All categories

2 years ago

Find the sum of the first 56 terms of the sequence {-8,-1, 6, ...}.

Mathematics

1 answer:

torisob [31]2 years ago

4 0

Answer:

Step-by-step explanation:

S56=56/2[2(-8)+(56-1)7]

S56=10332

You might be interested in

Enter the data to create a histogram. Then select the correct answer.

Verizon [17]

Answer: The histogram is not symmetrical

5 0

3 years ago

Read 2 more answers

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

Find the slope intercept form for the equation of the line which passes through the point (-4,-14) and has a slope of 1

Fudgin [204]

Use point slope form to answer this
Y = x - 10

5 0

3 years ago

A intersection b intersection c compliment

faust18 [17]

B intersection is the correct answer

7 0

2 years ago

Read 2 more answers

Given the data set {3, 7, 4, 10, 7, 11}, which of the following is NOT equal to the other three? Question 2 options: Mean Range

NNADVOKAT [17]

The answer is range
Mode = most common = 7
Median - Put then in order and find the middle number = 7
Mean - Add them all together and divide by how many there are = 7
Range - Biggest minus smallest = 11-3= 8

8 0

2 years ago