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3 years ago

What is the lenght of the distance between the chair and the end table ?

Mathematics

1 answer:

pentagon [3]3 years ago

8 0

check the picture below.

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I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

7 0

4 years ago

*Brainly* Find the equation of the line shown in the graph. Write the equation in slope-intercept form.

Brums [2.3K]

Answer:

y = (-4/3)x + 6

Step-by-step explanation:

The Y-intercept of the graph is 6. You can find the slope by following rise over run, or the change in y divided by the change in x. From (0,6) to (3,2), there is a negative 4 change in y and positive 3 change in x.

3 0

3 years ago

What is 36:39 in simplest form

vova2212 [387]

12:13

Hope that helped!

8 0

3 years ago

Read 2 more answers

Which inequality has no solution?<br> 6(x+2) > x-3<br> 3+4x2(1+ 2x)<br> -2(x+6) X-9 <3(x-3)

Juli2301 [7.4K]

Answer:

$6(x + 2) > x - 3$

$6x + 12 > x - 3$

$6x - x > - 12 - 3$

$5x > - 9$

$3 + 4 \times 2(1 + 2x)$

$3 + 8(1 + 2x)$

$3 + 8 + 16x$

$11 + 16x$

$- 2(x + 6)x - 9 < 3(x - 3)$

$- 2( {x}^{2} + 6x) - 9 < 3x - 9$

$- 2 {x}^{2} - 12x - 9 < 3x - 9$

5 0

3 years ago

Factor the expression<br> 10x+15y=

gayaneshka [121]

5(2x+3y) is the most it can be factored. You first have to find the greatest common factor and once thats done just try using methods such as the diamond. The only thing it was able to do using the methods was this.

8 0

3 years ago