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2 years ago

Use the identity below to complete the tasks:

Mathematics

1 answer:

pashok25 [27]2 years ago

4 0

Answer:

a = 5r² and b = r²s

Step-by-step explanation:

a3 - b3 = (a - b)(a + ab + b2)

Expressing 125q^6-r^6s^3 as a difference of 2 cubes

125q^6-r^6s^3

= 5³(r²)³ - (r³)²s³

= (5r²)³ - (r²s)³

Comparing with a³ - b³

a = 5r² and b = r²s

Hence the value of a is 5r² and b is r²s

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3 years ago

A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha

netineya [11]

Answer:

$(a)\ Area = 195\pi$

$(b)\ Volume = 700\pi$

Step-by-step explanation:

Given

$h = 12$

$d_1 = 10$ --- lower diameter

$d_2 = 20$ --- upper diameter

Solving (a): The curved surface area

This is calculated as:

$Area = \pi l(r_1 + r_2)$

Where

$r_1 = 0.5 * d_1 = 0.5 * 10 = 5$ --- lower radius

$r_2 = 0.5 * d_2 = 0.5 * 20 = 10$ --- upper radius

And

$l = \sqrt{h^2 + (r_1 - r_2)^2$ ---- l represents the slant height of the frustrum

$l = \sqrt{12^2 + (5 - 10)^2$

$l = \sqrt{12^2 + (-5)^2$

$l = \sqrt{144 + 25$

$l = \sqrt{169$

$l = 13$

So, we have:

$Area = \pi l(r_1 + r_2)$

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$Area = \pi * 13(15)$

$Area = 195\pi$

Solving (b): The volume

This is calculated as:

$Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))$

This gives:

$Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))$

$Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))$

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3 years ago

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Answer:

1) c 226

1. E

2. D

3. B

4. A

5. C

Step-by-step explanation:

6^3=216

5x(4-2)

5x2=10

216+10=226

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