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leva [86]
2 years ago
5

How do I solve this equation ???

Mathematics
1 answer:
Anastaziya [24]2 years ago
8 0

To solve for the variable b , we have to make it alone. The first thing we do is add 6.5 to both sides of the equation:

13.7b-6.5+6.5=-2.3b+8.3+6.5\\13.7b=-2.3b+14.8

Now add 2.3 to both sides:

13.7b+2.3b=-2.3b+14.8+2.3b\\16b=14.8

Finally, divide both sides by 16 to get the final answer:

\frac{16b}{16} =\frac{14.8}{16}

Therefore,

b=0.3

Hope this helps!

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3 years ago
A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h passes directly over a radar station. Find the rate a
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Answer:

The plane's distance from the radar station will increase about 8 miles per minute when it is 5 miles away from it.

Step-by-step explanation:

When the plane passes over the radar station, the current distance is the altitude h = 2. Then it moves b horizontally so that the distance to the station is 5. We can form a rectangle triangle using b, h and the hypotenuse 5. Therefore, b should satisfy

h²+b² = 5², since h = 2, h² = 4, as a result

b² = 25-4 = 21, thus

b = √21.

Since it moved √21 mi, then the time passed is √21/540 = 0.008466 hours, which is 0.51 minutes. Note that in 1 minute, the plane makes 540/60 = 9 miles.

The distance between the plane and the radar station after x minutes from the moment that the plane passes over it is given by the function

f(x) = \sqrt{((9x)^2 + 2^2)} = \sqrt{(81x^2+4)}

We have to compute the derivate of f in x = 0.51. The derivate of f is given by

f'(x) = \frac{162x}{2\sqrt{81x^2+4}}

also,

f'(0.51) = \frac{162*0.51}{2\sqrt{81*0.51^2+4}} = 8.2486

The plane's distance from the station will increase about 8 miles per minute.

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Step-by-step explanation:

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