Given that 3x-y : x+2y = 2 : 5, Determine the ratio x:y
1 answer:
Answer:
x : y = 9 : 13
Step-by-step explanation:
Given that
3x - y : x + 2y = 2 : 5
Express the ratio in fractional form, that is
=
( cross- multiply )
5(3x - y) = 2(x + 2y) ← distribute parenthesis on both sides )
15x - 5y = 2x + 4y ( subtract 2x from both sides )
13x - 5y = 4y ( add 5y to both sides )
13x = 9y ( divide both sides by 13 )
x = y ( divide both sides by y )
=
, that is
x : y = 9 : 13
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Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
