Answer: The side length of the pet shop sign=5/4 inches
Step-by-step explanation:
Given: Candy draws a square design with a side length of x inches for the window at the pet shop.
She takes the design to the printer and asks for a sign that has an area of 
square inches.
Let y(x) =
differentiating both sides w.r.t x we get
y'(x)=32x-40
to find critical point x ,Put y'(x)=0 then
⇒32x-40=0
⇒x=5/4
Therefore the side length of the pet shop sign=5/4 inches.
The answer is 4 because first numbers in orderes pair is always x cordinate
The value of the required integral is 50π where C is the positively oriented circle x2+y2=25
We are given a vector F = -yi + xj. A vector is a quantity with magnitude and direction that is commonly represented by a directed line segment, with length representing magnitude and orientation in space representing direction. We need to use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr where C is the positively oriented circle x² + y² = 25
Let the value of the integral be represented by the variable "I".
I = ∫∫[(/x)(x) - (/y)(-y)]dA
I = ∫∫[(1 - (-1)]dA
I = ∫∫2dA
I = 2∫∫dA
I = 2×(Area of the circle)
I = 2*(πr²)
I = 2*(π*25)
I = 50π
Hence, the value of the required integral is 50π.
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