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3 years ago

CE TASK

Mathematics

1 answer:

diamong [38]3 years ago

7 0

Determine how much money did the carpenter start with

The total money with the carpenter is $318.4

Given:

let

x = total money with the carpenter

Bags of sand = 7/8 of x

= 7/8x

Money remaining = x - 7/8x

= (8x-7x) / 8

= 1/8x

Bags of bunting bags = 1/2 of 1/8x

= 1/2 × 1/8x

= 1/16x

Money left = $19.90

Total money = bags of sand + bag of bunting flag + money left

x = 7/8x + 1/16x + 19.90

x = (14x + x) / 16 + 19.90

x = 15/16x + 19.90

x - 15/16x = 19.90

16x - 15x / 16 = 19.90

x/16 = 19.90

divide both sides by 1/16

x = 19.90 ÷ 1/16

= 19.90 × 16/1

= 318.4

Therefore, the total money with the carpenter is $318.4

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3 years ago

Cos^2x+cos^2(120°+x)+cos^2(120°-x) i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

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2 years ago