1. Find the area of a rectangle with a length of [tex]2^5a^4[/tex] metres and a width of [tex]3^2a^3[/tex] metres.

2. If the thickness of a sheet of paper is 0.000023 metres, calculate the thickness of 1000 such sheets. Express your answer in standard form.

Question

High School

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Answer :

EmmaGraceJohnson EmmaGraceJohnson · Answer 1 · 2025-04-14T23:44:23-04:00

To find the area of the rectangle, we use the formula for the area of a rectangle, which is given by:

[tex]\text{Area} = \text{Length} \times \text{Width}[/tex]

The length of the rectangle is given as [tex]2^5a^4[/tex] metres, and the width is [tex]3^2a^3[/tex] metres.

First, let's simplify the expressions:
[tex]2^5 = 32[/tex] and [tex]3^2 = 9[/tex].

Now substitute these values back into the expression for the area:

[tex]\text{Area} = 32a^4 \times 9a^3[/tex]

Now multiply the numbers and the like terms in the powers of [tex]a[/tex]:

[tex]\text{Area} = (32 \times 9) \times (a^4 \times a^3)[/tex]

[tex]\text{Area} = 288 \times a^{4+3}[/tex]

[tex]\text{Area} = 288a^7[/tex]

So, the area of the rectangle is [tex]288a^7[/tex] square metres.

Next, we calculate the thickness of 1000 sheets of paper, with each having a thickness of 0.000023 metres:

For 1000 sheets:

[tex]\text{Total thickness} = 1000 \times 0.000023[/tex]

[tex]\text{Total thickness} = 0.023 \text{ metres}[/tex]

Expressing 0.023 in standard form: [tex]2.3 \times 10^{-2}[/tex].

So, the thickness of 1000 sheets is [tex]2.3 \times 10^{-2}[/tex] metres.