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3 years ago

The perimeter of a rectangle is 84 Centimeters. the length is twice the width. find the length and width

Mathematics

1 answer:

KatRina [158]3 years ago

6 0

Length= 28
Width= 14

Work:

2(2x)+2(x)=84
4x+2x=84
6x=84
x=14

14x2=28 (length)

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A lighthouse keeper has a 10 degrees angle of depression between the horizontal light beam and the line of sight from the ship.

Andrei [34K]

107.75m
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
$tan \theta = \frac{opp}{adj}$
plus in values, we know.
$tan (10) = \frac{19}{x}$
switch tan(10) and x using the products property.
$x = \frac{19}{tan (10)}$
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x=107.75

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3 years ago

Find the nth term of this quadratic sequence<br> 3, 11, 25, 45, .

Hoochie [10]

The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

3, 11, 25, 45, ...

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

The sequence is expressed as follows:

3,3+8,11+11,25+20,...

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

6 $(\frac{n(n+1)}{2} )$

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

= 3n² - n + 1

Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Learn more about Principle of mathematical induction at:

brainly.com/question/29222282

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2 years ago

What is the solution to the compound inequality? –6 ≤ 2x + 6 ≤ 6

maw [93]

∈ ≤ ≥

-6 ≤ 2x + 6 ≤ 6 ( seperate the two inequalities)

2x + 6 ≥ - 6

2x + 6 ≤ 6 (solve the inequalities)

x ≥ -6

x ≤ 0 (find the intersection)

solution is : x ∈ { -6, 0 }

7 0

4 years ago

How do I find the length of SW?

baherus [9]

If we assume that ST = 2x + 2, and that TW = 4x - 4, then we can just add the two segments together, as shown below (IF you're asking for the length, that is).

(2x + 2) + (4x - 4)
2x + 2 + 4x - 4
Group together like terms.
(2x + 4x) and (2 - 4)
6x (+) - 2
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3 years ago

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kipiarov [429]

Answer:

1: 120

2: 138

3: Less than

Step-by-step explanation:

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4 years ago