Nice so
remember
t=d/s
a(b+c)=ab+ac
time=distance/speed
lets say s=jamie's normal speed
speed agains wind=s-4
speed with wind=s+4
30 miles is agains wind
distance is 54 with wind
t=d/s
t=30/(s-4)
t=54/(s+4)
since they are both equal to t, set them equal to each other
30/(s-4)=54/(s+4)
multipliy both sides by (s+4)(s-4)
30(s+4)=54(s-4)
distribute
30s+120=54s-216
subtract 30s from both sides
120=24s-216
add 216 to both sides
336=24s
divide both sides by 24
14=s
answer is 14 miles per hour without wind
Answer:
Step-by-step explanation:
-3(3/6) + 4(3/5)
-3(1/2) + 4(3/5)
-3/2 + 12/5
-15/10 + 24/10
9/10
Answer:
9![\sqrt{85}](https://tex.z-dn.net/?f=%5Csqrt%7B85%7D)
Step-by-step explanation:
9v = 9(2i + 9j) = 18i + 81j
|9v | =
=
= 9![\sqrt{85}](https://tex.z-dn.net/?f=%5Csqrt%7B85%7D)
Answer:
26
Step-by-step explanation:
Use the Pythagorean Theorem: ![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Answer:
2047
Step-by-step explanation:
We are given that
Growing rate=0.7%
![\frac{dp}{dt}=\frac{0.7}{100}P](https://tex.z-dn.net/?f=%5Cfrac%7Bdp%7D%7Bdt%7D%3D%5Cfrac%7B0.7%7D%7B100%7DP)
![\int \frac{dP}{P}=0.007\int dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdP%7D%7BP%7D%3D0.007%5Cint%20dt)
![lnP=0.007t+C](https://tex.z-dn.net/?f=lnP%3D0.007t%2BC)
Using the formula
![\int \frac{dx}{x}=ln x+C](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdx%7D%7Bx%7D%3Dln%20x%2BC)
![P=e^{0.007t+C}=e^{0.007t}\cdot e^C=Ae^{0.007t}](https://tex.z-dn.net/?f=P%3De%5E%7B0.007t%2BC%7D%3De%5E%7B0.007t%7D%5Ccdot%20e%5EC%3DAe%5E%7B0.007t%7D)
![e^C=A](https://tex.z-dn.net/?f=e%5EC%3DA)
Initially when t=0,P=323 million
Substitute the values
![323 million=A](https://tex.z-dn.net/?f=323%20million%3DA)
![P=323e^{0.007t}](https://tex.z-dn.net/?f=P%3D323e%5E%7B0.007t%7D)
Now, substitute P=400 million
![400=323e^{0.007t}](https://tex.z-dn.net/?f=400%3D323e%5E%7B0.007t%7D)
![ln\frac{400}{323}=0.007t](https://tex.z-dn.net/?f=ln%5Cfrac%7B400%7D%7B323%7D%3D0.007t)
![ln(1.2384)=0.007t](https://tex.z-dn.net/?f=ln%281.2384%29%3D0.007t)
![t=\frac{ln(1.2384}{0.007}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bln%281.2384%7D%7B0.007%7D)
![t=30.5\approx 31 Years](https://tex.z-dn.net/?f=t%3D30.5%5Capprox%2031%20Years)
Year=2016+31=2047
Hence,In 2047 the U.S population will reach 400 million people.