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2 years ago

30 secs on battery hurry for brainles

Mathematics

2 answers:

Gemiola [76]2 years ago

6 0

Answer:

It is 8 1/2

Step-by-step explanation:

;)

labwork [276]2 years ago

3 0

Answer:

$8\frac{1}{2}$

Step-by-step explanation:

$\frac{17}{2}=$ $8\frac{1}{2}$

17 ÷ 2 = 8.5

8.5 as a mixed number is $8\frac{1}{2}$ .

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What is 3 1/3 *2/3?

Molodets [167]

Answer:2 2/9

Step-by-step explanation:

3 1/3= 10/3, 10/3 x 2/3= 20/9= 2 2/9

6 0

2 years ago

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Help me with differentation and integration please!!

Marina86 [1]

Answer:

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

$y = \tan^n x$

Considering the power rule

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

we have

$\dfrac{dy}{dx} =n u^{n-1} \sec^2 x \implies \dfrac{dy}{dx} =n \tan^{n-1} \sec^2 x$

therefore,

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

Now, once

$\sec^2 x - 1= \tan^2x$

we have

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

Hence, we showed

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

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

For the integration,

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

considering the previous part, we will use the identity

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

thus

$\int\sec^4x\,dx=\int \sec^2 x(\tan^2x+1)\,dx = \int \sec^2 x \tan^2x+\sec^2 x\,dx$

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

$\int u^2 \, du = \dfrac{u^3}{3}+C$

Therefore,

$\int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx = \dfrac{\tan^3 x}{3}+\tan x + C$

$\boxed{\int \sec^4 x\, dx = \dfrac{\tan^3 x}{3}+\tan x + C }$

6 0

2 years ago

Finding Derivatives Implicity In Exercise, find dy/dx implicity.<br> ln y + y2 = 10

Harman [31]

Answer:

dy/dx = 0

Step-by-step explanation:

In y + y^2 = 10

Differentiating In y = 1/ydy/dx

Differentiating y^2 = 2ydy/dx

Differentiating a constant (10) = 0

1/ydy/dx + 2ydy/dx = 0

dy/dx(1/y + 2y) = 0

dy/dx = 0/(1/y + 2y) = 0

6 0

3 years ago

A die with faces numbered 1 to 6 is rolled once .what is the probability of obtaining 1 or 4

Radda [10]

Answer:

the answer is 2/6

Step-by-step explanation:

2 chances out of 6 events.

4 0

3 years ago

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Which of the following expressions can be used to find the area of a square with a side length of fraction 1 over 3 m?

Marina86 [1]

Sorry if it is wrong but i think it is D) 2 multiplied by fraction 1 over 3 m2

4 0

2 years ago

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