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2 years ago

Find P 20 of the following arithmetic sequence: 206, 212, 218, 224....

Mathematics

1 answer:

Yanka [14]2 years ago

7 0

Answer:

$p_{20} = 1.25528$

P₀ = 206 and difference d = 6

Step-by-step explanation:

Step(i):-

Given that the arithmetic sequence

206,212,218,224,.....

P₀ = 206 and difference d = 212-206 = 6

The $n^{th}$ term of the sequence

$t_{n} = ar^{n-1}$

Step(ii):-

The $n^{th}$ term of the sequence

$P_{n} = ar^{n-1}$

Put n=20

$P_{20} = 206 ( 6) ^{20-1}$

$p_{20} = 1.25528$

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Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

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Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

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Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

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Step 2: Identify Bounds of Integration

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Simply graph the functions to see where the functions intersect (See Graph Attachment).

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Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

6 0

3 years ago

Solve this equation for x 0.95 = log x

Lelechka [254]

Answer:

8.91

Step-by-step explanation:

Given: 0.95 = log x,

we can conclude that:

0.95 log x

10 = 10

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which in turn is equivalent to x = 10 whose value is 8.91

5 0

3 years ago

Tammy has 35 coins nickels and quarters. In all she has $4.15. How many of each kind of coin does she have

sergey [27]

The currency called the U.S dollar can be split into smaller forms or currency value of itself. Examples of these smaller forms are: dimes, nickels, pennies, and quarters.

Tammy has 23 nickels and 12 quarters.

Let's represent the number of:

Nickels = n

Quarters = q

It is important to note that the value of:

1 nickel = $0.05

1 quarter = $0.25

Tammy has 35 coins nickels and quarters. This statement can be represented using an algebraic equation below:

n + q = 35

This can be rewritten as :

n = 35 - q

In all, she has $4.15. This statement can be represented using an algebraic equation below:

0.05n + 0.25q = 4.15

We substitute 35 - q for n in the above equation.

0.05(35 - q) + 0.25q = 4.15

1.75 - 0.05q + 0.25q = 4.15

Collect like terms

- 0.05q + 0.25q = 4.15 - 1.75

0.2q = 2.4

Divide both sides by 0.2

0.2q/0.2 = 2.4/0.2

q = 12

Therefore, the number of quarters Tammy has is 12.

Solving for the number of nickels, we have the equation:

n = 35 - q

n = 35 - 12

n = 23

Therefore, the number of nickels Tammy has is 23.

To learn more, visit the link below:

brainly.com/question/13312288

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3 years ago

Please help me ASAP

Liula [17]

I would say answer choice 1. It’s the only one that makes sense.

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Mark this as Brainliest if you get a chance:)

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2 years ago

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I wasn’t able to fit the text in the space provided, so, please see the attached papers.

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3 years ago