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lions [1.4K]
3 years ago
14

Which equation is part of solving the system by substitution? 4(y + 11)2 – 3y2 = 8 4(11 – y)2 – 3y2 = 8 4(y – 11)2 – 3y2 = 8 4(–

11y)2 – 3y2 = 8

Mathematics
2 answers:
sweet [91]3 years ago
5 0

Answer : The equation which is the part of solving the system by substitution is,

4(11-y)^2-3y^2=8

Step-by-step explanation:

As we are given two equations as:

x+y=11      ............(1)

4x^2-3y^2=8    .............(2)

From equation 1, we get the value of 'x'.

x=11-y     ............(3)

Now substitute equation 3 in equation 2, we get:

4x^2-3y^2=8

4(11-y)^2-3y^2=8

Thus, the equation which is the part of solving the system by substitution is,

4(11-y)^2-3y^2=8

swat323 years ago
3 0

Answer:

4(11-y)^{2} -3y^{2}=8

Step-by-step explanation:

we have

x+y=11 ----> equation A

4x^{2} -3y^{2}=8 ----> equation B

Solve the system by substitution

step 1

isolate the variable x in the equation A

x=11-y ----> equation A1

step 2

Substitute the equation A1 in the equation B

4(11-y)^{2} -3y^{2}=8

Solve for y

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2 years ago
Find dy/dx if f(x) = (x + 8)^3x.
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This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)
8 0
3 years ago
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