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3 years ago

At a sandwich shop there are different kinds of chips

Mathematics

1 answer:

Sedaia [141]3 years ago

7 0

The answer is......... help me so I can help u

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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

Please help!!

sergij07 [2.7K]

Answer: B
Explanation: It’s linear because as y increases x also increases however it’s weak because there are a few anomalies/ outliers

6 0

2 years ago

A band went to a recording studio and recorded 4 songs in 3 hours. How many hours would it take the band to record 9 songs if th

Morgarella [4.7K]

Answer:

7 1/2 hours I believe is the correct answer. Hope it works!

6 0

3 years ago

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show how you could use the Commutative Property to simplify the evaluation of the expression -7/16-1/4-5/16

hram777 [196]

-7/16 - 1/4 - 5/16

1. -7/16 - 4x1/4x4 - 5/16
2. -(7/16 + 4/16 + 5/16)
3. -7 + 4 + 5/16
that will add up to be 16/16 then cancel them out and you get for your answer -1

4 0

4 years ago

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

Maksim231197 [3]

X + y = 24....multiply by -3
3x + 5y = 100
---------------
-3x - 3y = - 72 (result of multiplying by -3)
3x + 5y = 100
--------------add
2y = 28
y = 28/2
y = 14

x + y = 24
x + 14 = 24
x = 24 - 14
x = 10

solution is (10,14)...and x represents 3 point q's and y represents 5 point q's......so this tells me there are 10 three point q's and 14 five point q's.

8 0

4 years ago

Read 2 more answers