Answer:
114 ft
Step-by-step explanation:
Imagine or construct a right triangle with the 46 ft leg lying on the ground. This is the "adjacent side" of the triangle; it lies immediately adjacent to the 68 degree angle. The side opposite this angle is h, the height of the tree.
The tangent function includes angle, opp side and adj side:
tan 68 degrees = opp / adj = h / (46 ft), and so:
(46 ft)*tan (68 degrees) = opp = h
Then the height of the tree is h = (46 ft)(2.47) = 114 ft
Answer:
k = 10
Step-by-step explanation:
f(x) has been moved up 10 units to get g(x). So, k = 10
Do you mean <span><span><span><span>cos6</span>x+6<span>cos4</span>x+15<span>cos2</span>x+10</span><span><span>cos5</span>x+5<span>cos3</span>x+10cosx</span></span> ?</span>
or <span><span><span>cos6x+6cos4x+15cos2x+10</span><span>cos5x+5cos3x+10cosx</span></span> ?</span>
or <span><span><span><span>cos6</span>x+6<span>cos4</span>x+15<span>cos2</span>x+10</span><span><span>cos5</span>x</span></span>+5<span>cos3</span>x+10cosx ?</span>
or <span><span><span>cos6x+6cos4x+15cos2x+10</span><span>cos5x</span></span>+5cos3x+10cosx <span>?</span></span>
So, I came up with something like this. I didn't find the final equation algebraically, but simply "figured it out". And I'm not sure how much "correct" this solution is, but it seems to work.
![f(x)=\sin(\omega(x))\\\\f(\pi^n)=\sin(\omega(\pi^n))=0, n\in\mathbb{N}\\\\\\\sin x=0 \implies x=k\pi,k\in\mathbb{Z}\\\Downarrow\\\omega(\pi^n)=k\pi\\\\\boxed{\omega(x)=k\sqrt[\log_{\pi} x]{x},k\in\mathbb{Z}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csin%28%5Comega%28x%29%29%5C%5C%5C%5Cf%28%5Cpi%5En%29%3D%5Csin%28%5Comega%28%5Cpi%5En%29%29%3D0%2C%20n%5Cin%5Cmathbb%7BN%7D%5C%5C%5C%5C%5C%5C%5Csin%20x%3D0%20%5Cimplies%20x%3Dk%5Cpi%2Ck%5Cin%5Cmathbb%7BZ%7D%5C%5C%5CDownarrow%5C%5C%5Comega%28%5Cpi%5En%29%3Dk%5Cpi%5C%5C%5C%5C%5Cboxed%7B%5Comega%28x%29%3Dk%5Csqrt%5B%5Clog_%7B%5Cpi%7D%20x%5D%7Bx%7D%2Ck%5Cin%5Cmathbb%7BZ%7D%7D)
Answer:
4y^3/2
Step-by-step explanation:
The 4 will remain 4 so we'll leave that alone. √y³ can be written as y^3/2. The way I like to remember how to write fractional exponents is that the index of the radical is the denominator of the fractional exponent and the exponent inside the radical is the numerator.
