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3 years ago

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Need help please help me

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yanalaym [24]3 years ago

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Write me the question

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Elena painted 5/9 of a wall, Matthew painted 3/9 of the wall. Kevin painted the rest of the wall. What fraction of the wall did

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How many three letter arrangements can be made from the letters of<br> COMPLEXITY?*

Natali [406]

Answer:

720 arrangements

Step-by-step explanation:

We have three spaces that we want to fill with any letter from "complexity":

__ __ __

For the first space, we have 10 letters to choose from (there are 10 letters in the word "complexity"). For the second space, since we have already used up one letter for the first space, we have 9 letters remaining to choose from. Similarly, we only have 8 letters remaining to choose from for the last space.

Now, we multiply them all together: 10 * 9 * 8 = 720 arrangements.

Note that we multiply instead of add. This is because for any letter we place in space 1, it can be paired with any of the 9 letters for space 2 and any of the 8 letters for space 3.

Hope this helps!

5 0

3 years ago

A. Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of v is the negative

pishuonlain [190]

Answer:

Part A:

$m_1m_2=-1$

$\frac{b}{a}(\frac{-a}{b})=-1\\-1=-1$

Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.

Part B:

Slope of vector = $\frac{b}{a}$

Step-by-step explanation:

Condition for perpendicular is:

$m_1m_2=-1$

Part A:

Consider the vector v = ai + bj

x component of vector=a

y component of vector=b

Slope of vector= $m_1=\frac{y}{x}=\frac{b}{a}$

Consider the line ax + by = c:

Rearranging the equation:

ax+by=c

by=c-ax

y= $\frac{-ax}{b}+\frac{c}{b}$

According to general equation of line: $y=mx+c$

Where m is the slope

In our case the slope of above line is:

$m_2=\frac{-a}{b}$

According to the condition of perpendicular:

$m_1m_2=-1$

$\frac{b}{a}(\frac{-a}{b})=-1\\-1=-1$

Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.

Part B:

Slope of vector is also calculated above.

Since the slope of vector is negative reciprocal of the slope of the given line:

According to equation of line ax + by = c

y= $\frac{-ax}{b}+\frac{c}{b}$

According to general equation of line: $y=mx+c$

Where m is the slope

Slope of given line=m= $\frac{-a}{b}$

negative reciprocal of the slope of the given line = $\frac{b}{a}$

Slope of vector = $\frac{b}{a}$

5 0

2 years ago