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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 cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus s0.05 per text. Plan B costs $10 per m
jek_recluse [69]

Answer:

200

Step-by-step explanation:

7 0
3 years ago
David wants to pack 574 cereal bars into bags of 10 and bags of 8 the number of bags of 8 is 2 more than the bags of 10. How man
BabaBlast [244]

Answer: Number of bags of 8. = 33

Number of bags of 10. = 31

Step-by-step explanation:

Let x = Number of bags of 8.

y = Number of bags of 10.

As per given.

8x+10y= 574   (i)

x=y+2 (ii)

Put value of x from (ii) in (i)

8(y+2)+10y= 574\\\\\Rightarrow\ 8y+16+10y=574\\\\\Rightarrow\ 18y=574-16\\\\\Rightarrow\ 18y=558\\\\\Rightarrow\ y=\dfrac{558}{18}\\\\\Rightarrow\ y=18

Put this in (i), x= 31+2=33

Hence,

Number of bags of 8. = 33

Number of bags of 10. = 31

6 0
2 years ago
A chemist is using 336 milliliters of a solution of acid and water. If 19.4 % of the solution is acid, how many milliliters of a
denpristay [2]

Answer:

65.2 milliliters

Step-by-step explanation:

The quantity 336 milliliters is the 100% of the solution. We can represent this information on a table:

Milliliters        Percentage of solution

     336        ⇔            100%

we are told that 19.4% of this solution is acid, and we need to know how many milliliters represents this percentage. I will call the number of milliliters of acid on the solution 'x', and updating the last table:

Milliliters        Percentage of solution

     336        ⇔            100

     x             ⇔            19.4%

We can solve this problem for 'x' using the<u> rule of three</u> which is to multiply the cross quantities on the table (336 by 19.4) and then divide by the remaining amount (100):

x = 336(19.4)/100

x = 6,518.4/100

x = 65.184

which rounding to the nearest tenth is: 65.2 milliliters

8 0
3 years ago
What is the negative number between -3 and -2
neonofarm [45]
-2.5 would be inbetween
6 0
3 years ago
Read 2 more answers
I need help with this.
alekssr [168]

Answer:

x=7

Step-by-step explanation:

8 0
2 years ago
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