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4 years ago

A rotation maps point A to A’.

Mathematics

2 answers:

julsineya [31]4 years ago

8 0

C. 180° rotation .................

weeeeeb [17]4 years ago

5 0

Answer: The answer is (C) 180° rotation.

Step-by-step explanation: Given that the point A maps to the point A' by a rotation. We are to select the statement that describes the rotation.

In the given figure, the co-ordinates of point A are (-3, 5) and after rotation, the co-ordinates of point A' are (3, -5).

Therefore, the point (x, y) changes to (-x, -y) after rotation. This is the result of 180° rotation.

Therefore, the point A is rotated through an angle of 180° to reach at the point A'.

Thus, the correct option is (C) 180° rotation.

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A house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Com

Mariulka [41]

We know that
scale------------> 1 in/4 ft
[blueprint]=scale*[actual]

Part 1) Living room
lenght (20 ft) -------------> [blueprint]=(1/4)*20=5 in
width (8 ft) ----------------> [blueprint]=(1/4)*8=2 in

Part 2) Kitchen
length (16 ft) -------------> [blueprint]=(1/4)*16=4 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 3) Office
length (8 ft) -------------> [blueprint]=(1/4)*8=2 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 4) Bedroom 1
length (8 ft) -------------> [blueprint]=(1/4)*8=2 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 5) Bedroom 2
length (20 ft) -------------> [blueprint]=(1/4)*20=5 in
width (20 ft) ----------------> [blueprint]=(1/4)*20=5 in

Part 6) Bathroom
length (6 ft) -------------> [blueprint]=(1/4)*6=1.5 in
width (8 ft) ----------------> [blueprint]=(1/4)*8=2 in

see the attached figure to view the table

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4 years ago

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Miranda earned $c for working 8 hours. Write an expression to show how much Miranda earned for each hour worked.

mixer [17]

Answer: $c divided by 8

Step-by-step explanation:

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4 years ago

Which equation represents a line that passes through (2,-1/2) and has a slope of 3?

krok68 [10]

Answer:

the 3rd one

Step-by-step explanation:

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3 years ago

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In the math problem, "450 is 75% of what number?" 450 is the ___.

Anni [7]

Answer:

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Step-by-step explanation:

Since 3/4 of 100 is 75, we have to divide 450 by three.

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3 years ago

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

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4 years ago