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2 years ago

The image shown below shows the first 3 stages of a pattern.

Mathematics

2 answers:

alisha [4.7K]2 years ago

7 0

Answer:

A. 44

Step-by-step explanation:

Well, there is something interesting we see in this image. The number of tiles add by 2 every time which makes the 22nd the answer because 2 x 22 is 44

Nina [5.8K]2 years ago

5 0

It would be 44 tiles.

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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

2 years ago

Find all the factor pairs for 84 and complete the equations.

VMariaS [17]

1. 84 = 1 x 84

2. 84 = 2 x 42

3. 84 = 3 x 28

4. 84 = 4 x 21

5. 84 = 6 x 14

6. 85 = 7 x 12

Hope this helps!

5 0

2 years ago

How do you represent an unknown quantity?

Dennis_Churaev [7]

Answer: With a variable. A variable is a letter you use in an equation , like this: 7+x=14, X is a classic one but you can use any letter u please! (In my school at least.)

5 0

3 years ago

Ophelia read ⅕ of her 60 pages book in ½ hour. How many pages can she read in one hour?

marishachu [46]

Answer:

She can read 24 pages in one hour.

Step-by-step explanation:

$\frac{1}{5}*2$ = $\frac{2}{5}*60pages = 24pages$