Volumes of revolution are so fun
lets say you have 2 functions f(x) and g(x) where they intersect at c and d where c<d, and f(x) is on top of g(x) (like for a value r where c<r<d, f(r)>g(r)), the volume is
ok, so find the intersection points of
and y=9
9=9x^3
1=x^3
at x=1
so then the area will be from x=0 to x=1
which ones's higher?
try x=0.5
at x=0.5, 9(0.5)^3<9
so the y=9 is on top
therfor
limits are from 0 to 1
higher one is y=9
bottom function is y=9x^3
so the volume is
we can factor out the 81
factor out the constant
integrate
the area is
square units
Step-by-step explanation:
x+5x=180
6x=180
x=30
and 5x=150
Answer:
y=10x
Step-by-step explanation:
10 is the slope or the rate of change.
Answer:
13)
Line A - slope/constant of proportionality = 5/2
Line B - slope/constant of proportionality = 2/3
14)
unit rate = 3/2 or 1.5
The unit rate, 3/2, is greater than line B's unit rate but is less than line A's unit rate.
Step-by-step explanation:
To find the constant of proportionality for question 13 you use the graph. k = y/x so you find the point at (4, 10) and you go up 10 (y) and over 4 (x). So now you have 10/4 and then you simplify to 5/2. Use the same method for line B to find the slope. Now for question 14 you subtract 10 - 5 to get 5 which is your x and 15- 7.5 to get 7.5 which is the y. So this is now 7.5/5 (y/x) or 3/2. 3/2 is less than 5/2 and greater than 2/3.
Thank you so much!!! Hope this helps!!!
Answer: r>43
Step-by-step explanation
R is Raj's Height
The problem is Raj's height is 43
So this is the > less than sign
so by default is 43 is less than Raj's height then
r>43