Answer:
f'(N) = a(k² - N²)/(k² + N²)
The function increases in the interval
(-k < N < k)
And the function decreases everywhere else; the intervals given as
(-∞ < N < -k) and (k < N < ∞)
Step-by-step explanation:
f(N)=aN/(k²+N²)
The derivative of this function is obrained using the quotient rule.
Then to determine the intervals where the function is increasinumber and decreasing,
The function increases in intervals where f'(N) > 0
and the function decreases in intervals where f'(N) < 0.
This inequality is evaluated and the solution obtained.
The solution is presented in the attached image.
Hope this Helps!!!
Let's convert these inequalities to Slope Intercept Form so that we can graph them easily.
<span>−10x − 5y ≥ 15
Add 10x to both sides.
-5y </span>≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y <span>≤ -2x - 3
</span><span>x + y ≤ − 1
Subtract x from both sides.
</span><span>y ≤ -x − 1
When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.</span>
Answer: 1300 cm^3, 850 cm^2
Step-by-step explanation:
With a triangular prism, you need to calculate the surface area of the triangle first and then the length. Here's how to solve for the volume (A):
Triangles is b*h/2, plug in the equation
10*13/2
130/2
65
Now use the length of the rest of the shape, which is 20 cm.
65*20=1300
the volume is 1300 cm^3.
for B, finding the surface area requires you to analyze each individual part of the shape.
Each part colored in represents a different shape:
Red:
10*20=200
Blue:
13*10/2=65
65*2=130 (Two triangles)
Green:
13*20=260
260*2=520 (Two rectangles)
Add them all up together.
200+130+520= 850 cm^2
The equation of a straight line is given by:
y = mx + c
where m is the slope and c is the y-intercept.
From the given graph, the y-intercept is 1.
The slope of a straight line is given by:
Where
and
are two points on the line.
From the graph, (0, 1) and (14, 8) are two points on the line, thus:
Therefore, the equation representing the graph is
