How do i find the lateral area, total area, and volume of a triangular prism?

Mathematics

1 answer:

drek231 [11]3 years ago

4 0

Total Area = Lateral Area + Area of the Ends
Total Area = Height * Width * Number of Sides + Area of the 2 ends

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Which sequence is modeled by the graph below?

mariarad [96]

Answer:

$a_n=27\left(\dfrac{1}{3}\right)^{n-1}$

Step-by-step explanation:

From inspection of the graph, the given points are:

(2, 9)
(3, 3)
(4, 1)

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

$a_n=ar^{n-1}$

where:

a is the first term
r is the common ratio
$a_n$ is the nth term

Rewrite the given points as terms of the sequence:

(2, 9) ⇒ a₂ = 9
(3, 3) ⇒ a₃ = 3
(4, 1) ⇒ a₄ = 1

To find the common ratio r, divide consecutive terms:

$\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}$

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

$\implies a_2=9$

$\implies a\left(\dfrac{1}{3}\right)^{2-1}=9$

$\implies \dfrac{1}{3}a=9$

$\implies a=27$

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

$a_n=27\left(\dfrac{1}{3}\right)^{n-1}$

Learn more about geometric sequences here:

brainly.com/question/25398220

brainly.com/question/27783194

5 0

1 year ago

Read 2 more answers

Find the common ratio for the following sequence: 11, 121, 1331, 14641, ... PLZ HELP!!!!!!

frez [133]

Hi There!

The answer is multiplying by 11. Throughout the sequence you multiply 11 by the number before to get the next number. For example, the next number in the sequence is 14641 x 11 = 161051.

Hope This Helps :)

8 0

3 years ago

Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organism

mash [69]

Only letter a has an answer. Pls. see attachment.

The probability that one cubic meter of discharge contains at least 8 organisms is 0.7798