What is the distance between points (9, 4) and (

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

8 0

3 years ago

PLEASE EXPLAIN THIS 6th GRADE MATH

8090 [49]

Answer:

$b = l\times w$ to guarantee that both formulas are the same.

Step-by-step explanation:

Dimensionally speaking, the volume is the cube of length. By direct comparison, we find that $l,w,h$ have length units, whereas $b$ have area unit, that is, the square of length.

Hence, $b = l\times w$ to guarantee that both formulas are the same.

8 0

3 years ago

The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of ch

vladimir1956 [14]

<h2>Answer:</h2>

The rate of change between the points (–3, 0) and (–2, –5) is:

-5

<h2>Step-by-step explanation:</h2>

The rate of change between the points (-5, 10) and (-4, 5) is -5.

Now we are asked to find the average rate of change between (-3,0) and (-2,-5)

We know that the average rate of change between two points (a,b) and (c,d) is calculated by the formula:

$Rate\ of\ change=\dfrac{d-b}{c-a}$

Here we have:

(a,b)=(-3,0) and (c,d)=(-2,-5)

Hence, the average rate of change is:

$Rate\ of\ change=\dfrac{-5-0}{-2-(-3)}\\\\\\Rate\ of\ change=\dfrac{-5}{-2+3}\\\\\\Rate\ of\ change=-5$

Also, we know that for any linear function the average rate of change is same between any two points.

Hence, the answer is:

-5

8 0

3 years ago

Read 2 more answers

Help I don't understand I need the answer wuick

aksik [14]

Answer is 14 I think pretty sure hope so yeah

6 0

3 years ago

5. If f(X) = 2X^2 g(X) = 3X - 9 Find (f*g)(X)

Dmitry [639]

Answer:

the final answer will be:

6x^3 -9

4 0

3 years ago

What is the distance between points (9, 4) and (–3, 4) on a coordinate plane?