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muminat
3 years ago
10

Solve for x 3/4+x=1/2 Simplify your answer

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

Step 1. Subtract 3/4 from both sides

x = 1/2 - 3/4

Step 2. Simplify 1/2 - 3/4 to -1/4

x = -1/4

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Advocard [28]

Answer:

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Step-by-step explanation:

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7 0
2 years ago
Find dy/dx if f(x) = (x + 8)^3x.
vlabodo [156]
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 :)
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3 years ago
Simplify\:\frac{\sqrt{5}}{\sqrt{3}}
avanturin [10]

\dfrac{\sqrt 5}{\sqrt 3} =\sqrt{\dfrac 53} \approx 1.291

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3 years ago
If a=2,b=-1,c=-3 and d=-2.find the value of 7a2-3ac+d2​
hram777 [196]

Answer:

42

Step-by-step explanation:

It's just a distribution property where the given value of each variables (a, b, c, d) are being distributed to the given equation:

7a2-3ac+d2

7(2)(2) - 3(2)(-3) + (-2)(2)

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2 years ago
Draw to show how you can use models to compare 345 and 391.
Trava [24]
I have drop in a file for u to see it.

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3 years ago
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