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3 years ago

Find the rate if the principal is $900, the time is 3 years, and the interest is $135. A) 5% B) 7.5% C) 15% D) 20%

1 answer:

3 0

The answer would be A) 5%. You can solve this by dividing 135$ by three years to get 45. then divide 45 by 900 to get 0.05 which is 5% in decimal form.

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Leviafan [203]

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3 years ago

Read 2 more answers

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

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Soloha48 [4]

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2 years ago

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3 years ago

Find the first derivative?

professor190 [17]

You could do the question the way it is written, but it is far easier to bring the negative power up to the numerator.

y= x^2 - 3. The derivative of that is
dy/dx = 2x The three is a constant and is always dropped when a derivative is taken
d(-3)/dx = 0

If you are a purist and want to solve the question the way it is written, you could do it this way.

dy/dx = d(1)/dx x^-2 - d(x^-2)/dx * 1
======================
(x^-2)^2

dy/dx = - (-2 x^ - 3) / x^-4

dy/dx = 2 x^-3 * x^4
dy/dx = 2 x^(-3 + 4)
dy/dx = 2x ^ 1
dy/dx = 2x <<<<< answer

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3 years ago