Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
Part 1) Find the value of x
we know that
Triangles CDF and FDE are similar
therefore
The ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Part 2) Find the length of DE
substitute the value of x
Answer:
3.2
Step-by-step explanation:
3.21428571429 is the exact answer and rounded to the nearest tenth is the first number after the decimal.
Answer:
$14
Step-by-step explanation:
$20 minus the $6 she came back with equals $14, which is what she spent.
(20-6=14)
Answer:
x = 50*e∧ -t/100
Step-by-step explanation:
We assume:
1.-That the volume of mixing is always constant 300 gallons
2.-The mixing is instantaneous
Δ(x)t = Amount in - Amount out
Amount = rate * concentration*Δt
Amount in = 3 gallons/ min * 0 = 0
Amount out = 3 gallons/min * x/ 300*Δt
Then
Δ(x)t/Δt = - 3*x/300 Δt⇒0 lim Δ(x)t/Δt = dx/dt
dx/dt = - x/100
dx/ x = - dt/100
A linear first degree differential equation
∫ dx/x = ∫ - dt/100
Ln x = - t/100 + C
initial conditions to determine C
t= 0 x = 50 pounds
Ln (50) = 0/100 * C
C = ln (50)
Then final solution is:
Ln x = - t/100 + Ln(50) or
e∧ Lnx = e ∧ ( -t/100 + Ln(50))
x = e∧ ( -t/100) * e∧Ln(50)
x = e∧ ( -t/100) * 50
x = 50*e∧ -t/100
