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Answer:
19 by 38
Step-by-step explanation:
The area of the poster, A=xy
Margin at both up and bottom is 2inches, at the right and left is 1 inch
Then we can say
(x-4)(y-2)= 578
Let us make y subject of the formula
(y-2)= 578/(x-4)
y=[ 578/(x-4)] + 2
If we substitute into the area A equation we have
A= x { [ 578/(x-4)] + 2}
A= 2x + (578x)/(x - 4)
If we differentiate we have
A'(x)= [2+578(x-4)+578x ]/ (x-4)^2
=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2
=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2
If we simplify this we have
=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2
=( 2x^2 -16x - 2312) / (x-4)^2
At A'(x)= 0
= ( x^2 - 8x - 2312) / (x-4)^ =0
If we divide through by 2 we have
x^2 - 8x - 1156= 0
Solving the quadratic eqn( CHECK THE ATTACHMENT)
X= 38 or -30 then we choose the positive one, then x= 38
Then from area of the poster
A= (x-4)(y-2)= 578
Substitute 38 as value of x
(38-4)(y-2)= 578
34(y-2)=578
34y-68=578
34y=646
y=19
Hence dimensions of the poster is 19 by 38
CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION
The terms of this series may be arranged without changing the value of the series. The sum of the reciprocals of the squares of the odd positive integers is .
In mathematics, a sequence is the cumulative sum of a given collection of terms. Usually, those phrases are actual or complicated numbers, but plenty of extra generalities are feasible.
A series is described as an arrangement of numbers in a specific order. then again, a chain is described as the sum of the factors of a sequence.
In mathematics, a series is, more or less speaking, a description of the operation of including infinitely many quantities, one after the alternative, to a given beginning quantity. The look at of series is a primary part of calculus and its generalization, mathematical analysis.
k=1
1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.
up to ∞ terms = 2/6
[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+
..∞0] = T²/6
→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+
1/4(3)²+....0] =²/6
[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+
1/(3)²+....x] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6
⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6
=
↑
[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8
Learn more about the series here brainly.com/question/24295771
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