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3 years ago

The values of sine and cosine are always between 0 and 1. True or False

Mathematics

2 answers:

Nadya [2.5K]3 years ago

6 0

Answer:

False

Step-by-step explanation:

The range of the sine and cosine functions is -1 to 1, including those values. In interval notation, it is [-1, 1].

o-na [289]3 years ago

3 0

Answer: True

Step-by-step explanation:

The length of the sides of a right triangle are always less than the length of the hypotenuse.

Also, the ratio of any side of a triangle and the hypotenuse is always less than 1.

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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

3 years ago

Find the formula for an exponential function that passes through the two points give.

Ksenya-84 [330]

Answer:

$y=3(2)^{x}$

Step-by-step explanation:

Given.

Two points are given.

$(x, y)=(-1,\frac{3}{2})$ and $(x, y)=(3,24)$

An exponential function is in the general form.

$y=a(b)^{x}$ -------(1)

We know the points $(-1,\frac{3}{2})$ and $(3,24)$

put the first point value in equation 1

$\frac{3}{2}=a(b)^{-1}$

$\frac{3}{2}=\frac{a}{b}$

$a=\frac{3}{2}\times b$ --------(2)

put the second point value in equation 1

$24=a(b)^{3}$ ----------(3)

Put the a value from equation 2 to equation 3

$24=\frac{3}{2}\times b(b)^{3}$

$b^{3+1}=\frac{24\times 2}{3}$

$b^{4} = 16\\b=\sqrt[4]{16} \\b=2$

Put the b value in equation 2

$a=\frac{3}{2}\times 2$

$a=3$

Put the a and b value in equation 1

$y=3(2)^{x}$

So, the exponential function that passes through the points $(-1,\frac{3}{2})$ and $(3,24))$ are $y=3(2)^{x}$ .

6 0

3 years ago

A sandbox has an area of 32 square feet, and

Ksivusya [100]

The width is 8 because 4x8=32

7 0

3 years ago

What is the median price of rent for the university of oregon

almond37 [142]

Answer:

$11,450

Step-by-step explanation:

thats the median price according to Google

5 0

3 years ago

Plz help for points plzzz

White raven [17]

Answer: 5.3

Step-by-step explanation: Do 9.8 (Friend swim depth) - 4.5 (dolphin jump height) to get your answer.

4 0

4 years ago

Read 2 more answers