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Answer:
3/4x = -24
To isolate the "x" variable, divide both sides by 3/4 (multiply by its reciprocal, or 4/3)
3/4x · 4/3 = -24 · 4/3
x = (-24 · 4) / 3
x = -32.
Answer:
Dimensions of printed area
w = 8.95 cm
h = 13.44 cm
A(max) = 120.28 cm²
Step-by-step explanation:
Lets call " x " and "y" dimensions of the poster area ( wide and height respectively) . Then
A(t) = 180 cm² = x*y y = 180/ x
And the dimensions of printed area is
A(p) = ( x - 2 ) * ( y - 3 ) then as y = 180/x we make A function of x only so
A(x) = ( x - 2 ) * ( 180/x - 3 ) ⇒ A(x) = 180 - 3x - 360/x +6
A(x) = - 3x - 360 /x + 186
Taking derivatives on both sides of the equation we get:
A´(x) = -3 + 360/ x²
A´(x) = 0 -3 + 360/ x² = 0 -3x² + 360 = 0
x² = 120 ⇒ x = √120 x = 10.95 cm
And y = 180 / 10.95 ⇒ y = 16.44 cm
Then x and y are the dimensions of the poster then according to problem statement
w of printed area is x - 2 = 10.95 - 2 = 8.95 cm
and h of printed area is y - 3 = 16.44 - 3 = 13.44 cm
And the largest printed area is w * h = ( 8.95)*(13.44)
A(max) = 120.28 cm²
Answer:
The essence of Mathematics lies in its freedom
11/3 in a mixed number is 3⅔
The diagonal is solved by a^2+b^2=c^2
c=8 in this problem, so c^2=64
Since the figure is a square, a must equal b.
64/2=32, each side is root of 32 units
the square root of 32 is approximately 5.66.
