Answer:
![\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%3D%20kx%28t%29%5B1000-x%28t%29%5D%2C%24%20%20x%280%29%3D0)
Step-by-step explanation:
Total Number of People on Campus =1000
Let the number of people who have contracted the flu =x(t)
Therefore, the number of people who have not contracted the flu =1000-x(t)
Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.
![\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)]](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%5Cpropto%20x%28t%29%5B1000-x%28t%29%5D)
Introducing the proportional constant k, we obtain:
![\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)]](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%3D%20kx%28t%29%5B1000-x%28t%29%5D)
At t=0, there was no infected on the campus, therefore the initial condition is given:
Therefore, a differential equation for the number of people x(t) who have contracted the flu is:
Answer:
(∠C) ≅ (∠B)
∴ tan(∠B) = tan(∠C) and
Slope AB = Slope BC
Step-by-step explanation:
Part A:
To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;
The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)
The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)
The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal
Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C
Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)
The slope AB = tan(∠B)
Slope BC = tan(∠C)
(∠C) ≅ (∠B)
Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.
To use algebraic methods to solve geometric problems.
Answer:
1734
Step-by-step explanation:
3 times 17 to find the number of feet =51
51 time $34 (the price per foot ) to find total
Answer: x = 1/16
Step-by-step explanation:
Since the inverse of a Logarithm is an exponential function, we know that the final solution has to involve an exponential function somewhere in it.
1. log B(2) {x} = -4 || given
2. x = 2 ^ -4 || Logarithm rule that allows you to move the base of the logarithm to the base of the exponent on the other side. For example, if you had log B(5) {x} = 3, the base of 5 would move over to the other side and it would be raised to 3; x = 5^3.
3. x = (1) / (2^4) || Simplify. Use the negative exponent rule. This rule always leaves a numerator of 1, and a denominator of your exponent. In this case, it will be 2 ^ -4, so you will do 2^4 which is 16 and you will put that over 1. Resulting in your final answer of x = 1/16
