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kirza4 [7]
3 years ago
12

Draw at least six different sized rectangles that have an area of 64 square units

Mathematics
1 answer:
olga_2 [115]3 years ago
3 0

Let

x------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of a rectangle is equal to

A=x*y

A=64\ units^{2}

so

x*y=64 --------> equation 1

let's assume different values of x to get the different values of y

<u>case 1)</u> For x=64 units

substitute in the equation 1

x*y=64

y=64/x

y=64/64

y=1\ units      

the dimensions of the rectangle are 64 units x 1 unit

see the draw in the attached figure N 1

<u>case 2)</u> For x=32 units

substitute in the equation 1

x*y=64

y=64/x

y=64/32

y=2\ units

the dimensions of the rectangle are 32 units x 2 units

see the draw in the attached figure N 2

<u>case 3)</u> For x=16 units  

substitute in the equation 1

x*y=64

y=64/x

y=64/16

y=4\ units

the dimensions of the rectangle are 16 units x 4 units

see the draw in the attached figure N 3

<u>case 4)</u> For x=30 units

substitute in the equation 1

x*y=64      

y=64/x

y=64/30

y=\frac{32}{15} =2\frac{2}{15} \ units

the dimensions of the rectangle are 30 units x 2 (2/15) units

see the draw in the attached figure N 4

<u>case 5)</u> For x=40 units

substitute in the equation 1

x*y=64    

y=64/x

y=64/40

y=1.60\ units

the dimensions of the rectangle are 40 units x 1.60 units

see the draw in the attached figure N 5

<u>case 6)</u> For x=60 units

substitute in the equation 1

x*y=64    

y=64/x

y=64/60

y=\frac{16}{15} =1\frac{1}{15} \ units

the dimensions of the rectangle are 60 units x 1 (1/15) units

see the draw in the attached figure N 6

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A square has an area of 64 square meters.
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Answer:

Side is 8 meters, Perimeter is 32 meters

Step-by-step explanation:

<em>One side </em>

Squares have 4 equal sides.  Area is found using l*w, but the sides are all equal in squares. Therefore, the area can be found using:

a=s^2

We know the area is 64, so we can substitute that in

64=s^2

Take the square root of both sides

\sqrt{64}=\sqrt{s^2}

8=s

One side is 8 meters

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Squares have 4 equal sides, and the perimeter is all the sides added up.

p=s+s+s+s

We know the side is 8, so we can substitute that in

p=8+8+8+8

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3 years ago
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Answer:

-8

Step-by-step explanation:

1. x + 23 = 15

2. x + 23 = 15

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3. x = -8

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
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First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

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where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

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t=\pi\implies f(-10,0)=235

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So <em>f</em> has a minimum of -7 and a maximum of 299.

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Lina20 [59]

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