Answer:
See explanation
Step-by-step explanation:
The constant of variation is found using the slope formula:
The given relation is
X : -2 , -3, -4, -5
Y : -5, -7.5,-10,-12.5
We can use any two ordered pair to find the constant of variation.
Using (-2,-5) and (-3,-7.5), we have
The constant of variation is 2.5
We need to repeat this for all the options to identify the one with -2.5 as slope.
unfortunately, you did not provide the remaining options.
Answer:
<em>4,524 gallons</em>
Step-by-step explanation:
The volume of any cylinder is
π (radius)² (height) .
The pool's radius is 1/2 its diameter = 8 ft. So its volume is
π (8 ft)² (3 ft)
= π · (64 ft²) · (3 ft)
= π · 192 ft³
= 603.2 ft³ .
(603 ft³) · (7.5 gal / 1 ft³) = 4,524 gallons
Hope this helps :D
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
8 x 1.25 = 10
or you could do 8 x 0.25 = 2
8 + 2 = 10
