Answer:
90 cubic inches
Step-by-step explanation:
Answer:
Step-by-step explanation:
![\dfrac 12 \left[\sin(a+b)+\sin(a-b) \right]\\\\\\=\dfrac 12\left[ 2 \sin a \cos b\right]\\\\\\=\sin a \cos b](https://tex.z-dn.net/?f=%5Cdfrac%2012%20%5Cleft%5B%5Csin%28a%2Bb%29%2B%5Csin%28a-b%29%20%5Cright%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%2012%5Cleft%5B%202%20%5Csin%20a%20%5Ccos%20b%5Cright%5D%5C%5C%5C%5C%5C%5C%3D%5Csin%20a%20%5Ccos%20b)
Since they are right triangles use Pythagorean Theorem.
a^2 + b^2 = c^2 where c is the hypotenuse.
a. 12^2 + b^2 = 13^2
144 + b^2 = 169
subtract 144 from both sides
b^2 = 25
take the square root of both sides
t = 5 This is also know as a Pythagorean Triple 5-12-13
b. a^2 + 9^2 = 12^2
a^2 + 81 = 144
subtract 81 from both sides
a^2 = 63
take the square root of both sides
a = √63
a = √(9 * 7)
a = 3√7
c. 6^2 + 9^2 = c^2
36 + 81 = c^2
117 = c^2
take the square root of each side
c = √117
c = √(9*13)
x = 3√13
Top of Statue |
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Frank -----------------------------------------------Base
Frank - Base = 400 ft
Base- Top statue = 360 feet
Angle of elevation =Angle Top-Franck-Base, let it be angle Ф
tan (Ф) = 360/400 = 0.9
arc tan (0.9) = tan⁻¹(0.9) = 41.98 ,
Ten angle of elevation Ф ≈ 42°
So if x= number of trees, and y= rental applications, the owner wants to see if increasing x will increase y. The correlation coefficient is between -1 and 1. If the number of trees really does have a positive impact on rental applications, the correlation coefficient would be close to 1. If there is absolutely no relationship, the coefficient would be near zero. If planting trees causes a DECLINE in rental applications, the coefficient would be close to -1.
