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Anna [14]
3 years ago
11

What is the value of x? A)29 B)22 C)27 D)25

Mathematics
2 answers:
Step2247 [10]3 years ago
8 0

Answer:

C)  x = 27

Step-by-step explanation:

The angles 111 and 2x + 15 make a straight line, so their sum is equal to 180:

111 + 2x+15 = 180

2x + 126 = 180

2x = 54

x = 27

Hope that helped! :)

ryzh [129]3 years ago
4 0

Answer:

X= 27 2x27=54+15=69 111+69=180

Step-by-step explanation:

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A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat
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Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles                    

First, we need to find b:    

a^{2} + b^{2} = h^{2}   (1)    

b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})

2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:  

0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}

\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h  

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

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