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2 years ago

Write at least 5 arithmetic sequence and determine the common difference

Mathematics

2 answers:

Margarita [4]2 years ago

7 0

Answer: 1,6,11,16,21,26

Step-by-step explanation:

The common difference is 5 (n+5)

gulaghasi [49]2 years ago

7 0

An arithmetic sequence is a sequence where we use addition or subtraction to get to the next term.

Examples:

1, 3, 5, 7, 9...

Common Difference: Add 2

2, 6, 10, 14, 18, 22..

Common Difference: Add 4

100, 90, 80, 70, 60, 50..

Common Difference: Subtract 10.

25, 30, 35, 40, 45..

Common Difference: Add 5

1, 10, 19, 28, 37..

Common Difference: Add 9

Hope it helps!

$ANSWERED:\\GraceRosalia$

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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,

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

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

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3 years ago

What is y-2=5(x+7) in standard form?

Elina [12.6K]

Answer:

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3 years ago

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sertanlavr [38]

Answer

Step-by-step explanation:

Because the Q is on top of the 5 It is the absolute value

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3 years ago

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A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were c

allochka39001 [22]

Answer:

a) The test statistic is $z = -2.51$

b) The pvalue is 0.0060.

Step-by-step explanation:

Question a:

Ha: pB < pNY

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$H_a: p_{B} - p_{NY} < 0$

While the null hypothesis is:

$H_0: p_{B} - p_{NY} = 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis and s is the standard error

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This means that $X = 0.581 - 0.832 = -0.251$

0 is tested at the null hypothesis:

This means that $\mu = 0$

Standard error = 0.1

This means that $s = 0.1$

Test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{-0.251 - 0}{0.1}$

$z = -2.51$

The test statistic is $z = -2.51$

Question b:

The pvalue is the probability of finding a proportion less than -0.251, that is, a difference of at least 0.251, which is the pvalue of Z = -2.51.

Looking at the z-table, Z = -2.51 has a pvalue of 0.0060

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3 years ago

Write the following word phrases as inequalities: Seven times a number increased by one is at most twelve. If you need these sym

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Answer:

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