Answer:
a) The implied differential equation is 
b) The general equation is 
c) The particular equation is 
d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)
Step-by-step explanation:
The rate of change of N(t) can be written as dN/dt
According to the question, 
Integrating both sides of the equation
When t = 0, N = 400
When t = 3, N = 650
The equation for the population becomes:
At t = 5, the population becomes:
N(5) = 700 ( to the nearest 50)
Answer:
(1, 1), (2, 2.333) and (3, 3.666).
Step-by-step explanation:
So, for x = 1, we have:
4*1 - 3y = 1
3y = 3
y = 1
For x = 2, we have:
4*2 - 3y = 1
3y = 7
y = 2.333
For x = 3, we have:
4*3 - 3y = 1
3y = 11
y = 3.666
The points we need to plot is (1, 1), (2, 2.333) and (3, 3.666).
Answer:
200 feet per minute
Step-by-step explanation:
1000 / 5 gives us the feet per minute
200 feet per minute
Answer: 200 feet per minute
Answer:
x = 24
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
<em>a</em> = a leg
<em>b</em> = another leg
<em>c</em> = hypotenuse
Step 1: Plug in known variables
x² + 10² = 26²
Step 2: Evaluate
x² + 100 = 676
Step 3: Isolate <em>x </em>term
x² = 576
Step 4: Isolate <em>x</em>
√x² = √576
x = 24
Problem # 1
Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)
There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
(5x ) (x ) = 5x^2 +
2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3
3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.
For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6. This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.
As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.
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Problem # 2
Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
4x^2 (x - 3) (x - 4)
To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x )(x ) and guessing for which numbers will add to -7x and multiply to 12
