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Bumek [7]
2 years ago
14

Which number is between 8.270 and 8.280

Mathematics
1 answer:
Nezavi [6.7K]2 years ago
8 0

Answer:

8.275

Step-by-step explanation:

8.280 - 8.270 = 0.010

0.010/2 = 0.005

8.270 + 0.005 = 8.275

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Answer:

73.77 ft/s

Step-by-step explanation:

Let's imagine this situation as a right triangle where the distance between the two points is the hypotenuse.

-Applying Pythagoras theorem:

z^2=x^2+y^2\\\\z=\sqrt{x^2+y^2}\\\\x=dx*t+x_i, x_i=0\\\\y=dy*t+y_i\\\\y_i=160\ ft

#Take the derivative of the first equation and solve for dz:

d(z^2=x^2+y^2)\\\\2z*dz=2x*dx+2y*dy\\\\dz=\frac{x*dx+y*dy}{z}\\\\dz=\frac{x*dx+y*dy}{\sqrt{x^2+y^2}}\\\\\\dz=\frac{dx^2*t+dy(dy*t+160)}{\sqrt{(dx*t)^2+(dy*t)}}

#We then substitute the values given in the question to solve for dz:

dz=\frac{7*66^2+14(14*7+160)}{\sqrt{(66*7)^2+7*14+160}}\\\\=73.78

Hence, the rate of change of the distance between the motorcycle and the balloon 7 seconds ​later is 73.77 ft/s

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