Answer:
X= -45
Step-by-step explanation:
Subract 23 from both sides to solve for x.
Answer:
4 hours
Step-by-step explanation:
The speed of the first car is
![v_1 = 120 km/h](https://tex.z-dn.net/?f=v_1%20%3D%20120%20km%2Fh)
While the speed of the second car is
![v_2=80 km/h](https://tex.z-dn.net/?f=v_2%3D80%20km%2Fh)
The time it takes for each car to cover a distance d is
![t=\frac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv%7D)
where
d = 960 km is the total distance covered
For car 1, the time taken is:
![t_1=\frac{960}{120}=8 h](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B960%7D%7B120%7D%3D8%20h)
For car 2, the time taken is:
![t_2=\frac{960}{80}=12 h](https://tex.z-dn.net/?f=t_2%3D%5Cfrac%7B960%7D%7B80%7D%3D12%20h)
Therefore, the difference in time is:
![\Delta t =t_2-t_1 =12 -8 = 4 h](https://tex.z-dn.net/?f=%5CDelta%20t%20%3Dt_2-t_1%20%3D12%20-8%20%3D%204%20h)
the answer is 0 i used a calculator
A.) P(t) = P0exp(kt)
P(20/60) = 40 exp(20k/60)
80 = 40 exp(k/3)
exp(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = exp(8k) = exp(8(3ln(2)) = exp(24ln(2)) = exp(16.6355) = 16777216 cells / hour
e.) P(t) = 40(2)^3t; t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
Answer:
∠ABC= 180° -21° -37° (∠ sum of triangle ABC)
∠ABC= 122°
Using sine rule,
![\frac{AB}{sin21°} = \frac{200}{sin122°}](https://tex.z-dn.net/?f=%20%5Cfrac%7BAB%7D%7Bsin21%C2%B0%7D%20%20%3D%20%20%5Cfrac%7B200%7D%7Bsin122%C2%B0%7D%20)
AB= 200(sin21°)/sin 122°
AB= 84.5 units (3 s.f.)
![\frac{BC}{sin37°} = \frac{200}{sin122°}](https://tex.z-dn.net/?f=%20%5Cfrac%7BBC%7D%7Bsin37%C2%B0%7D%20%20%3D%20%20%5Cfrac%7B200%7D%7Bsin122%C2%B0%7D%20)
BC= 200(sin37°)/ sin122°
BC= 142 units (3 s.f.)