Grade For This Exam Selles U 3 4 5 6
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Grade For This Paper
3 4 5
9
6
7
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9
Volume of a sphere = ter where r is the radius
A container is a hemisphere of radius 30 cm
a) Find the volume of the container.
14137.16694
cm3
(1)
Sand fills the container at a rate of 4500 cm3 per minute.
(2)
b) How long, to the nearest minute, will it take to fill the container?
12x30=15
12x 4/3tr2
12x4/3xTTX152
=113 -60 = 1.88mintues
Total marks: 3​

Answer/Step-by-step explanation:

a. Volume of hemisphere = ½(⁴/3πr³)

r = 30 cm

Volume = ½(⁴/3 × π × 30³)

Volume = ⅔ × π × 27,000 = 56,548.6677 ≈ 56,549 cm³

b. 4,500 cm³ = 1 min

56,549 cm³ = (56,549 × 1)/4,500

= 12.5664444 ≈ 12.6 mins

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1