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amid [387]
3 years ago
14

Find two unit vectors orthogonal to a=⟨2,−2,−3⟩a=⟨2,−2,−3⟩ and b=⟨3,2,2⟩b=⟨3,2,2⟩ enter your answer so that the first non-zero c

oordinate of the first vector is positive.
Mathematics
1 answer:
Ronch [10]3 years ago
8 0
We need the cross product of the two vectors.
a x b
=<2,-2,-3> x <3,2,2>
=
i    j   k
2 -2 -3
3  2  2
=<-4+6, -(4+9), 4+6>
=<2,-13,10>
The second vector is obtained by reversing the direction, namely <-2,13,-10>
Thus the two vectors are <2,-13,10> and <-2,13,-10>.
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If You Have To Pay Someone $279 In Denominations Of $20 Or Less, What Is The Least Number Of Bills You Could Use?
Amiraneli [1.4K]
You can use 27 $10 bills which gets your at a total of $270 then you can use 1 $5 bill so now you're at $275 then you can use 4 $1 bills that gets you at your total of $279. The least number of bills you can use is 32.
5 0
3 years ago
A research company desires to know the mean consumption of meat per week among people over age 23. A sample of 164 people over a
Elan Coil [88]

Answer:

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.8}{2} = 0.1

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.1 = 0.9, so z = 1.28

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.28*\frac{0.7}{\sqrt{164}} = 0.07

The lower end of the interval is the mean subtracted by M. So it is 4.1 - 0.07 = 4.03 pounds

The upper end of the interval is the mean added to M. So it is 4.1 + 0.07 = 4.17 pounds

Rounded to one decimal place

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.

8 0
3 years ago
8-35. Use your knowledge of polygons to answer the questions below, if possible.
Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is 1980^0

Then:

(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13

The polygon has <u>13 sides.</u>

II. If the Interior angle is 900^0

Then:

(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7

The polygon has <u>7 sides.</u>

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: \frac{360^0}{n}

If the exterior angle of a regular polygon is 90°

Then:

90\°=\frac{360^0}{n}\\ 90n=360\\n=4

The regular polygon has 4 sides and it is called a <u>Square.</u>

<u>(c)</u>The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is:  \frac{(n-2)180^0}{n}

For a pentagon, n=5

Then:

\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0

(d)The <u>sum of the exterior angle of a polygon is 360 degrees.</u>

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

57+74+56+66+x=360^0\\253+x=360\\x=107^0

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180=1620^0

The sum of the interior angle <u>does not change either in a regular or irregular polygon.</u>

3 0
3 years ago
See screenshots for question and answer choices.
yawa3891 [41]

Answer:

I belive its 300

Step-by-step explanation:

Brainlist?

3 0
3 years ago
Read 2 more answers
What is the base for the expression -6 to the power of 4
natima [27]

For this case we have that by definition it is fulfilled:

a ^ b

Where:

a: It is the base

b: It is the exponent

So, if we have the following expression:

-6 to the power of 4, is equivalent to: (-6) ^ 4

So we have to:

-6: It is the base

4: It is the exponent

Answer:

-6: It is the base

4: It is the exponent

8 0
3 years ago
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