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3 years ago

How many irrational numbers are there between 1 and 6 ?f. 1g. 3h. 4j. 10k. infinitely many

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

3 0

Sorry honestly don't know probably 4j.

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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

WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!

MAVERICK [17]

7 < x. Here, you can solve the inequality by multiplying 2 by each quantity in the parentheses to get -18 < 24 - 6x. You can subtract -24 from both sides to get -42 < -6x. Then, you can divide each side by -6 and flip the inequality, and this leaves you with x > 7. You would check this answer by choosing a number greater than but close to 7, using the original equation.

3 0

3 years ago

Raul is trying to solve the equation below. 30+15y=480 What value of y makes Raul’s equation true?

emmainna [20.7K]

Answer:

30 answer

Step-by-step explanation:

30+15y=480

15y=480-30

15y=450

y=450/15

y=30

8 0

3 years ago

Multiply. Express your answer in lowest terms. 3/8 x 2/7 = ?/?

Murljashka [212]

Simple, multiply.

3/8*2/7

You can cross cancel the 2 and the 8, making them into a 1 and 4.

Making it,

3/4*1/7

Multiply,

3/28. This can't be simplified further; thus, 3/28 is your answer.

6 0

3 years ago

Read 2 more answers

What would the area be for a circle with the diameter of 7

Marina86 [1]

Answer:

The answer is 38.48

Step-by-step explanation:

Picture with explanation provided below.

3 0

3 years ago