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m_a_m_a [10]
3 years ago
12

Find the unit vector in the direction of u = (-3,2).

Mathematics
1 answer:
DENIUS [597]3 years ago
7 0
\bf \textit{unit vector for }(a,b)\implies \left( \cfrac{a}{\sqrt{a^2+b^2}}~~,~~\cfrac{b}{\sqrt{a^2+b^2}} \right)\\\\
-------------------------------\\\\
(-3,2)\qquad \stackrel{unit~vector}{\implies }\qquad \left( \cfrac{-3}{\sqrt{(-3)^2+2^2}}~~,~~\cfrac{2}{\sqrt{(-3)^2+2^2}} \right)
\\\\\\
\left( -\cfrac{3}{\sqrt{13}}~~,~~ \cfrac{2}{\sqrt{13}}\right)\\\\
-------------------------------

\bf \textit{and now let's \underline{rationalize} the denominator for each}
\\\\\\
-\cfrac{3}{\sqrt{13}}\cdot \cfrac{\sqrt{13}}{\sqrt{13}}\implies -\cfrac{3\sqrt{13}}{13} \qquad \qquad \qquad \qquad  \cfrac{2}{\sqrt{13}}\cdot \cfrac{\sqrt{13}}{\sqrt{13}}\implies \cfrac{2\sqrt{13}}{13}
\\\\\\
\textit{and written in \underline{ai+bj form}}\qquad -\cfrac{3\sqrt{13}}{13}i~~~~+~~~~\cfrac{2\sqrt{13}}{13}j
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A line passes through the point (–7, 5) and has a slope of One-half. Which is another point that the line passes through?
irina1246 [14]

Answer:

(13, 9)

Step-by-step explanation:

Make an equation for the line.

y = 0.5x + b

5 = -3.5 + b

b = 8.5

y = 0.5x + 8.5

Plug them into the equation.

(-13, 9) 9 ≠ -6.5 + 8.5

(-9, 13) 13 ≠ -4.5 + 8.5

(9, 13) 13 = 6.5 + 8.5

(13, 9) 13 ≠ 4.5 + 8.5

7 0
3 years ago
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What is the probability of getting a sum 9 from two throws of a dice?
Fittoniya [83]

1/9 is the answer for that question

8 0
3 years ago
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I need help with this homework can anyone help me. I need work too, help is appreciated:)
quester [9]
Let x = # of tickets sold in advance 
Let y = # of tickets sold the day of 


Cost of the tickets & total sales: 6x & 10y = 6828

You also know y = x + 206

Take the equation mentioned above y = x + 206 and sub it in anywhere the variable y is in the other equations so you'll have this:
6x + 10(x+206) = 6828

Now solve for x to get x = 298

To finish the problem, you must now find the number of y tickets sold.
Sub your x value that you found back into the equation y = x + 206 and you'll get y = 504.

So, 298 tickets were sold in advance and 504 tickets were sold the day of
3 0
3 years ago
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What is the value of the y-intercept of the line 2x+5y=12?
Paladinen [302]

Using the slope-intercept form, the slope is  

2 /5  2/5.M= 25

8 0
3 years ago
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Find the measure of angle XAZ in the figure below.
Bess [88]

Answer:

m∠XAZ = 40°

Step-by-step explanation:

Since ∠YAU, ∠YAZ and ∠XAZ are the angles based at a point on a straight line, and the sum of the all angles on a line is 180°.

Therefore, m∠YAU + m∠YAZ + m∠XAZ = 180°

50° + 90° + m∠XAZ = 180°

m∠XAZ = 180° - 140°

             = 40°

Therefore, measure of angle XAZ is 40°.

5 0
3 years ago
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