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Stels [109]
3 years ago
6

Find the partial derivatives of the following functions

Mathematics
1 answer:
Oliga [24]3 years ago
6 0

Answer:

Hello,

Step-by-step explanation:

a)

z=8x^2-4xy+5y^2\\\\\dfrac{\partial z}{\partial x} =16x^2-4y\\\\\dfrac{\partial z}{\partial y} =-4x+10y\\

b)

z=5xe^{y}\\\\\dfrac{\partial z}{\partial x} =5e^y\\\\\dfrac{\partial z}{\partial y} =5xe^y\\

c)

z=3xln(y)\\\\\dfrac{\partial z}{\partial x} =3ln(y)\\\\\dfrac{\partial z}{\partial y} =\dfrac{3x}{y}\\

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Help me out please an thank you
Jet001 [13]

Given:

The graph of a parabola.

To find:

The equation of the parabola.

Solution:

From the given graph, it is clear that the vertex of the parabola is at point (0,0) and it is a horizontal parabola.

The general equation of a horizontal parabola is:

x=ay^2

Where, a is a constant.

If a<0, then the parabola opens left and if a>0, then the parabola opens right.

Equations in options B and D are of the form x=ay^2 but a<0 in option B and a>0 in option D.

In the given graph the parabola opens right, so the value of a mus be a positive number. So, the required equation is:

x=\dfrac{1}{6}y^2

Therefore, the correct option is D.

3 0
3 years ago
Help, I need to find the solution to x I'm 7x-10(greater than or equal to) 16
Radda [10]
7x-10 is greater than or equal to 16.
First, add 10 to both sides.
This will give you 7x is greater than or equal to 26. 
Now, you dived 26 by 7.
This gives you 3.7142. Hope this helped!
7 0
4 years ago
Read 2 more answers
Let E= {prime numbers less than 30} Work out n(E)
Doss [256]

Answer:

10

Step-by-step explanation:

E={2,3,5,7, 11, 13, 17, 19, 23, 29}

therefore,

n(E)={10}

4 0
3 years ago
Read 2 more answers
Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.
Irina-Kira [14]
Hello,

x²+5x-6=0
Δ=5²+4*6=49=7²
x=(-5+7)/2 or x=(-5-7)2
==>x=1 or  x=-6

Answer B
5 0
4 years ago
Read 2 more answers
What is the slope- intercept form equation of the line that passes through (5, 7) and (8, 22)
kap26 [50]
M = (22 - 7)/(8 - 5) = 15/3 = 5 
<span>using point (5, 7) </span>
<span>y - 7 = 5(x - 5) in point-slope form </span>
<span>y - 7 = 5x - 25 </span>
<span>y = 5x - 18 in slope-intercept form.</span>
3 0
3 years ago
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