Mathematics, 18.07.2019 21:00 josephjannace12

If north is the direction of the positive y-axis and east is the direction of the positive x-axis, give the unit vector pointing northwest.

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North is the direction of positive y-axis. East is the direction of positive x-axis. So West will be the direction of negative x-axis.

Northwest will mean, in between north and west i.e. in between y-axis and the negative x-axis which is the mid of the 2nd quadrant. Thus the vector pointing northwest will form an angle of 135 degrees with positive x-axis.

The magnitude of unit vector is 1 and is forming an angle of 135 degrees. In terms of its components, we can write:

x-component = 1 cos (135) = $- \frac{ \sqrt{2} }{2}$
y-component = 1 sin (135) = $\frac{ \sqrt{2} }{2}$

Thus the unit vector will be = $- \frac{ \sqrt{2} }{2}x+ \frac{ \sqrt{2} }{2}y$

In vector form, component form the vector can be written as:

$(- \frac{ \sqrt{2} }{2}, \frac{ \sqrt{2} }{2})$

Answer from: lele650

A vector pointing northwest passes through point (-1, 1).

Thus an example of a unit vector pointing northwest is -i+j

.

Recall that a vector is made a unit vector by dividing each component of the vector by the magnitude of the vector.

The magnitude of vector -i+j

is given by $|-i+j|=\sqrt{(-1)^2+1^2}=\sqrt{1+1}}=\sqrt{2}$ .

Thus, a unit vector pointing northwest is $- \frac{1}{\sqrt{2}} i+ \frac{1}{\sqrt{2}} j$ which when we rationalize we have $- \frac{\sqrt{2}}{2} i+ \frac{\sqrt{2}}{2} j$ .

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

$w\geq 14$