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Zinaida [17]
2 years ago
7

A box contains only $2 coins and $10 coins and there

Mathematics
1 answer:
miss Akunina [59]2 years ago
8 0
<h3>Answer:   25</h3>

==========================================================

Work Shown:

x = number of $2 coins

y = number of $10 coins

x+y = 43 coins total

x = 43-y

2x = value of just the $2 coins only

10y = value of all the $10 coins only

2x+10y = total value of all coins mentioned

This value must be greater than $278, so,

2x+10y > 278

2( x ) + 10y > 278

2(43-y)+10y > 278

86-2y+10y > 278

8y+86 > 278

8y > 278 - 86

8y > 192

y > 192/8

y > 24

The smallest y can be is y = 25.

We need at least 25 coins worth $10 each.

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Answer:

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Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

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Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. \text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\

{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}

b) To find area of one lateral surface:

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Using equation (1) to find the area:

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c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\  mm^{2}

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a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

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3 years ago
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