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2 years ago

Asap! please help i’ll give brainliest

Mathematics

1 answer:

Aleonysh [2.5K]2 years ago

6 0

Answer: 2nd one

Step-by-step explanation: Look at the options. In all of the options, the number of 0's is 3 so you don't have to look for the zero's. Next look at the one's. The first 2 have 2 ones and the next 2 have 3. The number of ones in the data is 2 so you can eliminate the last 2. Then look at the 2's between the top 2. In the first one, there is 2 and in the second one there is only one. In the data table, there is one 2 so the answer has to be the 2nd one. Hope this helps :)

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Line g passes through points (5, 9) and (3, 2). Line h passes through points (9, 10) and (2, 12). Are line g and line h parallel

icang [17]

For this case we find the slopes of each of the lines:

The g line passes through the following points:

$(x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}) :( 5,9)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {9-2} {5-3} = \frac {7} {2}$

Line h passes through the following points:

$(x_ {1}, y_ {1}) :( 9,10)\\(x_ {2}, y_ {2}) :( 2,12)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}}{x_ {2} -x_ {1}} = \frac {12-10} {2-9} = \frac {2} {- 7} = - \frac {2} {7}$

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.

It is observed that lines g and h are not parallel. We verify if they are perpendicular:

$\frac {7} {2} * - \frac {2} {7} = \frac {-14} {14} = - 1$

Thus, the lines are perpendicular.

Answer:

The lines are perpendicular.

8 0

2 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

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

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

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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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