Find the derivative of y=sin^(2)(x)cos^(2)(x)

1 answer:

5 0

$sin^{2}x \ cos^{2} x= \frac{1}{2} (1-cos2x) \times \frac{1}{2} (1+cos2x) \\ = \frac{1}{4} (1- cos^{2} 2x) \\ = \frac{1}{4} ( sin^{2} 2x +cos^{2} 2x- cos^{2} 2x) \\ = \frac{1}{4} ( sin^{2} 2x) \\ = \frac{1}{4} ( \frac{1}{2} (1-cos2(2x))) \\ = \frac{1}{8} (1-cos4x) \\ \frac{d}{dx} (sin^{2}x \ cos^{2} x)= \frac{1}{8} \frac{d}{dx} (1-cos4x) \\ = \frac{1}{8} [-4(-sin4x) \\ \frac{1}{2} sin4x$

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If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.

babymother [125]

Answer:

event A and B are independent because P(A and B) = P(A) x P(B) = 0.15

Step-by-step explanation:

When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;

P(A and B) = P(A) x P(B)

Given;

P(A) = 0.25

P(B) = 0.60

P(A and B) = 0.15

Now, let's check if P(A and B) will be equal to P(A) x P(B)

P(A) x P(B) = 0.25 x 0.60 = 0.15

P(A and B) = P(A) x P(B), thus event A and B are independent.

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Amanda [17]

Answer: 3.78

Step-by-step explanation:

Because she bought 2 $1.89 loaves, she spent 2 * 1.89, or 3.78 dollars.

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2 years ago

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(3x^4y^5) ^ 3/7 in radical form

kobusy [5.1K]

The expression in radical form is $(\sqrt[7]{3x^4y^5}) ^3$

In order to express the given indices expression in radical form, we need to ensure there is a square root present in the resulting expression.

According to the law of indices,

$a^{m/n} = \sqrt[n]{m}$