Answer:
Angle of elevation at which the balloon must take off in order to avoid hitting the tree is 5 degrees
Step-by-step explanation:
Given:
The height of the tree = 65 foot
The distance between the tree and the spot from which the balloon is launched = 250 yards
To find:
The angle of elevation at which the balloon must take off in order to avoid hitting the tree = ?
Solution:
Converting the yards to feet
1 yards = 3 feet
250 yards = 3 x 250 = 750 yards
Refer the below figure, The angle x is the angle of elevation at which the the ball must be thrown so that it does not Hit the tree
![tan(x) = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=tan%28x%29%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Substituting the values
![tan(x) = \frac{65}{750}](https://tex.z-dn.net/?f=tan%28x%29%20%3D%20%20%5Cfrac%7B65%7D%7B750%7D)
![tan(x) = 0.086](https://tex.z-dn.net/?f=tan%28x%29%20%3D%200.086)
![x = tan^{-1}(0.086)}](https://tex.z-dn.net/?f=x%20%3D%20tan%5E%7B-1%7D%280.086%29%7D)
![x = 4.91^{\circ}](https://tex.z-dn.net/?f=x%20%3D%20%204.91%5E%7B%5Ccirc%7D)
![x \approx5^{\circ}](https://tex.z-dn.net/?f=x%20%5Capprox5%5E%7B%5Ccirc%7D)
Answer:
AD= 15
AB=30
Step-by-step explanation:
We are given that the Point D bisect the line segment AB
Hence AD = DB
AD= 4x-1
BD=9x-21
Hence
4x-1=9x-21
adding 21 on both sides and subtracting 4x from both sides
4x-4x-1+21=9x-4x-21+21
-1+21=5x
5x=20
dividing both sides by x we get
x=4
Hence
AD = 4x-1
= 4(4)-1= 16-1=15
AD= 15
AB = 2 x AD
= 2 x 15
= 30
Answer:
a) z=5w-3
we have w, so we multiply it by 5 to make it 5w
and then we subtract 3 to make it 5w-3
w⇒ ×5 ⇒ -3 ⇒ z
b) x⇒ +2 = x+2
Now × 7 makes it 7(x+2)
so y=7(x+2)