I think you have to first separate the integral:1/(1+v^2) + v/(1+v^2),
so the integral of the first term is ArcTan (v) and for the integral of the second term i recommend you to do a change of variable:
y= 1+v^2
so
dy= 2v
and
v= dy/2and then you substitute:v/(1+v^2) = (1/2)(dy/y)
and the integral is
(1/2) (In y)finally you plug in the initial variables:
(1/2)(In [1+v^2])
so the total integral is:
ArcTan (y) + (1/2)(In [1+v^2])
Answer:
31.5 in
Step-by-step explanation:
- Volume of a hemisphere = (2/3)
r³
(where r is the radius)
- Volume of a cylinder = r²h
(where r is the radius and h is the height)
- radius r = (1/2) diameter
First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:
Volume = (2/3) x 21³ = 6174 in³
Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:
14²h = 6174
196h = 6174
Divide both sides by : 196h = 6174
Divide both sides by 196: h = 31.5
Therefore, the height of the molten steel in the storage tank is 31.5 in
<h3>
Answer: -6/5</h3>
Explanation:
The blue diagonal line goes through the two points (0,2) and (5,-4). These are shown as the dark blue enlarged points. You can pick any other points you want that are on the diagonal line, though these are the easiest as they stand out the most.
Use the slope formula to find the slope through these points
m = (y2-y1)/(x2-x1)
m = (-4-2)/(5-0)
m = (-6)/(5)
m = -6/5
The negative slope means the line goes downhill as you move from left to right along the diagonal line.
-2x+4y=36
Add +2x to both sides
4y=2x+36
Decide every term by 4
y= 2/4x + 9
The slope is 2/4
Answer:
not sure
Step-by-step explanation:
