D-kt%5C%5C%5Cln%20%5Cleft%20%28%20%5Cfrac%7B37.5%7D%7B300%7D%20%5Cright%20%29%3D-k%28150%29%5C%5C-2.079%3D-k%28150%29%5C%5Ck%3D%5Cfrac%7B2.079%7D%7B150%7D%3D0.014)
So, half-life of the goo in minutes is calculated as follows:
![\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%20%28%20%5Cfrac%7B50%7D%7B100%7D%20%5Cright%20%29%3D-kt%5C%5C%5Cln%20%5Cleft%20%28%20%5Cfrac%7B50%7D%7B100%7D%20%5Cright%20%29%3D-%280.014%29t%5C%5Ct%3D%5Cfrac%7B-0.693%7D%7B-0.014%7D%3D49.5%5C%2C%5C%2Cminutes)
Half-life of the goo is 49.5 minutes
![\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%20%28%20%5Cfrac%7BM_f%7D%7BM_0%7D%20%5Cright%20%29%3D-kt%5CRightarrow%20M_f%3DM_0e%5E%7B-kt%7D)
So,
![G(t)= M_f=M_0e^{-kt}](https://tex.z-dn.net/?f=G%28t%29%3D%20M_f%3DM_0e%5E%7B-kt%7D)
Put ![M_0=300\,\,grams\,,\,k=0.014](https://tex.z-dn.net/?f=M_0%3D300%5C%2C%5C%2Cgrams%5C%2C%2C%5C%2Ck%3D0.014)
![G(t)= 300e^{-0.014t}](https://tex.z-dn.net/?f=G%28t%29%3D%20300e%5E%7B-0.014t%7D)
Put t = 32 minutes
![G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams](https://tex.z-dn.net/?f=G%2832%29%3D%20300e%5E%7B-0.014%2832%29%7D%3D300e%5E%7B-0.448%7D%3D191.7%5C%2C%5C%2Cgrams)
Answer:
see below
Step-by-step explanation:
f(x)= -(x-2)^2 +4
This is the vertex form of the equation for a parabola
y= a ( x-h)^2 +k where (x,k) is the vertex of the parabola
a = -1 h= 2 k = 4
The vertex is ( 2,4)