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Mars2501 [29]
3 years ago
8

When the sum of 7 and three times a positive number is subtracted from the square of the​ number, 0 results. find the number?

Mathematics
1 answer:
schepotkina [342]3 years ago
3 0
<span>The answer is...
x^2 - (7 + 2x) = 0
x^2 - 2x - 7 = 0</span>
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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
Rasek [7]

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.

4 0
3 years ago
Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain
sergey [27]
The rise or an increase in altitude is represented by positive sign and a decend or decrease in altitude is represented by negative sign. 

First the helicopter descended 1200 feet. So the change in altitude will be -1200 feet.

Then the helicopter rose by 800 feet. So the change in altitude will be 800 feet.

Finally the helicopter descended by 450 feet. So the change in altitude will be -450 feet.

The net change in altitude will be the sum of all the above 3 changes. 
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The negative sign indicates a descend i.e. loss in altitude. So the net change in altitude was a loss of 850 feet. 
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Step-by-step explanation:

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If an integer is chosen between 1 and 50 inclusive, you have 50 numbers total to deal with, so 50 is in the denominator of our ratio (fraction). All the numbers divisible by 3 in that interval total 16 numbers. So the ratio would be 16/50 for a percentage of 32%
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