Answer: 30°
Step-by-step explanation:
1. You know that:
- The length of the ladder is 30 feet.
- The window is located 15 feet above the ground.
2. Then, you can draw a right triangle as the one shown in the figure attached. So, you can calculate the angle asked as following:
Where:
α: the angle of the ladder with the ground.
opposite=15 feet
hypotenuse=30 feet
3. When you substitute values, you obtain:
°
Answer:
g(f(x)) = g(x²) = x²- 3
f(g(x)) = f(x-3) = (x-3)² = x²+ 6x + 9
$3
Because you have to also think about tax of the item. Plus add them both up and it costs $2.24 without tax. Which means it's already above $2.
Equation of Sphere = + + - 18x - 4/3y +10z + 142/3 = 0
Data Given:
P = (x,y,z)
Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)
Solution:
Find the equation of the sphere:
It is given that:
PA = 2PB
Squaring both sides:
+ + = 4 x + +
Solving the above equation:
+ + = 4 x { + + }
+ 9 + 6x + + 36 - 12y + + 9 - 6z = 4 { + 36 - 12x + + 4 - 4y + + 9 + 6z}
+ 9 + 6x + + 36 - 12y + + 9 - 6z = 4 + 144 - 48x +4 + 16 - 16y + 4 + 36 + 24z
Putting the right hand side = 0 and solving the equation:
- 4 + - 4 + - 4 + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0
-3 - 3 -3 + 54x + 4y -30z -142 = 0
Taking (-) common
- ( 3 + 3 + 3 - 54x - 4y +30z + 142) = 0
3 + 3 + 3 - 54x - 4y +30z + 142 = 0
dividing the whole equation by 3
+ + - 54/3x - 4/3y +30/3z + 142/3 = 0
+ + - 18x - 4/3y +10z + 142/3 = 0
less than , less than, minimum
got it right