Answer:
x(15) = 21 lb
Step-by-step explanation:
Rate of change in volume of salt water solution = rate of volume incoming - rate of volume outgoing
dV/dt = 4 - 2 =2gal/min
So, the equation for volume at cetain time t at given conditions and values becomes,
V(t) = 2t + V
V(t) = 2t + 20 gal-------------------euqation (1)
Rate of change in amount of salt = rate of salt in - rate of salt out
dx/dt = {0.5*4} - {[x(t)/V(t)]*2}
dx/dt = 2-2[(x(t))/(2t+20)]
dx/dt = 2-[(x(t))/(v(t))] lb/min
Now, with integrating factor, we get
exp[∫(1/(1+10))dt)] = t+10
the equation becomes
(t + 10)*x' + x = 2*(t+10)
((t+10)*x') = 2*(t+10)
(t+10)*x = t² + 20t + C
As x(0) = 0,
x(t) = (t²+20t)/(t+10)
x(15) = (15²+20*15)/(15+10)
x(15) = 21 lb
Answer:
10√2
Step-by-step explanation:
If x=1+√2, evaluate x³+1/x³
--------
- x³+1/x³= (x+1/x)(x²-x*1/x+1/x²)=(x+1/x)(x²+1/x²+2-3)= (x+1/x)((x+1/x)²-3)
- x+1/x= 1+√2 + 1/(1+√2)= 1+√2+(1-√2)/(1-√2)(1+√2)= 1+√2 - (1-√2)= 2√2
- x³+1/x³= 2√2((2√2)²-3)= 2√2(8-3)= 10√2
Answer:
543.24
Step-by-step explanation:
Expanded Notation Form:
500
+ 40
+ 3
+ 0.2
+ 0.04
Expanded Factors Form:
5 × 100
+ 4 × 10
+ 3 × 1
+ 2 × 0.1
+ 4 × 0.01
Expanded Exponential Form:
5 × 102
+ 4 × 101
+ 3 × 100
+ 2 × 10-1
+ 4 × 10-2
Word Form:
five hundred forty-three and twenty-four hundredths
Answer:
The number, x = { -5 < x < 14}
This means x is any integer between -5 and 14
Step-by-step explanation:
From the statement, let the number be x
3 + x = y; y = { -2 < y < 17}
This means that y is any integer between -2 and 17
Therefore, x = y - 3
Subtract 3 from the limits of y
i.e. -2 - 3 = -5 and 17 - 3 = 14
Hence, x = { -5 < x < 14}
