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3 years ago

-3b + 2.5 = 4 solve for x

Mathematics

2 answers:

Brums [2.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

b=−0.5

9966 [12]3 years ago

3 0

Let's solve your equation step-by-step.
−3b+2.5=4
Step 1: Subtract 2.5 from both sides.
−3b+2.5−2.5=4−2.5
−3b=1.5
Step 2: Divide both sides by -3.
−3b−3=1.5−3
b=−0.5

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Step-by-step explanation:

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Zanzabum

Here's the sum rule for the tangent function:

$\tan(a+b)=\dfrac{\tan(a)+\tan(b)}{1-\tan(a)\tan(b)}$

In the special case a=b, this becomes the double angle formula:

$\tan(a+a)=\tan(2a)=\dfrac{\tan(a)+\tan(a)}{1-\tan(a)\tan(a)}=\dfrac{2\tan(a)}{1-\tan^2(a)}$

In your case, you case use the sum rule once:

$\tan(3a)=\tan(2a+a)=\dfrac{\tan(2a)+\tan(a)}{1-\tan(2a)\tan(a)}$

And use it again, in the special case of the double angle:

$\dfrac{\dfrac{2\tan(a)}{1-\tan^2(a)}+\tan(a)}{1-\dfrac{2\tan(a)}{1-\tan^2(a)}\tan(a)}$

We can obvisouly simplify this expression a lot: let's deal with the numerator and denominator separately: the numerator is

$\dfrac{2\tan(a)}{1-\tan^2(a)}+\tan(a) = \dfrac{2\tan(a)+\tan(a)-\tan^3(a)}{1-\tan^2(a)}$

and the denominator is

$1-\dfrac{2\tan(a)}{1-\tan^2(a)}\tan(a) = \dfrac{1-\tan^2(a)-2\tan^2(a)}{1-\tan^2(a)} = \dfrac{1-3\tan^2(a)}{1-\tan^2(a)}$

So, the fraction is

$\dfrac{2\tan(a)+\tan(a)-\tan^3(a)}{1-\tan^2(a)}\cdot \dfrac{1-\tan^2(a)}{1-3\tan^2(a)} = \dfrac{2\tan(a)+\tan(a)-\tan^3(a)}{1-3\tan^2(a)}$

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