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Tju [1.3M]
3 years ago
15

Write the standard equation of a circle with center (−4, 0) and radius 3.

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0

The standard equation of a circle:

(x-h)^2+(y-k)^2=r^2

We have the center (-4, 0) → h = -4 and k = 0, and the radius r= 3. Substitute:

(x-(-4))^2+(y-0)^2=3^2\\\\\boxed{(x+4)^2+y^2=9}

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A stadium has 49 comma 000 seats. Seats sell for ​$35 in Section​ A, ​$30 in Section​ B, and ​$25 in Section C. The number of se
romanna [79]
A has 27,000 seats, B has 14,
200 seats, and C has 12,800 seats
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2 years ago
What is the solution to the equation sqrt n= sqrt 3n-3 +1?​
inna [77]
The answer would be n = 1
3 0
3 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 :)
8 0
3 years ago
Find the base of a parallelogram with the area of 60 in.² and height of 4 inches use the formula for the area of the parallelogr
Alexxx [7]
A = bh
60 in.² = b(4)
60/4 = b
b = 15 inches

Hope this helped!
7 0
3 years ago
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