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Nikolay [14]
3 years ago
5

Plz help asap!!!

Mathematics
1 answer:
Nookie1986 [14]3 years ago
7 0

Answer:

28 Inches

Step-by-step explanation:

10 ft x 12 = 120 inches

120/2 is 60 inches to the center of the wall

28+28+8 = 64 in   measure of the frames and the space between them

64 / 2 = 32 in measure from center of both paintings and the 8 in requirement

60 in - 32 in = 28 in is the measurement from the wall to the outer diameter of the paintings

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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
Fiona wrote out the description of each step for her multiplication of the binomial and trinomial (2x – 3)(5x2 – 2x + 7).
Valentin [98]

Answer:

Step 2

Step-by-step explanation:

Fiona did mistake step 2.

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The correct result is

-3(5x^2 - 2x + 7) = -15x^2 + 6x - 21

Fiona written -6x instead of + 6x.

That's the error.

The answer is "Step 2"

Hope you will understand the concept.

Thank you.

5 0
3 years ago
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Nadusha1986 [10]

Answer:

d

Step-by-step explanation:

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8 0
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andriy [413]

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7 0
3 years ago
9. Solve for x: 2x – y = (3/4)x + 6.​
AlekseyPX

Answer:

x = 4(y + 6)/5

Step-by-step explanation:

2x - y = (3/4)x + 6

2x - (3/4)x = y + 6

(8x - 3x)/4 = y + 6

5x/4 = y + 6

5x = 4(y + 6)

5x = 4y + 24

x = (4y + 24)/5

Therefore, x = 4(y + 6)/5

4 0
3 years ago
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