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aleksklad [387]
3 years ago
12

Factorise the expression

Mathematics
1 answer:
serg [7]3 years ago
3 0

Answer:

2x • (2x-1) • 4 + 1     16x2 - 8x + 1

———————————————————  =  —————————————

         4                    4      

Step-by-step explanation:

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Given the figure below, how much paper is needed to make the drinking cup to the nearest square inch?
miskamm [114]
To find this, we need to find the Surface area of the lateral surface of the cone (without the circle base). 
LSA _{cone} =  \pi rl
Now we just need to plug what we know into the equation
r=1.5 \\l=4
LSA _{cone} =  \pi (1.5)(4) \\LSA_{cone}= 6\pi
Wither you can keep your answer in pi or take it out of pi, depending on what the requirements are. 
To take it out of pi you need to multiply 6 by pi (remembering to use 3.14 as pi in most cases since that is what is generally accepted on tests and exams). 
6 \pi = 6(3.14)= 18.84
Then rounding to the nearest square inch which would mean that the amount of paper needed is =19in²


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3 years ago
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An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn
Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

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Henry sees 3 rabbits. Callie sees double that number of rabbits. How many rabbits does Callie see than Henry?
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