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Ber [7]
3 years ago
13

(fx) =

6%29" id="TexFormula1" title="(fx) = \sqrt[3]{ - 3x + 3} find f( - 13.6)" alt="(fx) = \sqrt[3]{ - 3x + 3} find f( - 13.6)" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
never [62]3 years ago
4 0
f(x)=\sqrt[3]{-3x+3}\\\\substitute\ the\ value\ of\ x\ to\ the\ equation:\\\\f(-13.6)=\sqrt[3]{-3(-13.6)+3}=\sqrt[3]{40.8+3}=\sqrt[3]{43.8}\approx3.525
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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
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natali 33 [55]

Answer:

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Step-by-step explanation:

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3 years ago
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Step-by-step explanation:

Given : A recent Harris Poll survey of 1010 U.S. adults selected at random showed that 627 consider the occupation of firefighter to have very great prestige.

i.e. The sample size of U.S. adults : n= 1010

The number of U.S. adults consider the occupation of firefighter to have very great prestige : x= 627

Now , the probability that a U.S adult selected at random thinks the occupation of firefighters has very great prestige will be :

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5 0
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The pic is my answer. try to be fast with it.
Nastasia [14]

Answer:

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