X^2 + 50
√x^2+ √50
x + 5√2
5√2 = ~7.07106
x + 7.07106
x = -7.07106
hope this helps
Answer:
4
Step-by-step explanation:
If she makes 4 sandwiches, she splits the 4 sandwiches among 8 children. 4/8 is 1/2 which is half a sandwich for everyone.
If
![A(t)](https://tex.z-dn.net/?f=A%28t%29)
is the amount of salt in the tank at time
![t](https://tex.z-dn.net/?f=t)
, then the rate at which this amount changes over time is given by the ODE
![A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{5\text{ lb}}{1\text{ gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}](https://tex.z-dn.net/?f=A%27%28t%29%3D%5Cdfrac%7B3%5Ctext%7B%20gal%7D%7D%7B1%5Ctext%7B%20min%7D%7D%5Ccdot%5Cdfrac%7B5%5Ctext%7B%20lb%7D%7D%7B1%5Ctext%7B%20gal%7D%7D-%5Cdfrac%7B3%5Ctext%7B%20gal%7D%7D%7B1%5Ctext%7B%20min%7D%7D%5Ccdot%5Cdfrac%7BA%28t%29%5Ctext%7B%20lb%7D%7D%7B300%2B%283-3%29t%5Ctext%7B%20gal%7D%7D)
![A'(t)+\dfrac1{100}A(t)=15](https://tex.z-dn.net/?f=A%27%28t%29%2B%5Cdfrac1%7B100%7DA%28t%29%3D15)
We're told that the tank initially starts with no salt in the water, so
![A(0)=0](https://tex.z-dn.net/?f=A%280%29%3D0)
.
Multiply both sides by an integrating factor,
![e^{t/100}](https://tex.z-dn.net/?f=e%5E%7Bt%2F100%7D)
:
![e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=15e^{t/100}](https://tex.z-dn.net/?f=e%5E%7Bt%2F100%7DA%27%28t%29%2B%5Cdfrac1%7B100%7De%5E%7Bt%2F100%7DA%28t%29%3D15e%5E%7Bt%2F100%7D)
![\left(e^{t/100}A(t)\right)'=15e^{t/100}](https://tex.z-dn.net/?f=%5Cleft%28e%5E%7Bt%2F100%7DA%28t%29%5Cright%29%27%3D15e%5E%7Bt%2F100%7D)
![e^{t/100}A(t)=1500e^{t/100}+C](https://tex.z-dn.net/?f=e%5E%7Bt%2F100%7DA%28t%29%3D1500e%5E%7Bt%2F100%7D%2BC)
![A(t)=1500+Ce^{-t/100}](https://tex.z-dn.net/?f=A%28t%29%3D1500%2BCe%5E%7B-t%2F100%7D)
Since
![A(0)=0](https://tex.z-dn.net/?f=A%280%29%3D0)
, we have
![0=1500+C\implies C=-1500](https://tex.z-dn.net/?f=0%3D1500%2BC%5Cimplies%20C%3D-1500)
so that the amount of salt in the tank over time is given by
![A(t)=1500(1-e^{-t/100})](https://tex.z-dn.net/?f=A%28t%29%3D1500%281-e%5E%7B-t%2F100%7D%29)
After 10 minutes, the amount of salt in the tank is
Answer:
51 miles/hour is the conversion of 75 feet/second rounding to nearest whole number.
Step-by-step explanation:
Given:
75 feet/second.
Now, to convert 75 feet/second into miles/hour.
So, to convert we divide the value of feet per second by conversion factor to get miles per hour.
Value of feet per second = 75.
Conversion factor = 1.4667.
Now, putting the formula to get the value in miles/hour:
Value in miles/hour = value of feet/second ÷ conversion factor.
Value in miles/hour = ![75\div 1.4667.](https://tex.z-dn.net/?f=75%5Cdiv%201.4667.)
= ![51.135\ miles/hour.](https://tex.z-dn.net/?f=51.135%5C%20miles%2Fhour.)
<em>Rounding nearest to whole number = 51 miles/hour.</em>
Therefore, 51 miles/hour is the conversion of 75 feet/second rounding to nearest whole number.
It's simple,
f(x)=x^2+2
is the formula that you start with
you are then given f(x). f(4x)
you then plug in 4x
4x=(4x)^2+2
you then solve for x
4x=16x+2
-16x. -16x
-12x=2
÷-12. ÷-12
x=0.16 is your answer