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:
2x= 3x-7
-x=-7
x=7
so, the first option
Step-by-step explanation:
Answer:
years later , karen withdrew the full amount to put toward the down payment on a new house. How much did she withdraw? ... gaines invested $15,000 in a money market account with an interest rate of 2.75% compounded semiannually. ... Median response time is 34 minutes and may be longer for new subjects.
Answer:
( 2x - 3 ) / 5
Step-by-step explanation:
2x - 6 = 5y - 3
2x - 6 + 3 = 5y
2x - 3 = 5y
y = ( 2x - 3 ) / 5
Answer:
x = 3
y = 2
Step-by-step explanation:
When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.
So we can say:
-2x + 6y = 6
and
-7x + 8y = -5
Let's multiply first equation by 7 and 2nd equation by -2, to get:
7 [-2x + 6y = 6] = -14x +42y = 42
and
-2 [-7x + 8y = -5] = 14x - 16y = 10
Now adding these 2 new equations and solving for y:
-14x +42y = 42
14x - 16y = 10
----------------------
26y = 52
y = 52/26
y = 2
Now we put y = 2 into 1st equation (or any other) and solve for x:
-2x + 6y = 6
-2x + 6(2) = 6
-2x + 12 = 6
6 = 2x
x = 6/2
x = 3
