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2 years ago

What is x? Super confused

Mathematics

1 answer:

Over [174]2 years ago

6 0

Answer:

$\\ from \: triangle \: applying \: pyth \\ \sqrt{ {3}^{2} + {3}^{2} } = 3 \sqrt{2} \\ from \: rectangle \:applying \: pyth \\ {x}^{2} = {7}^{2} - 3 \sqrt{2} \: units$

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Karo-lina-s [1.5K]

Here you go!!! I hope this helps

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2 years ago

The school band collected $2,892 for 480 tickets sold to their spring concert. Adult tickets were $8 each and student tickets we

kakasveta [241]

A + s = 480......s = 480 - a
8a + 5s = 2892

8a + 5(480 - a) = 2892
8a + 2400 - 5a = 2892
8a - 5a = 2892 - 2400
3a = 492
a = 492/3
a = 164 <=== there were 164 adult tickets sold

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3 years ago

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riadik2000 [5.3K]

Answer:

Step-by-step explanation:

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2 years ago

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frozen [14]

The answer is b

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2 years ago

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

konstantin123 [22]

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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2 years ago