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3 years ago

Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?

Mathematics

2 answers:

lina2011 [118]3 years ago

4 0

Answer:

Step-by-step explanation:

25.07 x 5.4 = 135.378

So D is the correct answer

Lana71 [14]3 years ago

3 0

2.52 * 27.94 = 70.4088, so not that one

94.1 * 2.5 = 235.25, so not that one

1.83 * 2.9 = 5.307, so not that one

25.07 * 5.4 = 135.378, so that one

Answer:

D. 25.07 * 5.4 = 135.378

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See below

Step-by-step explanation:

$\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x$

Recall

$\dfrac{d}{dx}\tan x=\sec^2$

Using the chain rule

$\dfrac{dy}{dx}= \dfrac{dy}{du} \dfrac{du}{dx}$

such that $u = \tan x$

we can get a general formulation for

$y = \tan^n x$

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$\boxed{\dfrac{d}{dx} x^n = nx^{n-1}}$

we have

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$\dfrac{d}{dx}\tan^3 x=3\tan^2x \sec^2x$

Now, once

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$3\tan^2x \sec^2x = 3(\sec^2 x - 1) \sec^2x = 3\sec^4x-3\sec^2x$

Hence, we showed

$\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x$

================================================

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$\int \sec^4 x\, dx$

considering the previous part, we will use the identity

$\boxed{\sec^2 x - 1= \tan^2x}$

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and

$\int \sec^2 x \tan^2x+\sec^2 x\,dx = \int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx$

Considering $u = \tan x$

and then $du=\sec^2x\ dx$

we have

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Therefore,

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