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2 years ago

9

Simplify: 20 sin(2x) cos(2x)

1 answer:

alexandr1967 [171]2 years ago

8 0

Use the the double angle formula:
sin(2A)=2sin(A)cos(A)

substitute 2x for A, then
20sin(2x)cos(2x)=10(sin(2(2x))cos(2(2x))=10sin(4x)

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3 years ago

Read 2 more answers

$0.\overline{5} + 0.19\overline{4}$.

Scilla [17]

Answer:

$0.\overline{5} + 0.19\overline{4}=0.75$

Step-by-step explanation:

Given expression:

$0.\overline{5} + 0.19\overline{4}$

To evaluate the expression.

Solution.

The values are

$0.\overline{5}=0.555555......$

Let $X=0.555555.....$ -----------1

Multiplying 10 both sides.

$10X=5.555555....$ ----------2

Subtracting 1 from 2.

$10X=5.555555....$

- $X=0.555555.....$

-------------------------------------------

$9X=5.0$

Dividing both sides by 9.

$\frac{9X}{9}=\frac{5}{9}$

$X=\frac{5}{9}$

$0.19\overline{4}=0.194444....$

Let $Y=0.1944444..$

Multiplying both sides by 100

$100Y=19.44444..$ ------------3

Multiplying 1000 both sides.

$1000Y=194.4444....$ ----------4

Subtracting 3 from 4.

$1000Y=194.4444....$

- $100Y=19.44444.....$

-------------------------------------------

$900Y=175.0$

Dividing both sides by 900.

$\frac{900Y}{900}=\frac{175}{900}$

$Y=\frac{175}{900}$

So, we can evaluate the given expression as:

⇒ $0.\overline{5} + 0.19\overline{4}$

⇒ $X+Y$

⇒ $\frac{5}{9}+\frac{175}{900}$

Taking LCD = 900

⇒ $\frac{5\times 100}{9\times 100}+\frac{175}{900}$

⇒ $\frac{500}{900}+\frac{175}{900}$

Adding numerators.

⇒ $\frac{500+175}{900}$

⇒ $\frac{675}{900}$

⇒ $0.75$ (Answer)

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