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3 years ago

Ivan is putting books in his bookcase. He has

Mathematics

2 answers:

tino4ka555 [31]3 years ago

4 0

151 books

There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.

Licemer1 [7]3 years ago

3 0

Answer:

151

Step-by-step explanation:

because 225-74 =151

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Write the numbers 3,2,8 in an addition sentence

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Ashely reads 3 chapters in her book each night. Jordon reads 8 chapters in a book each night. Will reads 2 chapters per night, but they are very long. How many chapters do they read per night all together?

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3 years ago

Given sin θ = 3/5 what is sec θ?

PIT_PIT [208]

Answer:

5/4

Step-by-step explanation:

To do this you must know that by definition secant is:

$sec(\theta)=\frac{1}{cos(\theta)}$

Furthermore:

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}$

Based on this information we know that 3 = opposite and 5 = hypotenuse. Assuming this is a right triangle we can determine the adjacent side by Pythagorean Theorem.

$c^2=a^2+b^2$

Where c is the hypotenuse, a is adjacent and b is opposite. Therefore,

$c^2=a^2+b^2\\\\a=\sqrt{c^2-b^2} \\\\a=\sqrt{5^2-3^2} \\\\a=4$

And so the adjacent side of this triangle is 4. Going back to the definition of secant we can now know that:

$sec(\theta)=\frac{1}{cos(\theta)}=\frac{1}{\frac{4}{5}}=\frac{5}{4}$

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3 years ago

Read 2 more answers

Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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