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,
To do this you must combine like terms as follows.
7x + 6x = 13x
7 - 9 = -2
Combine these together and you will get the following.
13 - 2 or -2 +13
Answer:
x=5
Step-by-step explanation:
Since both of these length are equal, 6x+4=8x-6, 2x=10, x=5
Answer:
The length of KH is 6 units and OH is 6.3 units.
Step-by-step explanation:
Given the figure with lengths LO=5 and OK=4. we have to find the length of OH and KH.
In ΔLOH
By Pythagoras theorem
→ (1)
In ΔKOH,
→ (2)
In ΔKHL,
Using eq (1) and (2), we get
⇒ 
⇒ 
Put the above value in eq 2, we get
⇒ KH=6 units.
Answer:
The equation is H = 495 -6t
Step-by-step explanation:
Here, we want to write an equation that will represent the height Juan is above the ground, after t seconds.
The height we want to calculate is H. The initial height is 495 foot;
At the first second, the decrease in height will be 6 * 1, at the second 6 * 2 and thus at t seconds, the decrease in height will be 6 * t = 6t
Ask the height after t seconds will be;
H = 495 - 6t
Where t represents the time in seconds
