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1 year ago

Simplify (2x²-9x-5)÷(2x+1) where x≠-1/2

Mathematics

1 answer:

Alex777 [14]1 year ago

8 0

$\frac{2x^2-9x-5}{2x+1}$

Using long division:

$\frac{2x^2-9x-5}{2x+1}=x-5$

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What is the range of the function represented by the graph? I need help ASAP

kumpel [21]

Step-by-step explanation:

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3 years ago

Solve the quadratic equation. (x + 1)2 = 16 x = 3 or-5 x= -3 or 5 X = 35

Damm [24]

Answer:

X=7

(x - 3 )(x +5)

(x+3) (x-5)

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3 years ago

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

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

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3 years ago