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ivann1987 [24]
2 years ago
14

Lionel created a picture to hang on his wall. The drawing is below. Each circle has a radius of 8cm. The circles touch each othe

r and the ends of the canvas. The background of Lionel’s picture is black. What is the area of the black portion?

Mathematics
2 answers:
valentinak56 [21]2 years ago
8 0

Answer:

219.7522cm^2

Step-by-step explanation:

To find area of black portion, we will find the area of the whole square first.

Length of square = 4xRadius of circle

= 4 x 8cm

= 32cm

Area of Square = Length x Width = 32x32

= 1024cm^{2}

Now we find the area of the 4 circles.

Area of 4 circles = 4 x Area of circle

= 4\pi r^{2}

= 4\pi (8)^{2} \\=4\pi (64)\\=256\pi cm^{2}

Area of black portion = Area of square - Area of 4 circles

= 1024cm^{2}  -256\pi cm^{2}

= 219.7522cm^{2}

Vikki [24]2 years ago
7 0

Answer:

888888

Step-by-step explanation:

88888888888888888888

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56/74 in simplest form

56/74×2/2=28/37

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3 years ago
With bases V1, V2 , V3 andw1, w2 , W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3 . T is a linear transformation. Find the m
Roman55 [17]

Answer:

See picture and explanation below.

Step-by-step explanation:

With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.

A is defined as T=([T(v_1)] [T(v_2] [T(v_3)])\text{ where }[T(v_i)] denotes the vector of coordinates of T(v_i) respect to the basis (we can apply this definition because forms a basis for the domain of T).

The vector of coordinates can be computed in the following way: if T(v_i)=a_1w_1+a_2w_2+a_3w_3 then [T(v_i)]=(a_1,a_2,a_3)^t.

Note that we have all the required information: T(v_1)=0w_1+1\cdot w_2+0w_3 then [T(v_1)]=(0,1,0)^t

T(v_2)=T(v_3)=1\cdot w_1+0w_2+0w_3 hence [T(v_2)]=[T(v_3)]=(1,0,0)^t

The matrix A is on the picture attached, with the multiplication A(1,1,1).

Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:

T(v_1+v_2+v_3)=T(v_1)+T(v_2)+T(v_3)=w_2+w_1+w_1=w_2+2w_1  

In this last case, we can either use the linearity of T or multiply by A.

4 0
3 years ago
Two opposite sides of the square are increased by 8 inches and the other two sides are decreased by 5 inches. the area of the ne
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Answer:

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Step-by-step explanation:

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Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material
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4 0
3 years ago
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Answer:

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