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Vitek1552 [10]
3 years ago
7

A bird (B) is spotted flying 6,000 feet from a tower (T)). An observer (O) spots the top of the tower (T) at a distance of 9,000

feet. What is the angle of depression from the bird (B) to the observer (O)? Right triangle OTB is shown. Side OT labeled 9000 and side TB is labeled 9000. The angle B is labeled x degrees.
Mathematics
2 answers:
Nina [5.8K]3 years ago
7 0

Answer:

The angle will be "48.7°".

Step-by-step explanation:

In ΔTBO, the given values are:

TB = 6,000 feet

BO = 9,000 feet

Now,

To find the angle,

⇒  Cos \ B =\frac{TB}{BO}

On putting the estimated values, we get

⇒   Cos \ x=\frac{6000}{9000}

⇒   Cos \ x=0.66

⇒          x=Cos^{-1} \ 0.66

⇒          x=48.7^{\circ}    

viktelen [127]3 years ago
3 0

Answer:

56.31

Step-by-step explanation:

9000/6000 (opposite/adjacent)=1.5

tan^{-1}(1.5)=56.30993247

Round the answer to 56.31

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Find the smallest 4 digit number such that when divided by 35, 42 or 63 remainder is always 5
alex41 [277]

The smallest such number is 1055.

We want to find x such that

\begin{cases}x\equiv5\pmod{35}\\x\equiv5\pmod{42}\\x\equiv5\pmod{63}\end{cases}

The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.

x\equiv5\pmod{35}\implies\begin{cases}x\equiv5\equiv0\pmod5\\x\equiv5\pmod7\end{cases}

x\equiv5\pmod{42}\implies\begin{cases}x\equiv5\equiv1\pmod2\\x\equiv5\equiv2\pmod3\\x\equiv5\pmod7\end{cases}

x\equiv5\pmod{63}\implies\begin{cases}x\equiv5\equiv2\pmod 3\\x\equiv5\pmod7\end{cases}

Taking everything together, we end up with the system

\begin{cases}x\equiv1\pmod2\\x\equiv2\pmod3\\x\equiv0\pmod5\\x\equiv5\pmod7\end{cases}

Now the moduli are coprime and we can apply the CRT.

We start with

x=3\cdot5\cdot7+2\cdot5\cdot7+2\cdot3\cdot7+2\cdot3\cdot5

Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.

Taken modulo 2, we end up with

x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod2

which means the first term is fine and doesn't require adjustment.

Taken modulo 3, we have

x\equiv2\cdot5\cdot7\equiv70\equiv1\pmod3

We want a remainder of 2, so we just need to multiply the second term by 2.

Taken modulo 5, we have

x\equiv2\cdot3\cdot7\equiv42\equiv2\pmod5

We want a remainder of 0, so we can just multiply this term by 0.

Taken modulo 7, we have

x\equiv2\cdot3\cdot5\equiv30\equiv2\pmod7

We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since 2\cdot4\equiv8\equiv1\pmod7, the inverse of 2 is 4.

So, we have to adjust x to

x=3\cdot5\cdot7+2^2\cdot5\cdot7+0+2^3\cdot3\cdot5^2=845

and from the CRT we find

x\equiv845\pmod2\cdot3\cdot5\cdot7\implies x\equiv5\pmod{210}

so that the general solution x=210n+5 for all integers n.

We want a 4 digit solution, so we want

210n+5\ge1000\implies210n\ge995\implies n\ge\dfrac{995}{210}\approx4.7\implies n=5

which gives x=210\cdot5+5=1055.

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2 years ago
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melamori03 [73]

Answer:

center is (1,-5)

the radius is 4

Step-by-step explanation:

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2 3/4 + 2 4/5 what is this math equation?
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Answer:

Step-by-step explanation:

5.55

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