The formula for gravitational force is F = G * m1 * m2 / r². The gravitational constant is G = 6.67 * 10^(-11) m³/kgs². Thus, we find r = sqrt(G * m1 * m2 / F) = sqrt(6.67 * 10^(-11) m³/kgs² * 1.3 * 10^(22) kg * 1.6 * 10^(21) / 3.61 * 10^(18) N) = sqrt(3.84 * 10^(14)) = 1.96 * 10^(7) m, which is approximately 2 * 10^(7) m.
A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour
e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
For this context, we examine the function:
presented as:
The definition of the discriminant in a quadratic equation is provided by:
Sentences correspond to the types of roots: Different real roots, equal real roots, or distinct complex roots
Upon substituting the provided values, we arrive at
This indicates that there are two equal real roots.
To discover the intersections along the x-axis, we apply the quadratic formula:
Plugging in the values yields: 
The intersection on the x-axis is
Answer: Indeed, because the input value ranges from 0 to 12.
Step-by-step explanation:
To address this query, we first need to formulate a function that reflects the situation.
Every student engaging in community service earns the club $5
E(s) = 5 s
Where:
- E= total earnings
- n = number of students participating in community services (input value)
Indeed, since the input value n indicates how many students from the club engage in community service, and with the total number of students being 12, the input can indeed vary between 0 and 12.
Answer:
Step-by-step explanation:
We start with the information provided
Next, we need to calculate V
To carry this out, we simply plug the values of P, r, and t into the formula.
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Convert the percentage to decimal form
Convert it to cents.
-- Approximated
