Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y =
x + ba/a
y =
x + b
so R is bounded by y =
x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π (
x + b )² dx
V = π ₀∫^a (
x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx
Answer:
(-1.92, 1.08)
Step-by-step explanation:
The <em>incenter</em> is the center of the largest circle that can be inscribed in the triangle. That circle is called the <em>incircle</em>. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the <em>inradius</em> (the radius of the incircle), is found from a simple formula:
r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs
In your triangle, the inradius is ...
r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452
Among other things, this means the coordinates of the incenter are about (1.08, 1.08) from the right angle vertex, so are about ...
incenter ≈ (-1.92, 1.08)
Answer:
There is a circle with a diameter[d] of 2.
Step-by-step explanation:
the Radius=diameter /2=2/2=1 units
now
circumference=2πr=2×π×1=6.29=6 units
area=πr²=3.14 unit²
Answer:
Yes
Step-by-step explanation:
5/4 = 1 1/4 or 1.25 and that I'd greater than 1
Answer: 3/64
Step-by-step explanation: I think you ask 3/4 divided by 32/2 if you are the answer is 3/64. How to divided is first simplify the expression, if possible, by canceling the common factors. But if your asking me to do 32/2 divided by 3/4 the answer is 64/3 if you want it to be an improper fraction but if you want it to be a mixed fraction it would be 21 1/3. How to divided is first simplify the expression, if possible, by canceling the common factors.