B. 13(y−10)=−4 1 3 ( y - 10 ) = - 4 y =

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

3 years ago

You have several options to add to your brand new car: leather seats, heated seats, sunroof, tinted windows, and back up camera.

scZoUnD [109]

Answer:

The number of different ways the car can be built is 31 different ways

Step-by-step explanation:

The given options are'

1), Leather seats, 2) Heated seats, 3) Sunroof, 4) Tinted windows, 5), back up camera

Therefore, the number of different ways the car can be built, n, is given as follows;

n = ₅C₁ + ₅C₂ + ₅C₃ + ₅C₄ + ₅C₅

n = 5 + 10 + 10 + 5 + 1 = 31 different ways

The number of different ways the car can be built = n = 31 different ways

3 0

3 years ago

5) Solve 5 - 2x < 7. A) x < -1 B) x>-1 0x<-12 D) X > -12

Bingel [31]

Answer:

i think B. x>-1 is answer

Step-by-step explanation:

good luck

6 0

2 years ago

Ariel needs to paint the trim of a triangular box. If A (-2,4), B (2,2), and C (-1, -2) are the vertices of the triangle, what i

Kisachek [45]

Total length of the trim painted is 15.75 unit.

Given:

Co-ordinate of point A = (-2,4)
Co-ordinate of point B = (2,2)
Co-ordinate of point C = (-1,-2)

Find:

Total length of the trim painted

Computation:

Distance between two point = √(x1 - x2)² + (y1 - y2)²

Distance between AB = √(-2 - 2)² + (4 - 2)²

Distance between AB = √16 + 4

Distance between AB = 2√5 unit = 4.47 unit

Distance between BC = √(2 + 1)² + (2 + 2)²

Distance between BC = √9 + 16

Distance between BC = 5 unit

Distance between AC = √(-2 + 1)² + (4 + 2)²

Distance between AC = √1 + 36

Distance between AC = √37 unit = 6.08 unit

Total length of the trim painted = 4.47 + 5 + 6.08

Total length of the trim painted = 15.75 unit (Approx.)

Learn more:

brainly.com/question/17485880?referrer=searchResults

5 0

2 years ago

HELP HELP I WILL MARK BRAINLIEST IF YOU HELP ME

Tpy6a [65]

Answer:

x = 8

Step-by-step explanation:

In order for the triangles to be similar, corresponding side must be in proportion.

So, FE/ZY = FD/ZX

6/12 = (2x - 5)/22

6(22) = 12(2x - 5)

132 = 24x - 60

24x = 192

x = 8

8 0

3 years ago