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3 years ago

Please help me i dont know how to do the down part.

Mathematics

1 answer:

torisob [31]3 years ago

8 0

Answer:

40, 60, 80, 100, 120, 140, 160, 180, 200

Step-by-step explanation:as the 12 goes up by 12 the 20 goes up by 20

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(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in

Sophie [7]

Answer:

Step-by-step explanation:

$\text{Show that a differentiable function f decreases most rapidly at x in the }$

$\text{direction opposite the gradient vector, that is, in the direction of}$ $-\bigtriangledown f(x)$ $\text{. Let}\ \theta \ \text{be the angle between} \bigtriangledown f(x) \ \text{and unit vector u. Then } D_u f = \mathbf{|\bigtriangledown f| \ cos \ \theta }}$

$\text{Since the minimum value of} \ \ \mathbf{cos \ \theta} \ \ is \mathbf{-1} \ \text{occuring \ for \ 0} \le \ \theta \ < 2x, \\ \\ when \ \theta = \mathbf{\pi} , \text{the mnimum value of} \ D_uf \ is} -|\bigtriangledown f|, \text{occuring when the direction of u is } \\ \\ \ \mathbf{the \ opposite \ of} \ \text{the direction of } \ \bigtriangledown f (assuming \ \bigtriangledown f\ is \ not \ zero)$

b) $\text{From part A:}$

$If \ f(x,y) = x^4y -x^2y^2 \ \ decreases \ fastest \ at \ the \point \ (2,-5)\\ \\ F(x,y) = x^4y -x^2y^3 \\ \\ f_x = \dfrac{df}{dx}= \dfrac{d}{dx}(x^4y-x^2y^3) \\ \\ f_x = \dfrac{df}{dx}= y4x^3 -2y^3x \\ \\ For(2,-5) \\ \\ f_x = (-5)4(2)^3 -2(-5)^3(2) \\ \\ \mathbf{ f_x = 340}$

$However; f_y = \dfrac{df}{dy} = \dfrac{d}{dy}(x^4y - x^2y^3) \\ \\ f_y = x^4 -3x^2y^2 \\ \\ Now, for (2, -5)\\ \\f_y = (2)^4 -3(2)^2(-5)^2 \\ \\ f_y = -284$

$So; \bigtriangledown = < 340,-284> \text{this is the direction of fastest decrease}$

6 0

3 years ago

Zero ∉ {whole numbers} True or False?

Artemon [7]

Step-by-step explanation:

thats true

3 0

3 years ago

The value of x is: xo 20° 300 20° 30°. 0000 50°. 60°

AysviL [449]

Answer:

x = 50°

Step-by-step explanation:

x + 20° + 30° = 180°

x = 180° - 20° - 30°

x = 130° (This one is other x)

x + 130° = 180°

x = 180° - 130°

x = 50°

5 0

3 years ago

what is the slope of the line that passes through the points (-6,1) and (-6,-4)? write your answer in the simplest form.

viva [34]

Answer:

Undefined

Step-by-step explanation:

-4-1/-6+6

Since the bottom adds up to zero and you cannot simplify a fraction with 0 as the denominator, the slope is undefined.

7 0

3 years ago

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What is the sign of the product of two positive integers and three negative integers?

8_murik_8 [283]

Answer:

Two positive integers: Positive

Three negative: Negative

Step-by-step explanation:

Is this what you meant?

8 0

3 years ago