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hammer [34]
3 years ago
7

A pollen grain is 3/10 to the third power centimeters wide. In an illustration, the pollen grain is 6 centimeters 10 wide. How m

uch larger is the illustration than the actual pollen?
Mathematics
1 answer:
statuscvo [17]3 years ago
6 0

Answer:

The illustration is approximately 226 times larder than the actual pollen grain.

Step-by-step explanation:

First of all, we have to write out the size of the actual pollen grain in a manner that is easy for us to work with.

This will be

(\frac{3}{10}) ^{3}=0.027cm wide

The original width of the pollen is 0.027 cm.

Next,

We can take the width of the illustration to be 6.10 cm  wide.

After this,

To get the magnification factor, we will have to use the formula

Magnification = illustrated size/ actual size

This will be the magnification = 6.10/0.027 = 255.92 times

Hence, the illustration is approximately 226 times larder than the actual pollen grain.

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4 \cot {}^{2} (45)  - 3 \tan {}^{2} (60)  + 2 \sec {}^{2} (60)  = 3 \\

LHS = 4 \cot {}^{2} (45)  - 3 \tan {}^{2} (60)  + 2 \sec {}^{2} (60)  \\

let us first take a look at the values of the trigonometric ratios given in the question so that we get quite clear about what is to be done.

here ,

\cot(45)  = 1 \\  \\  \tan(60)  =  \sqrt{3}  \\  \\  \sec(60)  = 2

now ,

we just have to plug in the values considering certain other things given in the question and we're done!

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4(1) {}^{2}  - 3( \sqrt{3} ) {}^{2}  + 2(2) {}^{2}  \\ \\ \dashrightarrow \: 4(1) - 3(3) + 2(4) \\ \\ \dashrightarrow \: 4 - 9 + 8 \\\\ \dashrightarrow \: 12 - 9 \\ \\\dashrightarrow \: 3 = RHS

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