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3 years ago

A number is six greater than 12 times another number the sum of the two numbers is 214 find both numbers

1 answer:

6 0

Let x and y represent the two numbers.
.. x = 6 +12y . . . . . one number is 6 greater than 12 times another
.. x + y = 214 . . . . their total is 214

Substitute for x in the second equation using the first equation.
.. (6 +12y) +y = 214
.. 13y = 208 . . . . . . . . simplify and subtract 6
.. y = 16 . . . . . . . . . . . divide by 13
.. x = 214 -y = 198

The numbers are 198 and 16.

_____
These are solved easily any of several ways on a graphing calculator. You should learn to use yours for that purpose.

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Shkiper50 [21]

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3 years ago

Find the unit vector in the direction of (4,-4). Write your answer in component form. Do not approximate any numbers in your ans

aniked [119]

Answer:

$(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$

Step-by-step explanation:

The unit vector for a nonzero vector, say u, in the direction of u is given by:

û = $\frac{u}{|u|}$ ---------------(i)

Where;

|u| = magnitude of vector u

From the question;

u = (4, -4)

First let's calculate the magnitude of u as follows;

|u| = $\sqrt{(4)^2 + (-4)^2}$

|u| = $\sqrt{16 + 16}$

|u| = $\sqrt{32}$ = $4\sqrt{2}$

Now, substitute u and |u| into equation (i) as follows;

û = $\frac{(4, -4)}{4\sqrt{2} }$

û = $(\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} } )$

û = $(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$

Therefore, the unit vector is $(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )$

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3 years ago

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