Answer:
x(t) = 5000*( 1 - e^-kt)
Step-by-step explanation:
Given:
- Total number of students n = 5000
Find:
Differential equation governing the number of students x(t) who have contracted the flu.
Solution:
- Number of non-affected students = (5000 - x)
Hence,
- Rate at which students are infected:
dx / dt = k*(5000 - x )
- separate variables:
dx / (5000 - x ) = k*dt
- Integrate both sides:
- Ln(5000 - x) = kt + C
- Evaluate C for x = 0 @ t = 0
- Ln(5000 - 0) = k*0 + C
C = - Ln(5000)
- The solution to ODE is:
Ln(5000 - x) = -k*t + Ln(5000)
5000 - x = 5000*e^-kt
x(t) = 5000*( 1 - e^-kt)
Answer:
Part a)
We need to find the equation of the line with a slope of -5 and a y-intercept of (0,3)
Part b)
The information that we have; we know the value of he slope, -5, and the y-intercept (0,3).
Part c)
strategies to use;
we can use the standard form of the equation of a straight line in slope -intercept form;
y=mx+c
Step-by-step explanation:
We have been given the slope is -5, thus the value of m is -5. moreover, the y-intercept is given as, (0,3) thus c is 3.
Final answer to the problem is;
y=-5x+3
Answer:
Answers are the last step of every problem
Step-by-step explanation:
1) 27+y<10
y<-17
2) 4x+5≥29
4x≥24
x≥6
3) 6y+1>7
6y>6
y>1
4) 3p+1≤-1
3p≤-2
p≤-2/3
5) 9≥12-x
-3≥-x
3≤x
6) 3-5x>13
-5x>10
x>-2
7) 5/6x-1/2<1/3
5x-3<2
5x<5
x<1
8) 7/8-1/4x≥3/4
7-2x≥6
-2x≥-1
x≤1/2
9) 4/5y-1/5>3
4/5y>16/5
4y>16
y>4
10) 3x+3>7+x
2x+3>7
2x>4
x>2
11) 8-x<10-2x
8+x<10
x<2
12) 11+x≤7+5x
11≤7+4x
4≤4x
1≤x
Answer:
The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6
Step-by-step explanation:
Let
x ----> represents the number of pounds of granola
y ----> represents the number of pounds of walnuts
we know that
The linear equation that represent this scenario is
2x+6y=12 -----> equation A
x=3 -----> equation B
substitute equation B in equation A and solve for y
2(3)+6y=12
6+6y=12
Subtract 6 both sides
6+6y-6=12-6
6y=6
Divide by 6 both sides
6y/6=6/6
y=1
so
The number of pounds of walnuts is 1
therefore
The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6
Answer:
B
Step-by-step explanation: