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
Malik earned $243.
When he bought the tires, he spent $90 ($45x2), and he sold them for $130 ($65x2). So his profit was $40 ($130-$90).
He bought three rims for $225 ($85x3) and sold them all for $378 ($126x3). His profit was $153 ($378-$225).
The headlight covers cost him $25 in total ($5x5). He sold them all and got $75 ($15x5). The profit was $50 ($75-$25).
The total amount of money made was $243 ($40+$153+$50).
:)
The first statement is false. A square DOES have 4 right angles.
Answer:
8
Step-by-step explanation:
1 serving=60cal
480÷60=8
hope this helps
Answer: 1620
Step-by-step explanation: This is for a parallelogram you would multiple 6 base x's 4.5 height= 27 area for each diamond.
He's using 60 tiles. Multiple the area of 1 tile which is 27 by 60 wooden tiles to find the area of the parallelogram. 27 multipled by 60 tiles= 1620 inches squared
