Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.
You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:
ft.
Answer: the height of the statue is 2.0565 ft.
On the bottom line, the 106 and number 1 make a straight line and needs to equal 180 degrees.
This means number 1 = 180-106 = 74 degrees.
Because x and y are parallel, the top outside angle is the same as number 1.
6x +8 = 74
Subtract 8 from both sides:
6x = 66
divide both sides by 6:
x = 66 / 6
x = 11
Now you have x, replace x in the equation for 7x-2 to find that angle:
7(11) -2 = 77-2 = 75 degrees.
The three inside angles need to equal 180 degrees.
Angle 2 = 180 - 74 - 75 = 31 degrees.
Answer:
tan G = 1.6071
Step-by-step explanation:
tan G = 45/28
tan G = 1.6071
1. Let a and b be coefficients such that
Combining the fractions on the right gives
so that
2. a. The given ODE is separable as
Using the result of part (1), integrating both sides gives
Given that y = 1 when x = 1, we find
so the particular solution to the ODE is
We can solve this explicitly for y :
![\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|](https://tex.z-dn.net/?f=%5Cln%7Cy%7C%20%3D%20%5Cln%5Cleft%7C%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%5Cright%7C)
![\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%7D)
2. b. When x = 9, we get
![y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B45%7D%7B21%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B15%7D7%7D%20%5Capprox%20%5Cboxed%7B1.29%7D)
