Hello.

79) The area of the swimming pool is 8w square metres, where w is the unknown width (in metres).

1 cubic metre of water results in an added volume of area times depth :

1 = area times 0.032
1 = 8w times 0.032
1 = 8x0.032 times w
1 = 0.256 w
w = 1 / 0.256
w = 3.90625 metres

When filled with water to a depth of 2.3 meters, the volume of water is :
8 x 3.90625 x 2.3 square metres
71.875 square metres
71,875 litres

66) I don't understand the terms of the problem.
Are you expected to find the area of the circle, minus the area of the rectangle that lays within ?
The position of the rectangle is not clearly defined : what do this 1 metre length stand for ? Is it supposed to be measured symmetrically in regards to the center of the circle ?

Ty.
Yes, #66 doesn't make sense.

Still ISO someone to knock the rest of these out for me vs. fg

77) Volume of the excavation = length times cross-section
Length = 620 feet = 620/3 yards
Cross-section = rectangle 8x14 square feet + rectangle 8x(8xtan(30°))
= 112 + 64.(1/√3) square feet
= (112 + 64/√3) / 9 square yards

Volume = 620 ( 112 + 64/√3 ) / 9 cubic yards

Cost is 1.75$ / cubic yard

Cost = 1.75 * 620 (112 + 64/√3 ) / 9 $

I'm not sure of what "plus 10% profit" means, probably add 10% to the cost.
In this case :

Cost with profit = 1.1 * 1.75 * 620 (112 + 64/√3 ) / 9 $
Cost with profit ~ 19,752.48 $
To the nearest dollar : 19,752 $


78) Volume of a prism equals area of the base times height.
For a right prism, height is what the text gives you : 12 cm
Base is the half part of a square with diagonal being 8.5 cm.
Area of the base is 8.5² / 4

Volume = 12 * 8.5² / 4 = 216.75 cm³

Surface is : 2 right triangles plus 3 rectangles.
Triangles have area = 8.5² / 4 each
2 rectangles have same dimensions : 12 cm by 8.5 / √2 cm
1 rectangle has dimensions : 12 by 8.5

Total surface = 2 * 8.5² / 4 + 2 * 12 * 8.5 / √2 + 12 * 8.5
= 8.5 * (8.5 / 2 + 12√2 + 12)
= 8.5 * ( 32.5 / 2 + 12√2 )
~ 282.375 cm²

72) radius = 60/2 = 30 cm
BF = 39
EB = 21

BC = 39 * 21 / 22

74) if I do no mistake, length of the belt is :
55 * pi + 80 √2 + 75 Arctan (1/√2) - 35 Arctan (1/√8)

~ 320.19 cm

It's not an easy problem...

May I ask in which class you're in ?

I am still watching.
I was having issues figuring this out and gave up.


Fean you get fg?

Ps, nice maths bro

This post was edited by Ep0ch on Dec 20 2017 03:08pm

Thanks for giving it a shot!
It is Technical Mathematics with Calculus

This post was edited by Hasted on Dec 20 2017 03:56pm