Add those equations together
<span>1. 4x = 16, x = 4

2. Multiple the second one by 2
2x+4y=22
4x-4y=-16
6x = 6, x = 1

3. Add them together
8x = 24, x = 3
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8 0

3 years ago

Read 2 more answers

Integration of sin^2 2x cos^3 2x dx

lilavasa [31]

$\int\left[\sin^2(2x)\cos^3(2x)\right]dx=\int\left[\sin^2(2x)\cos^2(2x)\cos(2x)\right]dx\\\\\text{Use the trigonometric identity}\sin^2(x)+\cos^2(x)=1\to\cos^2(x)=1-\sin^2(x)\\\\=\int\left\{\sin^2(2x)[1-\sin^2(2x)]\cos(2x)\right\}dx\\\\\text{substitute}\ \sin2x=t\ \to\ 2\cos2x\ dx=dt\ \to\ \cos2x\ dx=\dfrac{1}{2}\ dt\\\\=\dfrac{1}{2}\int\left[t^2(1-t^2)\right]dt=\dfrac{1}{2}\int(t^2-t^4)dt=\dfrac{1}{2}\left(\dfrac{1}{3}t^3-\dfrac{1}{5}t^5\right)+C$

$=\dfrac{1}{2}\left(\dfrac{1}{3}\sin^3(2x)-\dfrac{1}{5}\sin^5(2x)\right)+C$

4 0

3 years ago

For the filming of a recent sci-fi movie, a model spaceship made to a scale of 1:16 was used. In the movie, the ship is supposed

Lunna [17]

Answer: 6.5 feets

Step-by-step explanation:

The model of the spaceship was made to a scale of 1:16. Assuming the same unit of measurement used in the actual spaceship was also used in the model space ship and it was in feets. This means 1 foot on the model spaceship represented 16 feets on the actual spaceship.

In the movie, the ship is supposed to be 104 feet long. Let x be the corresponding length on the model. Therefore,

1:16 = x:104

1/16 = x/104

16x = 104

x = 104/16 = 6.5feets

So the length of the model is 6.5 feets

8 0

3 years ago