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3 years ago

An angle measures 104° more than the measure of its supplementary angle. What is the measure of each angle?

Mathematics

1 answer:

masya89 [10]3 years ago

8 0

Answer:

76°

Step-by-step explanation:

supplementary angles make a total of 180°

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To answer your question very literally, the united states only elects one president per term! The president can only serve two terms and is then forced to leave office! But if you where asking how many presidents the U.S. has had, as of 2016 the U.S. has had exactly 43 presidents and 44 presidencies (one served a second term)

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jim is selling greeting cards at a booth at a folk fair. he will be paid $12 plus $2 for each box that he sells how many boxes m

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Step-by-step explanation:

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3 years ago

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Derivative of tan(2x+3) using first principle

kodGreya [7K]

$f(x)=\tan(2x+3)$

The derivative is given by the limit

$f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h$

You have

$\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h$

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

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

By this identity, you have

$\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}$

So in the limit you get

$\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}$
$\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}$

The first two limits are both 1, and the single term in the last limit approaches 0 as $h\to0$ , so you're left with

$f'(x)=\dfrac12\sec^2(2x+3)$

which agrees with the result you get from applying the chain rule.

7 0

3 years ago

What are the solutions to

Svetllana [295]

Answer:

B and F

Step-by-step explanation:

Given

x² + 4x + 4 = 12 ( subtract 4 from both sides )

x² + 4x = 8

Using the method of completing the square to solve for x

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 8 + 4, that is

(x + 2)² = 12 ( take the square root of both sides )

x + 2 = ± $\sqrt{12}$ ( subtract 2 from both sides )

x = ± $\sqrt{12}$ - 2

= ± 2 $\sqrt{3}$ - 2

Hence

x = 2 $\sqrt{3}$ - 2 → B

x = - 2 $\sqrt{3}$ - 2 → F

4 0

3 years ago