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zubka84 [21]
2 years ago
7

Please please help help me with two questions!!

Mathematics
1 answer:
kykrilka [37]2 years ago
6 0

Answer:

A. True

B. False

Step-by-step explanation:

1: 30 + 10 = 40 and 8 x 5 = 40 (both match)

2: 75 - 25 = 50 and 5 x 9 = 49 (Doesn't match)

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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
A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw,
klasskru [66]

Answer:

length = (x − 8) units and width = (x − 9) units

Step-by-step explanation:

We need to factor

x^2 - 17x + 72

We need two numbers whose product is 72 and whose sum is -17.

The numbers are -8 and -9.

x^2 - 17x + 72 = (x - 8)(x - 9)

Answer: length = (x − 8) units and width = (x − 9) units

8 0
2 years ago
Read 2 more answers
6. A rectangle and a parallelogram have the same base and the same height. How are their areas
fomenos

Answer:

the height

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help with math
Crank

Answer:

i think it is y=2x

Step-by-step explanation:

8 0
2 years ago
PLEASE HELP ME pleasee!
kap26 [50]

Answer:

b 2

Step-by-step explanation:

x is an integer that is greater than 3 and less than or equal to 6.

x can be 4, 5, 6.

Answer: b 2

4 0
2 years ago
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