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3 years ago

Given the equation, y= 1/3 x - 4. what is the slope and the y-intercept?

Mathematics

1 answer:

tamaranim1 [39]3 years ago

3 0

Answer:

The slope (m) = 1/3 and the y-intercept (b) = -4

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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

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

7 0

3 years ago

If two supplementary angles are in the ratio of 4:5 the measure of the larger angle is

dimulka [17.4K]

Answer:

Step-by-step explanation:

Let the angles be 4x , 5x

4x + 5x = 180 { supplementary}

9x = 180

x = 180/9

x = 20

Larger angle= 5x = 5* 20 = 100

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3 years ago

What is 4 + x / 7=2

Taya2010 [7]

Answer:

-14

Step-by-step explanation:

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We can use division to solve real-life problems, such as: We can use division to solve real-life problems, such as:

Komok [63]

Answer:

we can use division to solve real life problem such as: how much candy each of 5 students will receive if 20 candy are shared equally

Step-by-step explanation:

cause 20/5 = 4

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2 years ago

Can someone please help me

Anettt [7]

Answer:

6, 12, 21, 10, then 4

Step-by-step explanation:

This is more difficult to answer than you would think, you can't actually see the picture when typing the answer

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3 years ago

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