Answer:
Step-by-step explanation:
Answer:
a) y-8 = (y₀-8) , b) 2y -5 = (2y₀-5)
Explanation:
To solve these equations the method of direct integration is the easiest.
a) the given equation is
dy / dt = and -8
dy / y-8 = dt
We change variables
y-8 = u
dy = du
We replace and integrate
∫ du / u = ∫ dt
Ln (y-8) = t
We evaluate at the lower limits t = 0 for y = y₀
ln (y-8) - ln (y₀-8) = t-0
Let's simplify the equation
ln (y-8 / y₀-8) = t
y-8 / y₀-8 =
y-8 = (y₀-8)
b) the equation is
dy / dt = 2y -5
u = 2y -5
du = 2 dy
du / 2u = dt
We integrate
½ Ln (2y-5) = t
We evaluate at the limits
½ [ln (2y-5) - ln (2y₀-5)] = t
Ln (2y-5 / 2y₀-5) = 2t
2y -5 = (2y₀-5)
c) the equation is very similar to the previous one
u = 2y -10
du = 2 dy
∫ du / 2u = dt
ln (2y-10) = 2t
We evaluate
ln (2y-10) –ln (2y₀-10) = 2t
2y-10 = (2y₀-10)
Here we are given the specific equation of:
amount of eroded soil = 0.4 + 1.3 x
where x is the flow rate
A linear equation has a general formula in the form of:
y = m x + b
where m is the slope and b is the y intercept of the equation
If we compare this with our specific equation, we can see that the slope and y intercept are both positive with values:
m = 0.4
b = 1.3
Therefore this only means that as the flow rate increases, the amount of eroded soil also increases.
Hence the correlation must be positive but we cannot solve for the exact value since we need the data for x and y.
Answer:
positive, but we cannot say what the exact value is
In this question, 10 people average running distance is 2.7miles. Then the sum of their running distance would be: 10 people * 2.7 miles/people= 27 miles.
The group then divided into 2, 4 people with 3 miles average and 6 people with unknown average. Since the people are same like the 10 people group, their total running distance would be the same. The calculation would be:
total distance = group1 * average1 + group2 * average2
27 miles= 4 people * 3 miles/people + 6 people* average2
6 people * average2 = 27 miles -12 miles = 15 miles
average2= 15 miles/6people= 2.5 miles/people
Answer:
The probability of the guess being correct is 1/150.
Step-by-step explanation:
The information provided for the game Clue is:
- Clue is a board game in which you must deduce three details surrounding a murder.
- The guilty person can be chosen from 6 people.
- There are 6 different possible weapons.
- There are 9 possible rooms.
Now it is provided that at some point the possibilities have been narrowed down to 5 people, 5 weapons, and 6 rooms.
The number of ways to select a guilty person from the 5 selected people is,
n (P) = 5
The number of ways to select a weapon from the 5 selected weapon is,
n (W) = 5
The number of ways to select a room from the 6 selected rooms is,
n (R) = 6
Then the total number of random guesses is,
N = n (P) × n (W) × n (R)
= 5 × 5 × 6
= 150
And only one of these 150 guesses is correct.
So, the probability of the guess being correct is 1/150.
