Write down all the prime numbers between 41 and 61
1 answer:
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Answer:
1.857 minutes
Step-by-step explanation:
From the given information:
Consider the amount of salt present in the tank as x(t) at a given time (t); &
The volume of the solution = V(t)
At t = 0 i.e. (at initial conditions) x(0) = 30; and V(0) = 50
However, the overall increase taken place for 1 gallon per minute is:
V(t) = 50 + t
The amount of salt x(t) at any given point for time (t) is;
After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:
Taking the integral of what we have above, we get:
In x(t) = - 5 In(t + 50) + In (C)
In x(t) = In (t+ 50)⁻⁵ + In (C)
In x(t) = In C ( t + 50)⁻⁵
x(t) = C(t + 50)⁻⁵ (General solution)
To estimate the required solution; we apply the initial conditions x(0) = 30;
Thus;
x(0) = C(50)⁻⁵ = 30
⇒ C = 30 × 50⁵
Hence; x(t) = 30 × 50⁵ × (t + 50)⁻⁵
The above expression can be re-written as:
i.e.
50 = 0.964192504t + 48.2096252
50 - 48.2096252 = 0.964192504t
1.7903748 = 0.964192504t
t = 1.7903748 / 0.964192504
t ≅ 1.857 minutes
We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.
Answer:
B
Step-by-step explanation:
<h3>Let's solve your inequality step-by-step.</h3>Step 1: Simplify both sides of the inequality.
Step 2: Subtract 2 from both sides.
Step 3: Divide both sides by 6.
Answer:
Option B is correct.
sum of given geometric series is, 255
Step-by-step explanation:
Evaluate the geometric series:
we can write this as:
Formula for the sum of the geometric series:
for r > 1
where
a is the first term
n is the number of terms
r is the common ratio
In the given series:
common ratio (r) = 2>1, n = 8 and first term(a) = 1
Since,
and so on...
then substitute the given values in [1] we have;
or
Therefore, the sum of given geometric series is, 255
Answer:
There are 68 dogs in the pound.
Step-by-step explanation:
Number of pit bull dogs in a pound = P = 23
Number of chihuahuas dogs in a pound = C = 17
Number of mutts dogs in a pound = M = 28
Total number of dogs in a pound = T
There are 68 dogs in the pound.