Step-by-step explanation:
∫ (sec x − tan x) dx
∫ sec x dx + ∫ -tan x dx
∫ (sec²x + sec x tan x) / (sec x + tan x) dx + ∫ (-sin x / cos x) dx
ln(sec x + tan x) + ln(cos x) + C
Answer:
a) 
b) 
Step-by-step explanation:
By definition, we have that the change rate of salt in the tank is 
, where 
is the rate of salt entering and 
is the rate of salt going outside.
Then we have, 
, and
So we obtain. 
, then
, and using the integrating factor 
, therefore 
, we get 
, after integrating both sides 
, therefore 
, to find 
we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions 
, so 
Finally we can write an expression for the amount of salt in the tank at any time t, it is
b) The tank will overflow due Rin>Rout, at a rate of 
, due we have 500 L to overflow 
, so we can evualuate the expression of a) 
, is the salt concentration when the tank overflows
Answer:
52 years.
Step-by-step explanation:
Represent my current age by c. Then 400 - 2c = 296, or
104 = 2c
Then c must be 104/2, or 52 years.
Answer:
Try as percentages so
7) 37.5%
8) 50%
9) 12.5%
10) 62.5%
11) 87.5%
12) 50%
13) 62.5%
14) 37.5%
15) 100%
Step-by-step explanation:
For this case we have to define trigonometric relations of rectangular triangles that:
- The cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.
- The sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle.
Then, according to the figure we have:
Answer:
Option D
