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2 years ago

Determine if the two expressions are equivalent and

Mathematics

1 answer:

boyakko [2]2 years ago

6 0

9514 1404 393

Answer:

yes. Commutative Property of Addition

Step-by-step explanation:

The commutative property of addition tells you that the order of the addends is immaterial. These expressions are equivalent.

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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

Select the answer choice that is equivalent to the expression given below.

pochemuha

Answer:

B. 23x-10

Step-by-step explanation:

3 0

2 years ago

The area of Jackson’s rectangular garden is 64 square ft. If the length of the garden is 16 ft, what is the width of the garden?

zlopas [31]

Answer:

Step-by-step explanation:

1,280 it ez bro

6 0

2 years ago

A radio is being discounted 30%. If the sale price of the radio is $29.82, what was the original price of the radio?

meriva

Answer: $42.60

Step-by-step explanation:

Original price: p

Discount: 30%

Sale price: 29.82

p x 0.7 = 29.82

p = 29.82/0.7 = 42.60

3 0

2 years ago

In a certain year the population of a country reached 321 million. The overall birth rate was births per 1000, and the overall

kkurt [141]

Answer:

Then it would stay at 321 million

Step-by-step explanation:

if the birth and death rate is both 1000 then nothing will change. Population wise.

4 0

2 years ago