Answer:
x = 7, y = 2
Step-by-step explanation:
I assume it is 3/(x-7) + 2.
When x = 7, there is an asymptote because it is undefined.
When y = 2, there is also one, because 3/(x-7) is never 0.
These are the only ones.
The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.
<h3>
How to s
olve the d
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Let x be the side of the square to remove. Then the volume of the box is:
V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³
To find the maximum volume, differentiate and set it to 0:
V'(x) = 324 - 144x + 12x²
0 = x² - 12x + 27
0 = (x - 9)(x - 3)
x = 3 or 9
When x = 3,
V"(x) =-144+24x
V"(3) =-144+72=-72<0
so volume is maximum at x=3
Therefore the box is 12x12x3 and the volume is 432.
Learn more about dimension on:
brainly.com/question/26740257
The sum of any geometric sequence, (technically any finite set is a sequence, series are infinite) can be expressed as:
s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=term number
Here you are given a=10 and r=1/5 so your equation is:
s(n)=10(1-(1/5)^n)/(1-1/5) let's simplify this a bit:
s(n)=10(1-(1/5)^n)/(4/5)
s(n)=12.5(1-(1/5)^n) so the sum of the first 5 terms is:
s(5)=12.5(1-(1/5)^5)
s(5)=12.496
as an improper fraction:
(125/10)(3124/3125)
390500/31240
1775/142
Answer:
See proof below
Step-by-step explanation:
One way to solve this problem is to "add a zero" to complete the required squares in the expression of xy.
Let 
and 
with 
. Multiplying the two equations with the distributive law and reordering the result with the commutative law, we get 
Now, note that 
by the commutativity of rational integers. Add this convenient zero the the previous equation to obtain 
, thus xy is the sum of the squares of 
.
