Which kind of triangle is shown
2 answers:
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See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
The formula of linear equation is:
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope
We can then choose a point from the line to find the eqaution.
We need to first find the slope:
In this case:
In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :
y-(-2) = 3(x-(-1))
y+2 = 3(x+1)
Therefore
is the answer.
Hope it helps!
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope
We can then choose a point from the line to find the eqaution.
We need to first find the slope:
In this case:
In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :
y-(-2) = 3(x-(-1))
y+2 = 3(x+1)
Therefore
is the answer.
Hope it helps!