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soldier1979 [14.2K]
3 years ago
11

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

15–√i+25–√j15i+25j. (Use symbolic notation and fractions where needed.)
Mathematics
1 answer:
Feliz [49]3 years ago
4 0

f(x,y,z)=2z^2x+y^3

f has gradient

\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k

which at the point (-1, 4, 3) has a value of

\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say \vec u=15\,\vec\imath+25\,\vec\jmath, in which case we have

\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}

Then the derivative of f at (-1, 4, 3) in the direction of \vec u is

D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}

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Talja [164]

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2 years ago
On December 1, Jasmin Ernst organized Ernst Consulting. On December 3, the owner contributed $85,360 in assets in exchange for i
blagie [28]

The income statement illustrates that the net income will be $3530.

<h3>How to calculate the income statement?</h3>

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The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past
galina1969 [7]

Complete Question

The complete question is shown on the uploaded image  

Answer:

1 ) The correct option B

2) The correct option is  C

3)  The correct option is  C

4)  The correct option is  C

Step-by-step explanation:

From the question we are told that

   The proportion that own a cell phone  is  p = 0.90

    The  sample  size is  n =  15

Generally the appropriate distribution for X is mathematically  represented as

      X  \ is  \ B( n , p )

So  

       X  \ is  \ B( 15 , 0.90 )

Generally the number students that  own a cell phone in a simple random sample of 15 students is mathematically represented as

              \mu  =  n  *  p

              \mu  =  15 *  0.90

              \mu  =   13.5

Generally the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is mathematically represented as

                \sigma  =  \sqrt{ n *  p *  q }

Where  q is mathematically evaluated as

          q =  1- p

           q =  1- 0.90

           q =  0.10

            \sigma  =  \sqrt{ 15 *  0.90 *  0.10 }

            \sigma  = 1.16

Generally the probability that all students in a simple random sample of 15 students own a cell phone is mathematically represented as

   P(X =  15) =  \left 15} \atop {}} \right.C_{15} *  p^{15} *  q^{15 - 15}    

     P(X =  15) =  \left 15} \atop {}} \right.C_{15} *  (0.90)^{15} *  (0.10 )^{15 - 15}

From the combination calculator  is      \left 15} \atop {}} \right.C_{15} =  1

     P(X =  15) = 1 *  0.205891 *  1

      P(X =  15) = 0.206

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chubhunter [2.5K]

Answer:

\large\boxed{y=3(x-2)^2-8}

Step-by-step explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

f(x)=a(x-h)^2+k

(h, k) - vertex

h=\dfrac{-b}{2a},\ k=f(h)

We have the equation:

y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4

Substitute:

h=\dfrac{-(-12)}{2(3)}=\dfrac{12}{6}=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8

Finally:

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jeyben [28]
The answer is 900
900/90=10. Therefore 90/900=1/10
5 0
3 years ago
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