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3 years ago

Need help with circle measurements in Geometry.

Mathematics

1 answer:

Ymorist [56]3 years ago

5 0

I got 0.999 which is 999/1000

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A rectangular sheet of perimeter of 36 cm and dimensions x cm by y cm is to rolled into a cylinder. what values of x and y give

elena55 [62]

Given that perimeter of the rectangular sheet= 36cm, Height of cylinder =y base circumference of the cylinder = x = 2pir

So x+y = 36/2 = 18 , y = 18-x, so height of the cylinder = 18-x and radius of cylinder = x/2pi

So volume of cylinder = pir^2h = pi(x/2pi)^2* (18-x) = (x^2* (18-x))/(4pi)

Let f(x) = (x^2(18-x))/(4pi)

We need to maximise this volume function.

So f'(x) = (1/4pi) ( -x^2 + 2x(18-x))= (1/4pi)(x)(-x+36-2x)= (1/4pi)(x)(-3x+36)

So f'(x) = 0⇒ (1/4pi)(x)(-3x+36)=0⇒x=0 or x= 12

Since x+y = 18, so 0<x<18

f'(x) = (1/4pi)(-3x^2+36x)

So f''(x) = (1/4pi)(-6x+36)⇒ f''(12) = (1/4pi)(-6*12+36) = -9pi <0

So using second derivative test x=12 gives the maximum volume.

Since x+y =18 so 12+y=18 ⇒y = 6

So x=12cm and y = 6cm give the largest volume.

6 0

3 years ago

A ladder reaches 2m up a wall. The foot of ladder is 0.4m from the wall. For safety reasons, the slope should be between 6.3 and

NeTakaya

Answer:

The slope of ladder is not within the safe range .

Step-by-step explanation:

Given as :

The height of the ladder up a wall = h = 2 meters

The distance of base of ladder from the wall = x = 0.4 meters

The estimated safety range of slope of ladder is between 6.3 and 9.5

Let The slope of the ladder = x

<u>According to question</u>

slope of the ladder = $\dfrac{\textrm height of ladder up wall}{\textrm distance of base of ladder from wall}$

Or, x = $\dfrac{2 meters}{0.4 meters}$

Or, x = 5

So, The slope of the ladder = x = 5

Since The estimated range of slope between 6.3 and 9.5

And The calculate slope of ladder = 5

Hence, The slope of ladder is not within the safe range . Answer

4 0

3 years ago

The product of n and 8

Jlenok [28]

Answer:

Step-by-step explanation:

The product of n and 8 means you will multiply n and 8. So, n x 8 is 8n.

8 0

3 years ago

I need help with these 2

Aneli [31]

2. Broken line
3. I think is no

5 0

4 years ago

Eugene had $57.93 to spend when he went to Staples. He bought 4 notebooks for $7.99 each and some pens for $2.49 each. After pay

Allisa [31]

Answer:$6.21

Step-by-step explanation:

57.93 - (4 X 7.99)

= $33.96

$33.96 - $18.50

= $15.46

$\frac{15.46}{2.49}$

= $6.2088

=$6.21

8 0

3 years ago