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PtichkaEL [24]
3 years ago
9

60

Mathematics
1 answer:
suter [353]3 years ago
4 0
882(88)-9 +u+ exhibit
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Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v
olga_2 [115]

We are given

f=z^3 -x^2y

Firstly, we can find gradient

so, we will find partial derivatives

f_x=0 -2xy

f_x=-2xy

f_y=0 -x^2

f_y=-x^2

f_z=3z^2

now, we can plug point (-5,5,2)

f_x=-2*-5*5=50

f_y=-(-5)^2=-25

f_z=3(2)^2=12

so, gradient will be

gradf=(50,-25,12)

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}

|v|=\sqrt{29}

now, we can find unit vector

v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })

now, we can find dot product to find direction of the vector

dir=(gradf) \cdot (v')

now, we can plug values

dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })

dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })

dir=-\frac{248\sqrt{29}}{29}.............Answer



7 0
3 years ago
Read 2 more answers
An electrician charges $40 dollars to come to your house. She also charges $55 for each hour that she works. The electricion cha
Alexxx [7]

Answer:

your question doesn't make sense if an electrician came to your house it would cost $40 then $55 dollars per hour but there is no way that you can solve that (40+(55•2)=150+55=205 which is already over $190 dollars

3 0
3 years ago
Casandra is training for 10 mile race. On the first day of training she runs 4 miles, each day after that she adds on 0.5 mile.
Naddik [55]
On day no 9, because to increase her mileage by 4 to reach 8 it will take her 4/0.5=8 days plus day 1 where she ran just 4 miles.
8 0
3 years ago
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Question is: Solve -7(x+6)=4(x+6)
Alina [70]

\huge\boxed{x=-6}

Hey there! Our goal here is to isolate the variable on one side of the equation.

\begin{aligned}-7(x+6)&=4(x+6)&&\smash{\Big|}&&\textsf{Start with the original equation.}\\-7x+(-7)(6)&=4x+4(6)&&\smash{\Big|}&&\textsf{Distribute.}\\-7x-42&=4x+24&&\smash{\Big|}&&\textsf{Multiply.}\\-7x-4x&=24+42&&\smash{\Big|}&&\textsf{Move the terms.}\\-11x&=66&&\smash{\Big|}&&\textsf{Combine like terms.}\\x&=\boxed{-6}&&\smash{\Big|}&&\textsf{Divide both sides by $-11$.}\end{aligned}

8 0
2 years ago
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What’s is the solution to the equation x to the power of 2 =16/25
skelet666 [1.2K]

Answer:

x=\dfrac{4}{5}

Step-by-step explanation:

The given equation is :

x^2=\dfrac{16}{25}

We need to find the value of x.

When the exponent 2 removes from LHS, it will shift to RHS as square root as follows :

x=\sqrt{\dfrac{16}{25}}

We know that, 4×4= 16 and 5×5 = 25

So,

x=\sqrt{\dfrac{4\times 4}{5\times 5}}\\\\x=\dfrac{4}{5}

So, the solution of the given equation is 4/5.

4 0
2 years ago
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