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Hi can someone please explain how to do this please?

Elza [17]

9514 1404 393

Answer:

(a) an = 2n -1

(b) an = n(n +1)/2

(c) an = n^2

Step-by-step explanation:

(a) The odd numbers are an arithmetic sequence with first term 1 and common difference 2. The general term is ...

an = a1 +d(n -1)

an = 1 + 2(n -1)

an = 2n -1

__

(b) The triangular numbers are a quadratic sequence with first term 1, first first difference 2, and second differences 1.

The first few terms and differences are ...

sequence: 1, 3, 6, 10, 15, 21, 28, ... (a1 = 1)

first diff: . . . 2, 3, 4, 5, 6, 7, ... (d1 = 2)

2nd diff: . . . . 1, 1, 1, 1, 1, ... (d2 = 1)

There is a sort of general formula* that can make use of these numbers to give the general term of the sequence:

an = a1 +(n -1)(d1 +(n -2)/2(d2))

For the values we have, this gives our general term as ...

an = 1 + (n -1)(2 +(n -2)/2(1))

an = n(n +1)/2

__

(c) The general term in the sequence of square numbers is simply the square of the term number:

an = n²

_____

* There are a number of other ways to get to the general formula for triangle numbers. You can search for it, since it is well-known. You can use a quadratic regression tool on the sequence of numbers. You can develop a system of equations to find the coefficients of the quadratic equation.

The general formula given can be used to find polynomial sequences of any degree. Coefficients at successive layers in the formula are of the form (n -k)/k. The first term in parentheses following that is the first k-th difference.

3 0

3 years ago

A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.

Stels [109]

Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, amount of water in tank is dependent variable and the time taken is the independent variable. Let y represent amount of water in tank and x represent the time it has been draining. Therefore:

a) This can be represented by the equation:

y = 450 - 20x

At 7 minutes (x = 7)

y = 450 - 20(7)

y = 310 gallons

b) For 200 gallons (y = 200), the time taken is:

200 = 450 - 20x

200 - 450 = -20x

-20x = -250

x = -250/-20

x = 12.5 minutes

c) y = 450 - 20x

d) The graph was plotted using geogebra onling graphing calculator.

e) When the tank is empty, y = 0, hence

0 = 450 - 20x

20x = 450

x = 450 / 20

x = 22.5 minutes

6 0

3 years ago

Divide the following polynomial and then place the answer in the proper location on the grid.

love history [14]

8/4=2
y^7-y^5= 2
answer: 2y^2

3 0

3 years ago

Degree 3 polynomial with zeros -7, 3i, and -3i

d1i1m1o1n [39]

A polynomial having degree 3 with zeros -7, 3i, and -3i is:
x³+ 7x² - 9x - 63

The correct answer is an option (A)

In this question, we need to find the polynomial whose degree is 3 polynomial and zeros are -7, 3i, and -3i

The zeros of the required polynomial = -7, 3i, and -3i

This means, the roots of the polynomial = (x + 7), (x - 3i) and (x + 3i)

We know that in complex numbers, i = √-1

So, 3i = 3√-1

= √-9

i.e., the roots of the polynomial are (x + 7), (x - √-9) and (x + √-9)

And the polynomial would be,

(x + 7)(x - √-9)(x + √-9)

= (x + 7)(x² - (√-9)²)

= (x + 7)(x² - (-9))

= (x + 7)(x² + 9)

= x³+ 7x² - 9x - 63

Therefore, a polynomial having degree 3 with zeros -7, 3i, and -3i is:
x³+ 7x² - 9x - 63

The correct answer is an option (A)

Learn more about the polynomial here:

brainly.com/question/14344049

#SPJ1

4 0

1 year ago

The price of mailing a small package is 0.32 for the first ounce and 0.21 for each additional ounce. simone paid 1.16 to mail he

slavikrds [6]

The package weighs 5 ounces <span>
</span>

<span>Thank you for posting your question. I hope you found what you were after. Please feel free to ask me more</span>

4 0

4 years ago