Given:
The system of equations that represent the constraints for the given situation is
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Multiply equation (i) by 4.
...(iii)
Subtracting (iii) from (ii), we get
Divide both sides by 12.90.
Put this value in (i).
The solution of system of equations is x=1.5 and y=2.75. It means, the yards of silk are 1.5 and yards of cotton are 2.75.
55°
<h2> Step-by-step explanation:</h2>To solve this, follow these steps:
i. <em>Make a sketch of the problem</em>.
The sketch has been attached to this response.
ii. <em>Label the sketch properly</em>
As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).
iii. <em>Solve using the tangent trigonometric ratio</em>
With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being 5 units and 7 units respectively.
Using the tangent formula,
tan θ = opposite / adjacent
tan θ = 7 / 5
θ = tan⁻¹ (7/5)
θ = tan⁻¹ (1.4)
θ = 54.46
θ = 55° to the nearest integer.
Therefore, the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°
