X^4+ 3x^3+4x^2-8 | x+2 = x^3+x^2+2x-4
-x^4-2x^3
-----------------------
x^3+4x^2-8
-x^3-2x^2
-------------------------
2x^2-8
-2x^2-4x
--------------
-4x-8
4x+8
----------------------------
/ /
is a factor because (x+2)(x^3+x^2+2x-4)=x^4+3x^3+4x^2-8
The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)
This is the vector equation; getting the parametric form is just a matter of delineating
<em>x</em>(<em>t</em>) = 1 + <em>t</em>
<em>y</em>(<em>t</em>) = 3<em>t</em>
<em>z</em>(<em>t</em>) = 6 + <em>t</em>
Each box had at most 13 apples
I hope that helps!!!!!!
: )
The area of the polygon with the given vertices: (-3,3) (-3,-1) (4,-1) (4,3) is 28 square units
<h3>What is rectangle ?</h3>
A rectangle is a polygon with four sides. The opposite sides of a rectangle are equal while the angles at the vertex is orthogonal
<h3>How to solve for area of the rectangle</h3>
The following are the data given in the question
polygon with the given vertices' as:
(-3,3)
(-3,-1)
(4,-1)
(4,3)
plotting the given polygon shows it is a rectangle with sides
Length, L = 7 units
Width, w = 4 units
Area if a rectangle is given by
= L * w
= 7 * 4
= 28 square units
The area of the polygon is 28 square units
Learn more in area of rectangle: brainly.com/question/16239445
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