Find, corrrect to the nearest degree, the three angles of the triangle with the given vertices. D(0,1,1), E(-2,4,3), C(1,2,-1)
Sholpan [36]
Answer:
The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.
Step-by-step explanation:
The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.
Thank you for reading this and I hope it is helpful to you.
Answer:
Step-by-step explanation:
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Good evening ,
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Look at the photo below for the answer,
:)
This is a good question!
The steps are like follows:
Form the confidence level (99%), we calculate the "alpha" value
alpha=1-(99/100)=0.01
Now, calculate the critical probability (p-start)
p*=1-(alpha/2)=1-(0.01/2)=0.995
z-score could be calculated from p*,,,
z-score=<span>2.57583
(http://www.socscistatistics.com/tests/ztest/zscorecalculator.aspx)
Now, calculate the Margin of Error:
</span>standard<span> deviation = s
number of adults = n
</span><span>
ME=(z*s)/(sqrt n)=(</span><span>2.57583*12)/(sqrt 250) = 1.955
The confidence interval = mean +or- ME
= 70+1.955</span> or 70-1.955
So that we can conclude that <span>the 99% confidence interval for the mean beats per minute is 68.045 and 71.955
</span>
I hope you got
the idea!
If you still need help, just let me know!
The greatest possible number of club members is 7
<em><u>Solution:</u></em>
Given that, local readers’ club has a set of 49 hardback books and a set of 21 paperbacks
Each set can be divided equally among the club members
To find the greatest possible number of club members, we have to find the greatest common factor of 49 and 21
The greatest number that is a factor of two (or more) other numbers.
When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
<em><u>Greatest common factor of 49 and 21:</u></em>
The factors of 21 are: 1, 3, 7, 21
The factors of 49 are: 1, 7, 49
Then the greatest common factor is 7
Thus, the greatest possible number of club members is 7
