Answer:
16.5km
Step-by-step explanation:
Liola drives 17km up a hill that is at a grade of 14 degrees. What horizontal distance, to the nearest tenth of kilometer, has she covered?
We solve using Trigonometric function of Cosine
cos theta = Adjacent/Hypotenuse
Theta = 14°
Hypotenuse = Distance up the hill = 17km
Adjacent = Horizontal distance = x
Hence,
cos 14 = x/17
Cross Multiply
x = cos 14 × 17
x = 16.495027347km
Approximately = 16.5km
The horizontal distance = 16.5km
To find ur sets of numbers, u simply plug in any number for x and solve for y
-x - 3y = -6.....lets say x = 0
-3y = -6
y = -6/-3
y = 2......so one set of pints is (0,2)
-x - 3y = -6...lets say x = 3
-3 - 3y = -6
-3y = -6 + 3
-3y = -3
y = -3/-3
y = 1....so another set of points is (3,1)
-x - 3y = -6.....,ets say x = 6
-6 - 3y = -6
- 3y = -6 + 6
-3y = 0
y = 0....and another point is (6,0)
so some points on ur line are : (0,2), (3,1), (6,0)
Answer: 45cm
Step-by-step explanation:
The spring stretches 1/3 of the weight attached. 1/3 of 15 is 5. However, the spring is already 40cm long so we must add 5 to 40 to find the total length and of the spring.
Answer:
![x = \frac{\sqrt{6}}{2}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B2%7D%20)
Step-by-step explanation:
Reference angle = 45°
Opposite side = x
Hypotenuse = √3
Use the following trigonometric ratios formula to find x:
![sin(\theta) = \frac{opp}{hyp}](https://tex.z-dn.net/?f=%20sin%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopp%7D%7Bhyp%7D%20)
Plug in the values
![sin(45) = \frac{x}{\sqrt{3}}](https://tex.z-dn.net/?f=%20sin%2845%29%20%3D%20%5Cfrac%7Bx%7D%7B%5Csqrt%7B3%7D%7D%20)
Multiply both sides by √3
![\sqrt{3}*sin(45) = x](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%7D%2Asin%2845%29%20%3D%20x%20)
![\sqrt{3}*\frac{\sqrt{2}}{2} = x](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%7D%2A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%3D%20x%20)
![\frac{\sqrt{3*2}}{2} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Csqrt%7B3%2A2%7D%7D%7B2%7D%20%3D%20x%20)
![\frac{\sqrt{6}}{2} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B2%7D%20%3D%20x%20)