<u><em>Answer:</em></u>
The bird is approximately 9 ft high up in the tree
<u><em>Explanation:</em></u>
The required diagram is shown in the attached image
Note that the tree, the cat and the ground form a right-angled triangle
<u>Therefore, we can apply special trigonometric functions</u>
<u>These functions are as follows:</u>
<u>Now, taking a look at our diagram, we can note the following:</u>
α = 25°
The opposite side is the required height (x)
The adjacent side is the distance between the cat and the tree = 20 ft
Therefore, we can use the <u>tan function</u>
<u>This is done as follows:</u>
which is 9 ft approximated to the nearest ft
Hope this helps :)
In order to invert a function, switch y and x in the definition, and solve for y again:
Solving for y, we have
Answer:
- <em>The value of the constant is </em><u>0.8</u>
Explanation:
<em>The graph</em> has the following properties:
- Horizontal-axis (independent variable): width
- Vertical-axis (dependent variable): height
- Points on the curve:
(0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)
<em>The equation</em> represented by the graph is an inverse variation:
- Height = constant / width.
From that equation, you can solve for the contstant:
- constant = height × width
Now, you can take any ordered pair to find the constant:
- (0.5, 1.6) ⇒ constant = 0.5 × 1.6 = 0.8
- (0.8, 1) ⇒constant = 0.8 × 1 = 0.8
- (1.6, 0.5) ⇒ constant = 1.6 × 0.5 = 0.8
- (2, 0.04) ⇒ constant = 2 × 0.4 = 0.8
Thus, you have obtained that the constant is 0.8.
<u>Solution</u><u>:</u>
- Now, square root and square gets cancel out in the LHS. And in the RHS, apply the identity: (a + b)² = a² + 2ab + b².
- Now, transpose 4x and 4 to LHS.
- Now, do the addition and subtraction.
<u>Answer</u><u>:</u>
<u>x </u><u>=</u><u> </u><u>±</u><u> </u><u>3</u>
Hope you could understand.
If you have any query, feel free to ask.