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4 years ago

HELPPP HELPPPP. iS this function or relation and why?

Mathematics

1 answer:

Taya2010 [7]4 years ago

8 0

Answer: This table is a relation because the x- intercepts repeat itself, -2 and -2, a in order for this table to be a function the x- intercept cannot repeat.

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Sin 2x + tan 2x = 4tan/ 1- tan^4 prove that

nalin [4]

$\dfrac{4\tan x}{1-\tan^4x}=\dfrac{4\tan x}{(1-\tan^2x)(1+\tan^2x)}$
$=\dfrac{4\tan x}{(1-(\sec^2x-1)\sec^2x}$
$=\dfrac{4\tan x\cos^2x}{2-\sec^2x}$
$=\dfrac{4\sin x\cos x}{2-\sec^2x}$
$=\dfrac{4\sin x\cos^3x}{2\cos^2x-1}$
$=\dfrac{2\sin2x\cos^2x}{\cos2x}$
$=2\tan2x\cos^2x$
$=2\tan2x\left(\dfrac{1+\cos2x}2\right)$
$=\tan2x(1+\cos2x)$
$=\tan2x+\sin2x$

7 0

3 years ago

Which of the following is a solution to tan^2 x-1=0? a.45 degrees, b.120 degrees, c.240 degrees, d.330 degrees

andrew-mc [135]

Do you want a general solution or from 0 <= x < 2pi?

tan^2(2x) - 1 = 0
tan^2(2x) = 1

Take the square root of both sides,

tan(2x) = +/- 1

Two equations:
tan(2x) = 1
tan(2x) = -1

Solve each equation.

tan(2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},
x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }

tan(2x) = -1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },
x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}

So for solutions within [0, 2pi),

x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }

6 0

3 years ago

A total of $6000 was invested, part of it at 3% interest and the remainder at 8%. If the total yearly interest amounted to $380,

Nastasia [14]

$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest

Solution:

Given that, total of $6000 was invested

Let "x" be the amount invested at 3 % interest

Then, (6000 - x) is the amount invested at 8 % interest

Given that,

The total yearly interest amounted to $380

Then, we can frame a equation as:

$x \times 3 \% + (6000 - x) \times 8 \% = 380$

Solve the above expression for "x"

$x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000$

Thus, $ 2000 is invested at 3 % interest

(6000 - x) = 6000 - 2000 = 4000

$ 4000 is invested at 8 % interest

4 0

4 years ago

Add. 1 1/2 + 3/5 + 1/8 A. 1 5/13 B. 27/15 C. 2 9/40 D. 1 3/8

Alex Ar [27]

Get the mixed number into one fraction
$\frac{3}{2} + \frac{3}{5} + \frac{1}{8}$
Get a common denominator
$\frac{60}{40} + \frac{24}{40} + \frac{5}{40}$
Now add
$\frac{89}{40}$
You can get it back to a mixed number
$2 \frac{9}{40}$

8 0

3 years ago

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What do double brackets around an x mean?

Anna [14]

[[x]] means to round down to the greatest integer less than or equal to x.

6 0

3 years ago

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