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mylen [45]
3 years ago
15

Find the lentgh of the missing side

Mathematics
1 answer:
adell [148]3 years ago
8 0

Answer:

8 is missinn

8 ixxdxx

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What is the next term in the pattern shown below? 10, 8.9, 7.8, 6.7, ...A. 6.6 C. 5.5B. 5.6 D. 1.1 please help!!
anzhelika [568]
You subtract 1.1 each time so the answer is 6.6 (a)
6 0
3 years ago
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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
If 2(4x + 3)/(x - 3)(x + 7) = a/x - 3 + b/x + 7, find the values of a and b.
zmey [24]

Answer:

a=3 and b=5.

Step-by-step explanation:

So I believe the problem is this:

\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}

where we are asked to find values for a and b such that the equation holds for any x in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)

2(4x+3)=a(x+7)+b(x-3)

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

2(4\cdot -7+3)=a(-7+7)+b(-7-3)

2(-28+3)=a(0)+b(-10)

2(-25)=0-10b

-50=-10b

Divide both sides by -10:

\frac{-50}{-10}=b

5=b

Now we have:

2(4x+3)=a(x+7)+b(x-3) with b=5

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

2(4\cdot 3+3)=a(3+7)+b(3-3)

2(12+3)=a(10)+b(0)

2(15)=10a+0

30=10a

Divide both sides by 10:

\frac{30}{10}=a

3=a

So a=3 and b=5.

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What is 40°F minus 32°divided by 1.8
grigory [225]


40 degrees - 32 degrees = 8 degrees

8 degrees divided by 1.8 = 4.4444444 degrees

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3 years ago
The absolute value of
MatroZZZ [7]
The correct answer is d
5 0
2 years ago
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