Component: (15, 75), magnitude about 76 is our correct answer.
Boxes of blue cups moving along a conveyor belt are described by a vector with components (6, 30).
Boxes of red cups are moving along the same conveyor belt but 2.5 times the distance blue cups moved.
We need to find the vector that describes the boxes of red cups and the magnitude of this vector.
What is a vector?
A vector is a quantity that has magnitude and direction denoted by:
[tex]V = (V_x, V_y)\\\\Where~~V_x = Vcos\theta~~and~~V_y = Vsin\thetaV_x ~and~V_y~are~ its~ components.[/tex]
Its magnitude is given by:
[tex]|V| = \sqrt{V_x+V_y}[/tex]
Since boxes of red cups move 2.5 times the distance along the same belt as blue cups moved.
We can describe the vector that shows the path of the boxes of red cups as:
= 2.5 x (6, 30)
= ( 2.5x6, 2.5x30 )
= ( 15, 75 )
The magnitude of the vector ( 15, 75 ) is:
[tex]|V| = \sqrt{15^2+75^2}\\\\|V| = \sqrt{225+5625}\\\\|V| = \sqrt{5850}\\\\|V| = 76.48\\\\|V| = 76[/tex]
Rounding 76.48 to its nearest whole number we get,76.
Thus, we have the required vector along with its component as (15, 75) and the magnitude about 76.
Learn more about finding the magnitude of a Vector here:
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