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2 years ago

The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum?

Mathematics

2 answers:

Serjik [45]2 years ago

6 0

Answer:

2√5

Step-by-step explanation:

Using the formula for calculating resultant

R = √Fx + Fy

\sum Fx = -2sin 45 + 4 cos 45

\sum Fx = 2cos45

\sum Fx = 2(1/√2)

\sum Fx = 2/√2

Similarly;

\sum Fy = 2 cos 45 + 4 sin45

\sum Fx = 2(1/√2) + 4(1/√2)

\sum Fx = 6/√2

Magnitude = √(2/√2)²+6/√2)²

Magnitude = √4/2 + 36/2

Magnitude = √2+18

Magnitude = √20

Magnitude = 2√5

Hence the magnitude of their sum is 2√5

Allisa [31]2 years ago

3 0

Answer:

2√5

Step-by-step explanation:

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QuizBIGPOINT

lianna [129]

The number of permutations of the problem is

This = 24
Outfit = 360

<h2>Combination</h2>

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Combinations are the number of ways to choose members from a certain number, namely from members of a set, combinations can also be interpreted as many ways to make subsets, namely with a certain number of members, namely from members of a set, if a set has n members then the selection of r members, and the combination of n is where r is less than n.

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<h3>The Formula : </h3>

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<h2>Permutation</h2>

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Permutations are a way to determine the number of arrangements that occur by paying attention to the order. So in permutations, position/order is very important, namely AB is considered different from BA (AB ≠ BA). Permutation formula

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<h3>The Formula :</h3>

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$\frac {n!}{k!}$ (With Double Elements)

n! (Without Double Elements)

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<h2>Factorial</h2>

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The factorial of a natural number is the successive multiplication of a natural number that begins with the number one and arrives at the natural number, the factorial is used in calculating combinations, probabilities, and permutations.

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<h3>For example</h3>

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》2! = 1 × 2
》3! = 1 x 2 x 3
》4! = 1 x 2 x 3 x 4
》5! = 1 x 2 x 3 x 4 x 5
》6! = 1 × 2 × 3 × 4 × 5 × 6
》7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
》8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8
》9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
》10! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10

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The following is an example of a factorial that does not involve mixed arithmetic operations, so if you want to add it up we just need to calculate it like a normal number, a factorial number that only multiplies the difference between a factorial number that is added up by addition, subtraction, multiplication, division, for example see below.

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6! x2! - 3! : 4!

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The example above is a mixed arithmetic operation that contains multiplication, subtraction, and division. Remember that in mixed arithmetic operations, multiplication/division must be completed before addition/subtraction.

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<h3>The Formula : </h3>

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n! (Combined Multiplication)

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<h2>Place Filling Rules</h2>

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The Place Fill Rule is a method or method that can be used to determine the number of ways an object occupies its place. The filling slots rule is a method of calculating how many possible ways there are in an experiment or event. If a first event can be done in m different ways and the second event can be done in a different way and so on until the last event in k.

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<h3>The formula</h3>

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n1 × n2 × n3 × ... × nr

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<h2><u>Question</u></h2>

Find the number of permutations of letters of the word

- this

- outfit

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<h2><u>Answer</u></h2>

"Number One"

=》This = Four Letters ( 4! )

P = 4!

P = 1 × 2 × 3 × 4

P = 2 × 3 × 4

P = 6 × 4

P = 24

==========

"Number Two"

=》Outfit = Six Letters ( 6! )

=》Outfit = Two Letters The Same ( "T" ) = 2!

P = $\frac {1×2×3×4×5×6}{2×1}$

P = $\frac {2×3×4×5×6}{2}$

P = $\frac {6×4×5×6}{2}$

P = $\frac {24×5×6}{2}$

P = $\frac {120×6}{2}$

P = $\frac {720}{2}$

P = 360

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<h2><u>Conclusion</u></h2>

So, the number of permutations of the problem is

This = 24
Outfit = 360

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<h2>Learn More</h2>

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<h2>Answer Detail</h2>

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➽ Subject: Mathematics
➽ Class : 12
➽ Chapter : 7 - The Rule of Counting:
➽ Maple Code
➽ Categorization code : 12.2.7
➽ Keywords : This, Outfit

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3 years ago

Compare negative 7 and positive 7

Zarrin [17]

They are inverse operations

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3 years ago

Length of a rectangle is 3 times it’s width perimeter 48 find area

valkas [14]

Answer:

Let width = l

Therefore, length = 3l

Perimeter = 2(l+b)

48 = 2(l+3l)

48 = 2× 4l

48 = 8l

8l = 48

l = 48/8

l = 6

Width = 6

Therefore, length = 3×6

= 18

Area = l×b

= 18×6

= 108

Step-by-step explanation:

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3 years ago

In rhombus FGHJ, m∠1=37°.<br><br> What is m∠2?

777dan777 [17]

Answer:

m∠2 = 53°

Step-by-step explanation:

We will use two properties of a rhombus to solve this problem.

1). Opposite angles of a rhombus are equal.

2). Diagonals bisect the angles.

Since ∠JFG and ∠JHG are the opposite angles of the rhombus,

m∠JFG = m∠JHG

Since, diagonal FH bisect ∠JHG,

m∠FHJ = m∠GHF = m∠JFH = m∠GFH = 37°

In triangle JFH,

m∠FHJ + m∠JFH + m∠HJF = 180°

37° + 37° + m∠HJF = 180°

m∠HJF = 180 - 74

= 106°

Since, diagonal GJ bisects angle HJF,

m∠FJG = $\frac{106}{2}$ = 53°

Therefore, m∠2 = 53°.

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