Find the surface area of the composite figure,

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

Arithmetic Sequence

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

5 0

2 years ago

Algebra help needed. Overwhelmed with other papers. See attached

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

whitch answer how do you want us to answer

5 0

3 years ago

Charlotte recorded the number of minutes she spent exercising in the past ten days: 9, 13, 5, 2, 9, 1, 14, 3, 5, 7. Find the med

Nuetrik [128]

Answer:

The median is 7.

Step-by-step explanation:

In order to find the median, you need to ut the numbers in either least to greatest form, or greatest to least (FIRST).

I'm gonna do both as an example.

Greatest to least:

14, 13, 9, 9, 7, 5, 3, 2, 1

Least to greatest:

1, 2, 3, 5, 7, 9, 9, 13, 14

It is REALLY important that you use ALL of the numbers you are given, even if there are two or more of the same number.

The next thing you need to do is find the number that is in the middle.

It will be the same for both least to greatest AND greatest to least.

You can either count one from either side, going in a pattern, OR you can count how many there is, divide it by 2, and whatever answer you get, count that many times over from one side.

In this case, your answer goes like this:

since there are 9 numbers, and 9 is not an even number, you will have only one median. Having 2 medians IS normal and it IS ok.

In this case, you want to go down one number (from 9) and divide that. So you do 8 divided by 2, which is 4. Count that many times over and you have your answer, 7.

I hope this helped you!

Have a great dayyyy

5 0

3 years ago

I need help with these 2 questions!! please 20 points!!!

bezimeni [28]

9514 1404 393

Answer:

45 cm²
38 cm²

Step-by-step explanation:

The conventional way to work these problems is to make use of the formulas for areas of a triangle, rectangle, and semicircle. If you've used these formulas for a while, you recognize that they give you certain relationships that may make these problems easy to do mentally.

__

1. The area of a triangle is half the product of height and width, so is equivalent to the area of a rectangle either half as high, or half as wide. We note that the width of the sail is 5 cm, so half that is 2.5 cm--exactly the same as the height of the boat's hull. That means we can add the height of the sail to the length of the boat, and the total area can be considered to be the same as that of a rectangle that is

2.5 cm high × (12 cm + 6 cm) long = (2.5)(18) cm² = 45 cm²

__

2. The usual formula for the area of a circle is ...

A = πr²

When expressed in terms of diameter, this becomes ...

A = π(d/2)² = (π/4)d²

Then the area of a semicircle is half that, or (π/8)d². This is equivalent to the area of a rectangle that is "d" wide and "π/8·d" high. That is, the approximate area of the semicircle is that of a rectangle 4 cm high by (π/8·4 cm) = π/2 cm wide. In other words, the semicircle effectively adds π/2 cm to the left end of the 6 cm central rectangle of the figure.

As discussed above, the area of a triangle is equivalent to the area of a rectangle half as high. In this figure, the triangle is 10-6 = 4 cm wide, so can be considered to contribute 4/2 = 2 cm to the right end of the 6 cm central rectangle.

If we consider π ≈ 3, then the approximate area of the figure is ...

(4 cm)(3/2 cm + 6 cm + 2 cm) = (4)(9.5) cm² = 38 cm²

__

The exact value is 4(8+π/2) = 32+2π ≈ 38.283 cm².

7 0

2 years ago

Max spends three times as long on his math homework than he does on his science homework

iren [92.7K]

Answer: Max is a very intelligent boy.

6 0

3 years ago

Read 2 more answers