Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

The angle between vector and is approximately radians, which is equivalent to approximately .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

To be precise, if denotes the angle between and (assume that or equivalently ,) then:

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The first component of is and the first component of is also

The second component of is while the second component of is . The product of these two second components is .

The dot product of and will thus be:

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Apply the Pythagorean Theorem to both and :

Let represent the angle between and . Apply the formula to find the cosine of this angle:

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Since is the angle between two vectors, its value should be between and ( and .) That is: and . Apply the arccosine function (the inverse of the cosine function) to find the value of :

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b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: