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Snezhnost [94]
3 years ago
5

What is the amplitude of y=1/2 sin2x

Mathematics
2 answers:
Colt1911 [192]3 years ago
8 0
(-\frac{1}{2},\frac{1}{2})
Amplitutde:
(\frac{1}{2}-(-\frac{1}{2}))=1
Normally for sinx amplitude is 2 (1 +1). In the case when it is half sine amplitude is halved, therefore 0.5 +0.5 = 1 Paramers alpha = 2x does not matter because it only stretches the graph horizontally.
Alborosie3 years ago
7 0
for\ each\  \alpha \in R\ \ \ \ (for\ example\  \alpha =2x) \\\\the\ max\ of\ y=sin \alpha \ is\ 1\ \ \ and\ \ \ the\ min\ of\ y=sin \alpha \ is\ -1\\\\ the\ amplitude\ of \ \ \ \ y=sin \alpha \ \ \ \ is\ \ \ \ 1-(-1)=2\\\\\\then\  the\ amplitude\ of \ \ \ \ y= \frac{1}{2} sin 2x \ \ \ \ is\ \ \ \  \frac{1}{2} \cdot2= 1
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Step-by-step explanation:

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For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then wri
Anna007 [38]

Answer:

a)

Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.

Proof by Contrapositive:

Assumed statement: Suppose that integers x and y do not have opposite parity.

Proven Statement: x and y are not a pair of consecutive integers.

Proof -

x = 2u₁ , y = 2u₂

Then

(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)

If y = 2u₁ + 1

Not possible

⇒x and y are not a pair of consecutive integers.

Hence proved.

Proof by Contradiction:

Assumed statement: Suppose x and y are not a pair of consecutive integers.

Proven Statement: Suppose x and y do not have opposite parity.

Proof -

If x and y are not a pair of consecutive integers.

⇒ either x and y are odd or even

If x and y are odd

⇒x and y have same parity

Contradiction

If x and y are even

⇒x and y have same parity

Contradiction

(b)

Proof by Contrapositive:

Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)

Proven Statement: n² is not odd (i.e n² is even)

Proof -

Let n is even

⇒n = 2m

⇒n² = (2m)² = 4m²

⇒n² is even

Hence proved.

Proof by Contradiction:

Assumed statement: Let n be an integer such that n² be odd.

Proven Statement:  suppose that n is not odd (i.e n is even)

Proof -

Let n² is odd

⇒n² is even

⇒n² = 2m

⇒2 | n²

⇒2 | n

⇒n = 2x

⇒ n is even

Contradiction

8 0
3 years ago
What is the sale of the original price?
Lady bird [3.3K]

Answer:

50 dollars

Step-by-step explanation:

40*25%=10

40+10= 50 dollars

Add it to find the original sales price which would end up being 50 dollars! Hope this helps, have a good day. c;

3 0
3 years ago
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B 2y - 3x = 1
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