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3 years ago

What is the simplest form of this expression? -x^3(5x+1)+4x^4

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Answer:

-x^3*(x + 1)

Step-by-step explanation:

Perform the indicated multiplication and then write out all the terms in descending order by powers of x:

-x^3(5x+1)+4x^4 = -5x^4 - x^3 + 4x^4

= -x^4 - x^3, or = -x^3*(x + 1)

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I need help is it A B C or D

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3 years ago

A stick of butter weighs a quarter pound.

olga nikolaevna [1]

Answer:

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3 years ago

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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

What operation should be used to solve the equation 153=g+45

Advocard [28]

Answer:

Subtraction

Step-by-step explanation:

Subtraction

153 - 45 = g + 45 - 45

108 = g

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3 years ago

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denis23 [38]

Answer:

B & D

Step-by-step explanation:

We use percents in decimal form to multiply it with the price. We convert percents into decimals by dividing the percent number by 100. For example, 78% divided by 100 becomes 0.78.

There are two ways to look at it:

For finding the price we pay during a sale, we focus on the percent we pay. If 22% off is the sale, then we spend 78% or 100-22=78. If 20% off is the sale, then we pay 80% or 0.80. Multiply that by x an unknown price and we have 0.8x.
We can find the percent off by multiplying the price by the percent conversion. So 20% is 0.20. Then subtract it from the original price to find the leftover that we pay. This is x-0.2x.

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3 years ago

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