The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where 
is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
Add all the numbers inside the shape
Answer:
The range of values for x is; 5 < x < 29
Step-by-step explanation:
The given parameters are;
= 15
= 18
= 
Given
= by reflexive property
∠BCA = 2·x - 10
∠DCA = 48°
Since 15 < 18, given the common sides of the tringle ΔABC and triangle ΔADC, angle ∡(2·x - 10)° < 48°
Therefore;
2x - 10 < 48
2·x < 48 + 10
∴ x < 29
Also, given that 2·x - 10 is real, 0 < 2·x - 10
10 < 2·x
10/2 < x
5 < x
Therefore, an acceptable range is 5 < x < 29
Answer:
c²(1 + 3d)
Step-by-step explanation:
The sum of square of c and d is;
c² + d
Twice the product of c and d is;
2c²d
Because c² + d is increased by 2c²d the algebraic expression becomes;
c² + d + 2c²d
or
c²(1 + 3d)
