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Let's simplify step-by-step.
5x^3 + 3 + 2x^3 − x^2 + 1
= 5x^3 + 3 + 2x^3 + −x^2 + 1
Combine Like Terms:
= 5x^3 + 3 + 2x^3 + −x^2 + 1
= ( 5x^3 + 2x^3 ) + ( −x^2 ) + ( 3 + 1 )
= 7x^3 + −x^2 + 4
Answer:
= 7x^3 − x^2 + 4
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round too? hundreds? thousand? ones? where do we round too? i need to know so i can help you :)
The correct answer is -15 because the absolute value is 15 but there is a negative outside the absolute value lines making it negative :)
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
So the question is the original price was $791 and they bought it at the marked down price at $474.60? then they saved $316.40 but i’m not really sure if that’s the question lol
