Answer:
Sec (x) - 2 tan (x)
Step-by-step explanation:
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
Use the midsegment theorem
Step 1: 198 × = 66, the number of men who left the party
Step 2: 256×= 64, the number of women who left the party
66+64=130
Since 130 is the number of people that left, you would subtract it from the total number of people at the party originally.
198+256=454
454-130=325
So, 325 people are left at the party