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alexdok [17]
3 years ago
8

Please show the solving

Mathematics
1 answer:
alisha [4.7K]3 years ago
8 0

Step-by-step explanation:

<u>YELLOW TRIANGLE:</u>

<u>\sin(30)  =  \frac{x}{12}  \\ x = 12 \sin(30)  = 6</u>

<u>PURPLE TRIANGLE:</u>

Since one of the angle is 45°, x = BC = 6

To prove:

\tan(45)  =  \frac{bc}{x}  \\ bc = x \tan(45)  = 6 \tan(45)  = 6

<u>PINK TRIANGLE:</u>

<u>\tan(60)  =  \frac{bc}{y}  \\ y =  \frac{bc}{ \tan(60) }  \\  =  \frac{6}{ \tan(60) }  \\  = 2 \sqrt{3}</u>

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Answer:

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√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q. ​
frutty [35]

Answer:  

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

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Those factorizations then lead to the following

\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

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2 years ago
Despite control measures, the pigeon population in Winchester is increasing by 10% each year. If there are currently 9,520 pigeo
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Using an exponential function, it is found that there will be 32,866 pigeons in 13 years.

<h3>What is an exponential function?</h3>

An increasing exponential function is modeled by:

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Answer:

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