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3 years ago

Simplify. Express your answer using a single exponent. (2m3)4

Mathematics

1 answer:

Lorico [155]3 years ago

8 0

Answer:

16m^12

Step-by-step explanation

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Find the distance between A (6, -1) and B ( -18, 15)

timama [110]

Answer:

8√13 units

Step-by-step explanation:

We use the distance formula.

The distance formula states that the distance between two points (x, y) and (a, b) is equal to:

d = $\sqrt{(x-a)^2+(y-b)^2}$

Here, x = 6, y = -1, a = -18, and b = 15. Plug these in:

d = $\sqrt{(x-a)^2+(y-b)^2}$

d = $\sqrt{(6-(-18))^2+(-1-15)^2}=\sqrt{24^2+(-16)^2} =\sqrt{576 + 256} =\sqrt{832}$ = 8√13

The answer is thus 8√13 units.

<em>~ an aesthetics lover</em>

7 0

3 years ago

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X/5 - 12 = -8 equals what

Luda [366]

The answer is X = 20

5 0

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

The smiths have saved $25,000 toward the purchase of a new car. If the sales tax is 5%, the purchase price of smiths new car bef

lukranit [14]

Answer:

26,250

Step-by-step explanation:

25,000 + 5% = 26,250

:) please mark Brainliest

8 0

3 years ago

When Willie walked up to his grandfather's cuckoo clock, it showed 12 hours and 5 minutes. He started turning the minute hand un

Reptile [31]

Answer:

24 and 5 minutes

Step-by-step explanation:

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3 0

2 years ago

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