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BaLLatris [955]
2 years ago
13

Find the missing dimension use the scale factor 1:12 model 32 cm find the actual in m

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
6 0

Given:

The scale factor is 1:12.

Dimension of model = 32 cm

To find:

The actual dimension in m.

Solution:

Let x be the actual dimension.

The scale factor is 1:12 and the dimension of model is 32 cm.

\dfrac{1}{12}=\dfrac{32}{x}

On cross multiplication, we get

x=32\times 12

x=384\ cm

x=3.84\ m             [\because 1\ m=100\ cm]

Therefore, the actual dimension is 3.84 m.

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Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
mezya [45]

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

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