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Mathematics 12 Online
hardlyhuman:

Please can I get help with geometry? Tomorrow's my birthday and I really don't want to have to do any work.

hardlyhuman:

1 attachment
Vocaloid:

|dw:1520447220369:dw| if we notice, we can "cut off" the upper triangle and move it down here

Vocaloid:

|dw:1520447267770:dw|

Vocaloid:

similar principle here after we move these triangles around we end up with a giant rectangle with length 7 and width 6, what's this area?

hardlyhuman:

42?

Vocaloid:

good, so 42 is your ans

hardlyhuman:

thanks so much, would you mind helping me with the others?

Vocaloid:

sure

hardlyhuman:

thanks so much I'll post it

hardlyhuman:

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Vocaloid:

volume of a square pyramid = (1/3)(b)(h), b is the area of the base, h is height so if the base is a square w/ side lengths 4 what's the total area of the base?

hardlyhuman:

48?

Vocaloid:

oh, 48 for the entire volume? yeah that's the final answer

hardlyhuman:

okay great :) I'll put up the next one

hardlyhuman:

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Vocaloid:

similar concept area of cone = (1/3)(base)(height) the base this time is a circle so you will first need to calculate the area of a circle with diameter 12

hardlyhuman:

okay I'll try

hardlyhuman:

113.1 is the area of the circle

Vocaloid:

good but let's leave it as 36pi for now and round at the very end if we multiply (1/3)(bh) we get (1/3)(36pi)*27 = 972pi, then we plug in 3.14 for pi at the very end, getting 972 * 3.14 = 3052.08 = your ans

hardlyhuman:

okay, thanks. questions like this one I don't understand since im not sure what to do with pi

Vocaloid:

for accuracy/precision, we would leave it in terms of pi until the very end, if we start rounding in between steps we run the risk of losing accuracy

hardlyhuman:

okay, is there anything left to do with this one or was that the final answer?

Vocaloid:

that's it

hardlyhuman:

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Vocaloid:

V = (4/3)pi* r^3, you are given diameter not radius, so you'll have to divide the diameter by 2 to find the radius, then plug everything into the formula for V

hardlyhuman:

25 m radius

hardlyhuman:

so it would by V=(4/3)3.14 25^3 =

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Vocaloid:

good but they want it to the nearest hundredth so you would round that decimal to 2 places

hardlyhuman:

okay

hardlyhuman:

would it happen to be this? 523,333.33

Vocaloid:

|dw:1520448574267:dw|

Vocaloid:

|dw:1520448580075:dw|

Vocaloid:

then round up to 65416.67 = your ans

hardlyhuman:

i was way off XD thank you though

hardlyhuman:

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Vocaloid:

Perimeter = 48 = 2(L+W) dividing both sides by 2 we get L + W = 24 "length and width scaled up by 1.5" means the new length and new width are 1.5L and 1.5W respectively new perimeter = 2 * 1.5(L+W) = ? remember we determined what L + W was before, what would 2 * 1.5(L+W) be?

hardlyhuman:

48?

Vocaloid:

if (L+W) = 24 what does 2 * 1.5 * (L+W) equal?

hardlyhuman:

3

Vocaloid:

|dw:1520448991809:dw|

Vocaloid:

|dw:1520448997550:dw|

Vocaloid:

since (L+W) = 24, we can replace "L+W" with "24" whenver (L+W) shows up so 2 * 1.5 * (L+W) = 2 * 1.5 * 24 = ?

hardlyhuman:

72?

Vocaloid:

good, so 72 is your final answer

hardlyhuman:

yay :)

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Vocaloid:

for area, since it's base * height we have to multiply the scale factor twice to get the new area so new area = old area * scale factor * scale factor = ?

hardlyhuman:

8?

Vocaloid:

the old area is 30 the scale factor is 4 so new area = old area * scale factor * scale factor = ?

hardlyhuman:

im not understanding what im supposed to do here

Vocaloid:

|dw:1520449356348:dw|

hardlyhuman:

120 is new area

Vocaloid:

30 * 4 * 4 = ?

hardlyhuman:

480 i mean

Vocaloid:

good so 480 = your ans

hardlyhuman:

awesome

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Vocaloid:

for volumes, we need to multiply the scale factors three times, since there are 3 dimensions being scaled so the ratio is 6^3 : 7^3, express this ratio in lowest terms

Vocaloid:

anyway I got to go, it just ends up being 216: 343 I believe, it doesn't simplify any further

hardlyhuman:

okay, thank you so much for all your help i really appreciate it. have a good day :)

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