I think it is A. 76 degrees
Step-by-step explanation:
after I answered the other one(s), you should be really able to do this yourself.
it is precisely the same method and formula just with different numbers.
what's the problem now ?
y = -16x² + 247x + 141
we assume, the ground is at 0 ft.
so, we need to solve
0 = -16x² + 247 x + 141
the general solution for such quadratic equations is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -16
b = 247
c = 141
x = (-247 ± sqrt(247² - 4×-16×141))/(2×-16) =
= (-247 ± sqrt(61009 + 9024))/-32 =
= (-247 ± sqrt(70033))/-32
x1 = (-247 + 264.6374879...)/-32 = -0.551171497... s
x2 = (-247 - 264.6374879...)/-32 = 15.9886715... s
again, the negative solution for time did not make any sense, so, x2 is our solution.
the rocket will hit the ground after about 15.99 seconds.
I hope this helps you
6x-4 (x+2)= -10x
6x-4x-8= -10
2x= 2
x= 1
y=1+2=3
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Answer:
A
Step-by-step explanation:
You should know the area of a circle, A = πr².
So, all you need to find is the area of half a circle, or A = 
πr²
We see that the radius is half of the diameter or r = 6 in.
A = (3.14)(6)²
A = 56.52 in²
