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3 years ago

How do you know if a number is smaller or bigger

1 answer:

4 0

Use a number line and plot it with zero in the middle and the positive numbers on the right and the negative numbers on the left
the farther to the right a number is, the bigger it is
the farther to the left a number is, the smaller it is

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

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

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

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

8 0

3 years ago

What is an equation of the line that passes through the point (2,−6) and is parallel to the line x−2y=8?

lorasvet [3.4K]

Answer:

y = x/2 - 7

Step-by-step explanation:

First, we need to find the slope of the given equation: x - 2y = 8

Subtract x from both sides

x - 2y = 8

- x - x

-2y = 8 - x

Divide both sides by -2

-2y/-2 = (8 - x)/-2

y = -4 + x/2

The slope of this equation is 1/2

So the equation of our parallel equation is y = x/2 + b

We have to find b, so plug in the given coordinates

-6 = 2/2 + b

-6 = 1 + b

Subtract 1 from both sides

-6 = 1 + b

- 1 - 1

b = -7

Plug it back into the original equation

y = x/2 - 7

6 0

2 years ago

Please help ! I don’t know this one :(

zheka24 [161]

Answer:

Step-by-step explanation:

answer is C the y intercept is (0,3)

7 0

3 years ago

Which of the following is divisible by 2 70581 16853 90000

Svetllana [295]

90000 is divisible by 2

6 0

2 years ago

Read 2 more answers

A bouncy ball is dropped such that the height of its first bounce is 5.5 feet and each successive bounce is 64% of the previous

ahrayia [7]

Answer:

0.4 ft

Step-by-step explanation:

It can be convenient to let a spreadsheet compute the values for you. Here, we have written an explicit formula for the height of the n-th bounce:

h = 5.5×0.64^(n-1)

We have written the formula this way because we are given the height of the first bounce, not the starting height. Each bounce multiplies the height by a factor of 0.64. Then the 7th bounce will have a height of ...

h = 5.5×0.64^6 ≈ 0.378 ≈ 0.4 . . . . feet

6 0

3 years ago