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yKpoI14uk [10]
3 years ago
13

B. Using the net, find the surface area of the total shape if the height of the triangles is 4 cm and the bottom edge is 2 cm. S

how your work and label your answer appropriately.

Mathematics
1 answer:
Margarita [4]3 years ago
3 0
In the above diagram, there are 4 triangles and one square

Base of the triangle (b) = 2 cm
Height of the triangle (h) = 4 cm

Side of the square = 2 cm

Area of triangle = 1/2 bh = 1/2 x 2 x 4 = 4 cm²
Area of 4 triangles = 4 x 4 cm² = 16 cm²

Area of the square = 2 cm x 2 cm = 4 cm²

Surface area of the total shape = Area of 4 triangles + Area of the square = 16 cm² + 4 cm² = 20 cm²
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The endpoints of a line segment graphed on the coordinate system are (−7, 3) and (2, 5). What is the range of the graph?
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3 years ago
An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft 3 . Find the d
denpristay [2]

Answer:

The dimensions of the box that minimize the materials used is 6\times 3\times 2\ ft

Step-by-step explanation:

Given : An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft³.

To find : The dimensions of the box that minimize the materials used ?

Solution :

An open top box is to be built with a rectangular base whose length is twice its width.

Here, width = w

Length = 2w

Height = h

The volume of the box V=36 ft³

i.e. w\times 2w\times h=36

h=\frac{18}{w^2}

The equation form when top is open,

f(w)=2w^2+2wh+2(2w)h

Substitute the value of h,

f(w)=2w^2+2w(\frac{18}{w^2})+2(2w)(\frac{18}{w^2})

f(w)=2w^2+\frac{36}{w}+\frac{72}{w}

f(w)=2w^2+\frac{108}{w}

Derivate w.r.t 'w',

f'(w)=4w-\frac{108}{w^2}

For critical point put it to zero,

4w-\frac{108}{w^2}=0

4w=\frac{108}{w^2}

w^3=27

w^3=3^3

w=3

Derivate the function again w.r.t 'w',

f''(w)=4+\frac{216}{w^3}

For w=3, f''(3)=4+\frac{216}{3^3}=12 >0

So, it is minimum at w=3.

Now, the dimensions of the box is

Width = 3 ft.

Length = 2(3)= 6 ft

Height = \frac{18}{3^2}=2\ ft

Therefore, the dimensions of the box that minimize the materials used is 6\times 3\times 2\ ft

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Elena has 14 pieces of bannana bread. She gives an equal amount of bannana bread to 4 friends. How many peices of bannana bread
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