Given:
Consider the below figure attached with this question.
To find:
The measure of angle r by using the cosine rule.
Solution:
According to Law of Cosine,

Using the Law of Cosine, we get




On further simplification, we get






Therefore, the measure of angle r is 106.78 degrees.
Answer:
0.495
Explanation:
Given the expression:
![0.55-1.645\sqrt[]{\frac{0.55(1-0.55)}{220}}](https://tex.z-dn.net/?f=0.55-1.645%5Csqrt%5B%5D%7B%5Cfrac%7B0.55%281-0.55%29%7D%7B220%7D%7D)
Begin by simplifying the expression under the radical (square root) sign.
![\begin{gathered} =0.55-1.645\sqrt[]{\frac{0.55(0.45)}{220}} \\ =0.55-1.645\sqrt[]{\frac{0.2475}{220}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%3D0.55-1.645%5Csqrt%5B%5D%7B%5Cfrac%7B0.55%280.45%29%7D%7B220%7D%7D%20%5C%5C%20%3D0.55-1.645%5Csqrt%5B%5D%7B%5Cfrac%7B0.2475%7D%7B220%7D%7D%20%5Cend%7Bgathered%7D)
Using a calculator, we evaluate the radical:
The amount of water Julian and Stacey needed to fill the tank = 10 liters
Amount of water filled by Stacey individually = 3 11/12 liters
= 47/12 liters
It is given in the question that Julian poured 12/5 liters less than Stacey.
Then Amount of water filled by Julian = (47/12) - (12/5) liters
= (235 - 144)/60
= 91/60
So Julian filled 91/60 liters of water in the tank.
Amount of water still needed to fill the tank = 10 - [(47/12) - (91/60)]
= 10 - [(235 - 91)/60]
= 10 - (144/60)
= 10 - 12/5
= (50 - 12)/5
= 38/5
= 7 3/5
so 7 3/5 liters of water is still required to fill the tank.
Answer:
combining 2x and 4x to make 6x
Step-by-step explanation:
Function s is the set of points: {(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)}
aksik [14]
Given:
The function in the form of set of points is

To find:
(a) The inverse of function s.
(b) whether the inverse of function s is a function?
Solution:
(a)
If a function is
, then its inverse function is

We have,

So, inverse of this function is

Therefore, the inverse of function s is
.
(b)
A set of point is a function if there exist unique output for each input.
In inverse of s, we have two output values y=4 and y=5 for single input x=3.
Therefore, the inverse of function s is not a function.