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Katarina [22]
3 years ago
15

Consider f and c below. f(x, y, z) = yzexzi + exzj + xyexzk,

Mathematics
2 answers:
zepelin [54]3 years ago
4 0
\mathbf f(x,y,z)=yze^{xz}\,\mathbf i+e^{xz}\,\mathbf j+xye^{xz}\,\mathbf k

We're looking for a scalar function f(x,y,z) such that its gradient is equal to the given vector-valued function \mathbf f(x,y,z):

\nabla f(x,y,z)=\mathbf f(x,y,z)

That is, we require

\dfrac{\partial f}{\partial x}=yze^{xz}
\dfrac{\partial f}{\partial y}=e^{xz}
\dfrac{\partial f}{\partial z}=xye^{xz}

Integrating the first equation with respect to x gives

f(x,y,z)=\dfrac{yz}xe^{xz}+g(y,z)

Differentiating with respect to y gives

\dfrac{\partial f}{\partial y}=e^{xz}=\dfrac zxe^{xz}+\dfrac{\partial g}{\partial y}

but from this step we can see that it's not possible for g to be a function of y and z, independent of x. So there is no such function f(x,y,z).
xenn [34]3 years ago
4 0

Answer:

a) ye^(xz)

b) 16

Step-by-step explanation:

Look at https://answers.yahoo.com/question/index?qid=20160531012407AAtnrQj for similar example

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Q ,# 13 Graph the function<br>Y = - X + X ^2
GalinKa [24]
We have the following function that is a quadratic function:

y=-x+x^2

So the graph of this function is shown in the figure below. This is a <em>parabola</em> as you can see. The roots of this functions, that is, the x-intercepts are:

y=-x+x^2 \\ y=x(x-1) \\ \\ x_{1}=0 \ and \ x_{2}=1

As you can see in the figure. This function decreases from (-\infty,0.5) and increases from (0.5, \infty)

Finally, another thing we can see from the graph is that the vertex is the point:

V(0.5,-0.25)


4 0
4 years ago
Read 2 more answers
HELPP ME PLZ WILLING TO SEND MONEY! It’s urgent
ExtremeBDS [4]

Answer:

I think it would be 5 and 5 of each solution

7 0
3 years ago
Read 2 more answers
The base of a triangle is 10cm greater than the height .the area is 28cm .find height and base
Naya [18.7K]

Answer:

Height = 5.6cm

Step-by-step explanation:

Area = 1/2bh

b = 10cm, area = 28cm^2

:- 28 = 1/2 × (10)h

28 = 5h

h = 28/5

h = 5.6cm

8 0
3 years ago
A rental truck costs $96 per day plus $0.60 per each mile. If Calvin can spend a maximum of $120, how many miles can he drive th
nikdorinn [45]

Answer:

40 miles

Step-by-step explanation:

You would have to start by doing $120 - $96 for the per-day fee, which leaves Calvin with $24 to spend on miles.

Next you would do $24 ÷ $0.60 to find the number of miles he can drive, which is 40 miles.

5 0
3 years ago
WHAT IS THE ANSWER TO y= 4x + 11 pls. Hurry!!!! :)
lesya [120]

Slope is 4

Y-intercept is 11

7 0
3 years ago
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