We can start this problem by finding out what the lowest consecutive number's value is (x). Since consecutive numbers are numbers that are 1 apart from each other, the sum of 9 consecutive numbers would look like
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)
Since we know that they equal 153,
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 153
Now we combine like terms
9x + 36 = 153
Simplify
9x = 117
x = 13
Now, we need to find what the 5th consecutive number is equal to. The fifth consecutive number is (x+4), so 13 + 4 is 17, meaning that the 5th of 9 consecutive numbers that add up to 153 is 17.
You didn’t include a graph so it cannot be answered, sorry
Answer:
Dh/dt = 1.273 ft/min
Step-by-step explanation:
Volume of cone V = 1/3 * π *r² * h
Then
DV/dt = 1/3* π *r² * Dh/dt (1)
We have to find out values of r when h = 5
By symmetry in a cone (we have proportion between h and r
when h = 10 ft r = 3 ft from problem statement
Then h = 5 ft r = 1.5 ft
That is from proportion 3/10 = X/5
Then by subtitution in (1)
DV/dt = 3 ft³/min r = 1,5 ft
3 = 1/3*π*(1.5)²* Dh/dt
3 = 2.355 Dh/dt
Dh/dt = 1.273 ft/min