Since you are trying to find the direction you have to use
tan theta= y/x
tan theta= 26/-5
theta= tan^-1I26/-5I
theta= 79.11 degrees but since (-5,26) is found in the second quadrant you have to substract 180 - a to obtain the direction angle
theta= 180 -a
=180 - 79.11
theta = 100.88 degrees
vector v has a direction angle of 100.88 degrees
2 1/2 + 3 5/8 - 1 5/6 = ?
First let's convert all the mixed numbers to improper fractions.
5/2 + 29/8 - 11/6
Now find the common denominator.
We have 2, 8, and 6. We can disregard 2 because it is a factor of both 8 and 6 so any common denominator for 8 and 6 will work for 2.
Multiples of 8: 8, 16, 24
Multiples of 6: 6, 12, 18, 24
Now rewrite each fraction with a denominator of 24.
60/24 + 87/24 -44/24
(60+87-44)/24
Answer: 103/24 pounds
With exponents of 10, the exponent really just tells you how many zeroes there are behind the 1. So, for example, 10^4=10000 (4 zeroes behind 1). When multiplying decimals by exponents of 10, you move the decimal to the right, and the amount of places is the exponent number. For example, if I multiply 5.34 by 10^2, I move the decimal over to the right 2 times and get 534.
So, if you just multiply these you get 9.36*10000, which is 93600.
Answer:
![(C)\dfrac{9+\sqrt{14} }{9+\sqrt{14} }](https://tex.z-dn.net/?f=%28C%29%5Cdfrac%7B9%2B%5Csqrt%7B14%7D%20%20%7D%7B9%2B%5Csqrt%7B14%7D%20%7D)
Step-by-step explanation:
To rationalize the expression:
![\dfrac{5-\sqrt{7} }{9-\sqrt{14} }](https://tex.z-dn.net/?f=%5Cdfrac%7B5-%5Csqrt%7B7%7D%20%7D%7B9-%5Csqrt%7B14%7D%20%7D)
In order to rationalize any Surdic expression, what is needed is <u>to multiply both the numerator and the denominator</u> of the rational function by the <u>conjugate of the denominator.</u>
In the example above:
The denominator is: ![9-\sqrt{14}](https://tex.z-dn.net/?f=9-%5Csqrt%7B14%7D)
Its conjugate therefore is: ![9+\sqrt{14}](https://tex.z-dn.net/?f=9%2B%5Csqrt%7B14%7D)
Therefore, we multiply the fraction by the expression:
![\dfrac{9+\sqrt{14} }{9+\sqrt{14} }](https://tex.z-dn.net/?f=%5Cdfrac%7B9%2B%5Csqrt%7B14%7D%20%20%7D%7B9%2B%5Csqrt%7B14%7D%20%7D)