All categories

3 years ago

Help please ASAP !!!

Mathematics

1 answer:

Arisa [49]3 years ago

3 0

For this case we have that by definition of trigonometric relations of rectangular triangles, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. So:

$Sin (45) = \frac {leg} {h}$

Where h is the hypotenuse.

$\frac {\sqrt {2}} {2} = \frac {leg} {h}$

We cleared h:

$h = \frac {2leg} {\sqrt {2}}$

We rationalize:

$h = \frac {2leg} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}}\\h = \frac {2 \sqrt {2} * leg} {2}\\h = \sqrt {2} * leg$

ANswer:

Option A

You might be interested in

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

3 years ago

The spanish club has 78 members, 42 girls and 36 boys whats the ratio

Makovka662 [10]

The ratio fo boys to girls is 12:16

5 0

3 years ago

Read 2 more answers

Shawna works at a local pet store. When she works 3 hours, she earns $27. When she works 8 hours, she earns $72. Which equation

finlep [7]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What does the strategy 'Dont get bogged down' mean

kap26 [50]

It means not to get too invested in details or to become so invested in something that you can’t focus on anything else.

5 0

2 years ago

Determine the following probability

Masja [62]

Probability is 7/8. Sorry if I got it wrong, but since no others are answering, thought I might give it a go.

7 0

2 years ago

Read 2 more answers