Answer:

Step-by-step explanation:
apply the inverse properties of logarithmic and exponential functions to simplify

all logs has base 'e'
Inverse property of log says that
, the value of ln e=1
we apply this property in our problem. ln has same base 'e' . ln and 'e' gets cancelled


Answer:
Step-by-step explanation:
Given that cesar left the college traveling 12 mph. Then, 4 hours later, Gabriel left traveling the same direction at 24 mph.
Before Gabriel started Cesar would have travelled for 4 hours
So distance travelled by Cesar in 4 hours 
Thus Cesar is ahead of Gabriel by 48 miles
Difference of speed 
So to catch Cesar time required = 48/difference in speed
= 4 hours
It will take 4 hours.
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
60% of 20 is (0.6 x 20) = 12 passes
There are a further 30 quizzes remaining (50 total during the year minus 20 already written)
80% of 30 is (0.8 x 30) = 24 passes
The student has passed (12 + 24) = 36 quizzes out of 50 total, giving an overall pass percentage of ((36 / 50) x 100)) = 72%.