Triangles with height 
and base 
, with 
have area 
.
Such cross sections with the base of the triangle in the disk 
(a disk with radius 5) have base with length
i.e. the vertical (in the 
plane) distance between the top and bottom curves describing the circle 
.
So when 
, the cross section at that point has base
so that the area of the cross section would be 6^2/2 = 18.
In case it's relevant, the entire solid would have volume given by the integral
Let's convert the problem into Arithmetic progression:
It would be: 5, 9, 13, ....
Here, a = 5, d = 9 - 5 = 4
We know, S(n) = n/2 [ 2a + (n-1)d ]
Substitute the known values,
434 = n/2 [ 2(5) + (n - 1)4 ]
434 * 2 = n [ 10 + 4n - 4 ]
868 = 10n + 4n² - 4n
= 4n² + 6n - 868 = 0
d = b² - 4ac
d = 6² - 4(4)(-868)
d = 36+13888
d = 13924
Now, roots = -b +- √d / 2a
= (-6 + √13924) / 2(4) OR (-6 - √13924) / 2(4)
= (-6 + 118) / 8 OR (-6 - 118) / 8
= 112/8 OR -124/8
= 14 OR -15.5
As number of sticks can't be in negative/decimal or fraction form, -15.5 would be fully rejected.
In short, Your Answer would be 14 [ Remaining root ]
Hope this helps!
Answer:
E. If two angles are complimentary, then the sum of the measures of the angles is 90.
Step-by-step explanation:
When making two logarithms one logarithm you keep the base (in this case that would be 2) and multiply the two numbers (in this case 7 times 6 = 42) so the answer is
log(2) 42
Draw out a number line with the values 0, 5, 10, 15, 20, 25, 30, etc (basically multiples of 5)
Then plot a point at 25
-----------------
Or you can draw out a number line with the multiples of 10, so with the values 0, 10, 20, 30, ...
Then plot a point at the exact midway point between 20 and 30 to represent the value 25
