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givi [52]
3 years ago
6

The polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.

Mathematics
1 answer:
zaharov [31]3 years ago
4 0
Use the lengths of corresponding sides
so answer is 16:40  which simplifies to  2:5.
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Find two unit vectos that are orthogonal to both [0,1,2] and [1,-2,3]
alekssr [168]

Answer:

Let the vectors be

a = [0, 1, 2] and

b = [1, -2, 3]

( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.

Let the cross product be another vector c.

To find the cross product (c) of a and b, we have

\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]

c = i(3 + 4) - j(0 - 2) + k(0 - 1)

c = 7i + 2j - k

c = [7, 2, -1]

( 2 ) Convert the orthogonal vector (c) to a unit vector using the formula:

c / | c |

Where | c | = √ (7)² + (2)² + (-1)²  = 3√6

Therefore, the unit vector is

\frac{[7,2,-1]}{3\sqrt{6} }

or

[ \frac{7}{3\sqrt{6} } , \frac{2}{3\sqrt{6} } , \frac{-1}{3\sqrt{6} } ]

The other unit vector which is also orthogonal to a and b is calculated by multiplying the first unit vector by -1. The result is as follows:

[ \frac{-7}{3\sqrt{6} } , \frac{-2}{3\sqrt{6} } , \frac{1}{3\sqrt{6} } ]

In conclusion, the two unit vectors are;

[ \frac{7}{3\sqrt{6} } , \frac{2}{3\sqrt{6} } , \frac{-1}{3\sqrt{6} } ]

and

[ \frac{-7}{3\sqrt{6} } , \frac{-2}{3\sqrt{6} } , \frac{1}{3\sqrt{6} } ]

<em>Hope this helps!</em>

7 0
2 years ago
Solve:<br> (a+b+c) (a+b-c)
Katen [24]

Answer:

<h2><u><em>a²+2ab+b²-c²</em></u></h2>

Step-by-step explanation:

Solve:

(a+b+c) (a+b-c)=

(a²+ab-ac+ab+b²-bc+ac+bc-c²)=

a²+ab-ac+ab+b²-bc+ac+bc-c²=

a²+2ab+0ac+b²+0bc-c²=

a²+2ab+b²-c²

7 0
2 years ago
Read 2 more answers
Tickets for a concert cost $2 each for children and $5 each for adults.A group of 30 people consisting of children and adults pa
noname [10]
Let,
the no. of adults be "x"
then, the no. of childern = total people - total adults 
                                   = (30 - x)
Now,
According to the quesiton,
2 (30 - x) + 5x = 87
60 - 2x + 5x = 87
60 + 3x = 87
3x = 87 - 60
3x = 27
x = 27 / 3
x = 9

So, there were 9 adults in the group

3 0
2 years ago
How do I draw a quick picture to divide
Goshia [24]
what do u mean by ur question. it doesn't make sense
3 0
3 years ago
49 POINTS!!!
Tema [17]
Sphere to 1
cone to 7 
 cylinder to 5
<span>triangular prism to 4 
</span><span>cube to 3
</span><span>rectangular pyramid to 6
</span><span>triangular pyramid to 2
</span><span>rectangular prism to 8</span>
3 0
2 years ago
Read 2 more answers
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