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4 years ago

5.

Mathematics

1 answer:

Talja [164]4 years ago

5 0

Answer:

y = -3x

Step-by-step explanation:

Given the illustration of the graph, we can see that the line is going downhill. This would indicate that the slope is negative, so the choices would be narrowed down y = -3x or y = -x. Looking at the line, we can use two points to find the difference in 'y' over the difference in 'x', or slope. Using the origin (0,0) as one point, we can go down 3 and over 1 to get to the second point of (1, -3). This would be an overall change of -3, giving us the final answer of:

y = -3x

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D. 75(5r+3d+4f) and 75(5r)+75(3d)+75(4f)

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3 years ago

The triangles shown are similar. which side of triangle JGH corresponds to PM of trangle PMO

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3 years ago

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3 years ago

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

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

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

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

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3 years ago

What is x? 3x+43=100

jenyasd209 [6]

Answer:

x = 19

Step-by-step explanation:

Solve for x:

3 x + 43 = 100

Subtract 43 from both sides:

3 x + (43 - 43) = 100 - 43

43 - 43 = 0:

3 x = 100 - 43

100 - 43 = 57:

3 x = 57

Divide both sides of 3 x = 57 by 3:

(3 x)/3 = 57/3

3/3 = 1:

x = 57/3

The gcd of 57 and 3 is 3, so 57/3 = (3×19)/(3×1) = 3/3×19 = 19:

Answer: x = 19

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