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3 years ago

Find the value of x

Mathematics

2 answers:

Elina [12.6K]3 years ago

4 0

Answer:

d=60°

Step-by-step explanation:

Both angles are equal to each other because they are vertical angles and are therefore congruent.

Bogdan [553]3 years ago

3 0

Answer:

60 degrees

Step-by-step explanation:

Hi,

These angles are actually equal to each other. That means that d = 60 degrees. They are vertical angles.

I hope this helps :)

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In how many ways can the letters in the word MATHEMATICS be reshuffled so that all consonants appear together?

steposvetlana [31]

Answer:

75600

Step-by-step explanation:

We are given that a word MATHEMATICS

Total letters =11

M repeated 2 times

T repeated 2 times

A repeated 2 times

Total vowels=4

Let MTHMTCS=P

Total number of ways in which MTHMTCS can be arranged= $\frac{7!}{2!2!}$

PAEAI

Total number of ways in which PAEAI can arranged= $\frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!}{2!2!}\times \frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!5!}{2\times 2\times 2}=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1}{8}=75600$

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4 0

3 years ago

Find y as a function of x if y"' + 9y' = 0, y(0) = 6, y'(0) = 9, y"(0) = 18. y(x) =

Andreas93 [3]

Answer:

y(x) = 8 - 2cos 3x + 3sin 3x

Step-by-step explanation:

Given the equation:

y''' + 9y' = 0

The characteristic equation :

⇒r³ + 9r =0

Solving for r, we get r = 0 and r = ± 3i

The general equation for such equation is :

y = C₁ + C₂cos 3x + C₃sin 3x

Given:

y(0) = 6

Thus, Applying in the above equation, we get

6 = C₁ + C₂ .......................................................1

Differentiating y , we get:

y' = -3C₂sin 3x + 3C₃cos 3x

Given:

y'(0) = 9

Thus, Applying in the above equation, we get

9 = 3C₃

or,

C₃ = 3

Differentiating y' , we get:

y'' = -9C₂cos 3x - 9C₃sin 3x

Given:

y''(0) = 18

Thus, Applying in the above equation, we get

18 = -9C₂

or,

C₂ = -2

Applying in equation 1 , we get:

C₁ = 8

Thus,

y(x) = 8 - 2cos 3x + 3sin 3x

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Answer:

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Step-by-step explanation:

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