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3 years ago

Tell what part of the circle is shaded

Mathematics

1 answer:

DIA [1.3K]3 years ago

3 0

Answer:

Fraction = 1/4, Decimal = 0.25, Percent = 25%

Step-by-step explanation:

Given the picture, we can see the circle is divided into four pieces. One of the pieces is shaded. So, since we have one out of four pieces shaded, we would represent this as 1/4 as a fraction. As a decimal, enter 1 divided by 4 into your calculator, and it will give you 0.25. To find a percentage value, take your decimal and multiply it by 100. 0.25*100= 25%

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Of the 81 astronauts in the space program, 43 are in outer space. What is the ratio of the number of astronauts on Earth to the

erastovalidia [21]

Answer:

38:81

Step-by-step explanation:

There are a total of 81 Astronauts in the space program.

Out of these, 43 are in outer space.

We are to determine the ratio of the number of astronauts on Earth to the total number of astronauts.

Number of Astronauts on Earth = Total Number - Number in Outer Space

=81-43 = 38

Therefore:

Number of astronauts on Earth : The total number of astronauts. = 38:81

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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

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

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In trigonometry

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

Subtract $tan^2x$ from both sides

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

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

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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;

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In trigonometry

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

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

Substitute the expressions for secx and tanx

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

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

Make $sin^2x$ the subject of formula

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

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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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Tell what part of the circle is shaded​

Tell what part of the circle is shaded