Given:
θ = 60°
Opposite side of θ = 6
Adjacent side of θ = x
Hypotenuse = y
To find:
The value of x and y.
Solution:
Using basic trigonometric ratio formula:
![$\tan\theta =\frac{\text{Opposite side of } \theta}{\text{Adjacent side of } \theta}](https://tex.z-dn.net/?f=%24%5Ctan%5Ctheta%20%3D%5Cfrac%7B%5Ctext%7BOpposite%20side%20of%20%7D%20%5Ctheta%7D%7B%5Ctext%7BAdjacent%20side%20of%20%7D%20%5Ctheta%7D)
![$\tan60^\circ=\frac{6}{x}](https://tex.z-dn.net/?f=%24%5Ctan60%5E%5Ccirc%3D%5Cfrac%7B6%7D%7Bx%7D)
The value of tan 60° = √3
![$\sqrt{3} =\frac{6}{x}](https://tex.z-dn.net/?f=%24%5Csqrt%7B3%7D%20%3D%5Cfrac%7B6%7D%7Bx%7D)
Multiply by x on both sides.
![$\sqrt{3} \times x=\frac{6}{x} \times x](https://tex.z-dn.net/?f=%24%5Csqrt%7B3%7D%20%5Ctimes%20x%3D%5Cfrac%7B6%7D%7Bx%7D%20%5Ctimes%20x)
![$\sqrt{3} \times x=6](https://tex.z-dn.net/?f=%24%5Csqrt%7B3%7D%20%5Ctimes%20x%3D6)
Divide by √3 on both sides, we get
![$\frac{\sqrt{3} \times x}{\sqrt{3} } =\frac{6}{\sqrt{3} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%7B3%7D%20%5Ctimes%20x%7D%7B%5Csqrt%7B3%7D%20%7D%20%3D%5Cfrac%7B6%7D%7B%5Csqrt%7B3%7D%20%7D)
![x=2\sqrt{3}](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B3%7D)
Using Pythagoras theorem:
![\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2](https://tex.z-dn.net/?f=%5Ctext%7BHypotenuse%7D%5E2%20%3D%20%5Ctext%7BOpposite%7D%5E2%20%2B%20%5Ctext%7BAdjacent%7D%5E2)
![y^2 = 6^2 +({2\sqrt {3}})^2](https://tex.z-dn.net/?f=y%5E2%20%3D%206%5E2%20%2B%28%7B2%5Csqrt%20%7B3%7D%7D%29%5E2)
![y^2 = 36 +12](https://tex.z-dn.net/?f=y%5E2%20%3D%2036%20%20%2B12)
![y^2 = 48](https://tex.z-dn.net/?f=y%5E2%20%3D%2048)
Taking square root on both sides, we get
![y=4 \sqrt{3}](https://tex.z-dn.net/?f=y%3D4%20%5Csqrt%7B3%7D)
Therefore, the exact values of x and y are
.
An example of an exponential graph function has been attached and its' properties are as below.
<h3>How to draw the graph of an exponential function?</h3>
The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.
The reasons for the restrictions are because;
If a ≤ 0, then when you raise it to a rational power, you may not get a real number.
The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.
- The graph passes through the point (0,1)
- The domain is all real numbers
- The graph is asymptotic to the x-axis as x approaches negative infinity
- The graph increases without bound as x approaches positive infinity
Read more about Exponential Function Graphs at; brainly.com/question/2456547
#SPJ1
Answer:
81.9%
Step-by-step explanation:
(65.50 ÷ 79.99) X 100
Answer:
Rate of snow fall per hour ≥ 1 inches per hour
Step-by-step explanation:
Given:
Amount of snow already settled = 4 inches
Time period of snow fall = 2 hour
New amount of snow = least 6 inches
Computation:
Extra amount of snow ≥ New amount of snow - Amount of snow already settled
Extra amount of snow ≥ 6 - 4
Extra amount of snow ≥ 2 inches
Rate of snow fall per hour ≥ Extra amount of snow / Time period of snow fall
Rate of snow fall per hour ≥ 2 / 2
Rate of snow fall per hour ≥ 1 inches per hour
First,we need to understand the point-slope form:
![y1 - y2 = m(x1 - x2)](https://tex.z-dn.net/?f=y1%20-%20y2%20%3D%20m%28x1%20-%20x2%29)
Where x and y are the coordinates and m is the slope.
Put the above information into the equation:
y-(-6)=-3/4(x-2)
y+6 = -3/4 (x-2)
Therefore the answer is C.y+6 = -3/4 (x-2).
Hope it helps!