What are the monthly expenses? Here is the total money Mr.Watkins makes, $5600
Answer:
![\displaystyle \cos(A + B) =\frac{969}{1769}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28A%20%2B%20B%29%20%3D%5Cfrac%7B969%7D%7B1769%7D)
Step-by-step explanation:
We are given that:
![\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%20A%3D%5Cfrac%7B20%7D%7B29%7D%5Ctext%7B%20and%20%7D%20%5Ctan%20B%3D%5Cfrac%7B11%7D%7B60%7D)
Where A and B are positive acute angles.
And we want to find cos(A + B).
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:
![o=\sqrt{29^2-20^2}=21](https://tex.z-dn.net/?f=o%3D%5Csqrt%7B29%5E2-20%5E2%7D%3D21)
Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:
![h=\sqrt{11^2+60^2}=61](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B11%5E2%2B60%5E2%7D%3D61)
In summary:
With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.
With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.
We can rewrite our expression as:
![\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28A%2BB%29%3D%5Ccos%20A%5Ccos%20B-%5Csin%20A%5Csin%20B)
Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:
![\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28A%20%2B%20B%29%3D%5Cleft%28%5Cfrac%7B20%7D%7B29%7D%5Cright%29%5Cleft%28%5Cfrac%7B60%7D%7B61%7D%5Cright%29-%5Cleft%28%5Cfrac%7B21%7D%7B29%7D%5Cright%29%5Cleft%28%5Cfrac%7B11%7D%7B61%7D%5Cright%29)
Simplify:
![\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28A%20%2B%20B%29%20%3D%5Cfrac%7B1200-231%7D%7B1769%7D%3D%5Cfrac%7B969%7D%7B1769%7D)
A line that's perpendicular would have a slope that the negative reciprocal of the line in the question
1. use the points to find the slope
(y1-y2)/(x1-x2)
=(-3-7)/(-7+5) (it's +5 because --5=+5)
=-10/-2
-5
slope of the line is -5
2. The negative reciprocal is basically flipping over a fraction (3/4 would become 4/3) and then multiplying it by -1 (4/3 would become -4/3)
Because -5 is really -5/1 you would flip it to -1/5 then multiple by -1 to equal 1/5.
3. Now we just need any line that has a slope of 1/5
y=mx+b where m=1/5 and b is whatever number you want
y=1/5x+8
y=1/5x-193748
y=1/5x-103595
All these are right answers just pick your favourite number for b
Always, ALWAYS remeber this format: y = mx + b
In this equation, 'm' is the slope, and 'b' is the y-intercept
When you're trying to find a slope, remember that the equation is ![\frac{rise}{run}](https://tex.z-dn.net/?f=%5Cfrac%7Brise%7D%7Brun%7D)
When finding the rise and run, look at two points that are on the graph AND on the line as well. Essentially, make sure the points you're using are integers.
In this, case, the rise is -3, and the run is 2. This means that the slope is ![\frac{-3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B2%7D)
Now we have the first part of our equation:
y = -
+ b
But wait! How do we find b?
Sometimes you have to input x in order to find it, but only when you're not supplied with a graph. In this case, all you have to do is look!
The point of the line that is on the y-axis is called the y-intercept.
In this graph, the y-intercept is -1
Now we have our complete equation!
y = -
- 1
Good luck!
Answer: about 54 ft." .
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Explanation:
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A = L * w ;
A square is a rectangle that has all equation sides;
so; for a square. (L = w).
or, "A = s² " ; in which "s" in the length of any one side.
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Since "A = s² "
And "A = 182 ft² " ;
we need to solve for "s" ;
and then find the perimeter of the square with is: "4*s" .
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A = s² ; ↔ s² = A ; s² = 182 ft² ;
Take positive square root of each side of the equation; to isolate "s" on one side of the equation ; and to solve for "s" ;
√(s²) = √(182 ft²) ;
to get: s = √182 ft, = 53.9629502529281659 ft.
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The perimeter: 4* s = 4√(182 ft) = 4* (13.4907375632320415 ft.) ;
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= 53.9629502529281659 ft.
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round to 54 ft.
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