Answer:
225 m³ or 225 cubic meters
Step-by-step explanation:
Actually it has 5 sides, the 2 bases, the 3 lateral faces.
The formula for the volume of a triangular prism is: 
Using the given measurements, we get:
The volume of the prism is 225 m³
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
The HTTP 404, 404 Not Found, 404, 404 Error, Page Not Found, File Not Found, or Server Not Found
75 hundreds 0 tens(or skip) 2 ones
Answer:
8.0
Step-by-step explanation:
Sin theta = opposite /hypotenuse
sin 53 = x/10
Multiply each side by 10
10 sin 53 = x
7.9863551
To the nearest tenth
x = 8.0
