) Find the value of x. 3 A) 9 B) 10 C) 11 D) 12

Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

$D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}$

It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

7 0

3 years ago

Help! I need help. My teacher made it an anime one. If todoroki had 7 ’s how much will he get when he has 67352 if you needed to

deff fn [24]

Answer:

Step-by-step explanation: 471,464

4 0

2 years ago

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What is the solution of the system? Use the elimination method. 2x+y=20 6x?5y=12

Whitepunk [10]

Answer:

(22, - 24)

Step-by-step explanation:

Multiply the first equation by -5 to make the y's so you can add the up to zero.

-5(2x + y = 20)

-10x - 5y = -100 Add the second equation thn solve for x

6x + 5y = 12

-4x = -88

x = 22

Plug 22 in for x in either equation

2x + y = 20

2 (22) + y = 20

44 + y = 20

y = -24

3 0

3 years ago

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Jackie found the area of a square to be 25/16 square feet.Which shows the side length of the square?

svlad2 [7]

The side length is the square root of the area, so is ...

... √(25/16 ft²) = (√25)/(√16) ft = 5/4 ft

4 0

3 years ago

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Sophie bikes at a speed of s miles per hour. Her friend Rana is slower, her biking speed is only r miles per hour.

Rzqust [24]

2x 23 8>×××683 83u2 282i2 e7uwww2uw727w828282828i882iii29owo999292

8 0

2 years ago