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Alex Ar [27]
3 years ago
8

18

Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer: Leia pays more to fly from the UK to Australia

Step-by-step explanation:

We have two persons, Andy and Leila; both travel from UK to Australia but in different ways:

<u>For Andy:</u>

-He first flies from UK to Japan and the cost of the ticket is \£ 554

-Then he flies from Japan to Australia and the cost of the ticket is 70140 Yen

So, the cost of Andy's trip is:

\£ 554+70140 Yen (1)

Taking into account that we have to use the same units to sum two quantities, we have to convert the Yens to \£; knowing that \£ 1=140 Yen:

70140 Yen \frac{\£ 1}{140 Yen}=\£501

Then, (1) is rewritten as:

\£ 554+\£501=\£1055 (2) This is the total cost of Andy's trip

<u>For Leila:</u>

She flies directly from UK to Australia and the cost of her ticket is \$ 1860 (Australian dollars)

Taking into account that we have the price of Andy's trip in \£, we have to convert the Australian dollars to \£, in order to compare.

So, knowing that \$ 1=\£ 0.62 we have:

\$ 1860 \frac{\£ 0.62}{\$ 1}=\£1153.2 (3) This is the total cost of Leila's trip

Hence, comparing (2) and (3) we can see that <u>Leila paid more to fly from UK to Australia.</u>

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1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an
Musya8 [376]

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

\begin{gathered} AM=\sqrt{AB^2-BM^2} \\  \\ AM=\sqrt{6^2-3^2} \\  \\ AM=\sqrt{36-9} \\  \\ AM=\sqrt{27} \\  \\ AM=5.2\text{ cm} \end{gathered}

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

SO=\sqrt{SM^2-MO^2}

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\  \\ SO=\sqrt{15-6.76} \\  \\ SO=2.9\text{ cm} \end{gathered}

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

A=\frac{1}{2}*BC*AM

Thus, we have:

\begin{gathered} A=\frac{1}{2}*6^*5.2 \\  \\ A=15.6\text{ cm}^2 \end{gathered}

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

SA=\frac{1}{2}*p*h

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\  \\ A=34.86\text{ cm}^2 \end{gathered}

• (5). Total surface area:

To find the total surface area, apply the formula:

TSA=base\text{ area + area of side surface}

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

V=\frac{1}{3}*area\text{ of base *height}

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\  \\ V=15.08\text{ cm}^3 \end{gathered}

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

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1 year ago
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