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2 years ago

The graph below shows the relationship between life expectancy and income in a random sample of countries.

Mathematics

1 answer:

leonid [27]2 years ago

4 0

Answer:

its b

Step-by-step explanation:

because it answered it on khan

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3 years ago

What are some examples of Adjacent Congruent Angles.

Anastasy [175]

Answer:

base angles of an isosceles triangle
angles at successive corners of any regular polygon
angles either side of an angle bisector
angles made by a perpendicular to a line (excluding vertical angles)

Step-by-step explanation:

When it comes to angles, the term "adjacent" means different things in different contexts. Any pair of angles in a triangle are considered to be adjacent. The base angles of an isosceles triangle are adjacent congruent angles.

Angles at successive corners of any regular polygon are congruent adjacent angles.

Angle that have a common vertex and a common side are also called adjacent angles. Angles on either side of an angle bisector are adjacent congruent angles. Likewise any non-vertical pair of angles where lines cross at right angles are adjacent congruent angles.

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3 years ago

I need some help on Slope-Intercepts

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3 years ago

Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

$f(x,y)=2xy(x^2+y^2)^2$

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago