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Readme [11.4K]
2 years ago
13

The radius of a cylinder is doubled and its height is halved. Find the ratios of their surface areas.

Mathematics
1 answer:
Inessa [10]2 years ago
5 0

Answer: 1:1

Step-by-step explanation:

Let r be the radius and h be the height of a cylinder.

Formula: Curved surface area of cylinder = 2\pi rh

Now, if  radius of a cylinder is doubled and its height is halved, then new radius will be R= 2r and new height  will be  H=\dfrac{1}{2}

Now, new surface area = 2\pi RH= 2\pi(2r)\dfrac{h}{2}= 2\pi rh

Ratio of curved surface areas : \dfrac{\text{Surface area}}{\text{New surface area}}=\dfrac{2\pi rh}{2\pi rh}=\dfrac{1}{1}

Hence, the ratios of their surface areas = 1:1 .

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Find the equation of a straight line passing throught the point listed and having the given gradient. Express your answer in the
Igoryamba
First let's try to find the equation in this form : <span>y = mx + c 

The gradient is given 3 . In a line's equation, x's coefficient represents the line's gradient.

So equation of a line with the gradient of 3, would look like this ;

</span>y= 3x + c
<span>
Now a point that the line passes through is given, (1, 2) 

This point's x-coordinate is 1 and y-coordinate is 2.

So we'll plug its x-coordinate value in the equation and also y-coordinate value. So we can solve it.

As you know, </span>x=1 and y=2

y = 3x + c

2\quad =\quad 3\cdot 1+c\\ \\ 2\quad =\quad 3+c\\ \\ 2-3\quad =\quad c\\ \\ -1\quad =\quad c

We found c = -1 

Also in a line's equation, c is constant and it represents the line's y-intercept

So let's build the line's equation.

m=3 and c=-1

y= mx + c

y= 3x -1

We found the line's equation in this form, y= mx + c

Now let's turn it into this form, ax + by + c = 0

y\quad =\quad 3x-1\\ \\ y-3x\quad =\quad -1\\ \\ y-3x+1\quad =\quad 0\\ \\ -3x+y+1\quad =\quad 0

Final answers,

\boxed { y\quad =\quad 3x-1 }

and 

\boxed { -3x+y+1\quad =\quad 0 }

I hope this was clear enough :)




<span>


</span>
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3 years ago
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Add all of those up and you get 44,286

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Find the complex zeros of x^3+27. write f in factored form
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3 years ago
Five distinct numbers are randomly distributed to players numbers 1 through 5. Whenever two playerscompare their numbers, the on
ad-work [718]

Answer:

Observe that the first and the second player have equal probability to get any of number. Using the principle of that symmetry, we have that  

P(X=0)=\frac{1}{2}

<u>Event X = 1 </u>means that the first player has got greater number than the second player, but not than the third player. So, choose any three numbers out of five of them and say that the minimal number out of these three goes to the second player, mean number to the first one and the largest to the third one. Permute remaining two numbers on remaining two people. Hence

P(X=1)=\frac{1}{6}

<u>Event X = 2</u> means that the first player has got greater number than the second and the third player, but not than the fourth player. So, choose any four numbers out of five of them and say that the minimal number and the next minimal out of these four go to the second and the third player (and permute them), third number to the first one and the largest to the fourth player. Give remaining number to the last person. Hence

P(X=2)=\frac{1}{12}

<u>Event X = 3</u> means that the first player has got greater number than the second, the third, and the forth player, but not than the fifth player. So, permute these five numbers as follows: give the highest to the last person, the second highest to the first, and permute remaining numbers on the remaining people. Hence  

P(X=3)=\frac{1}{20}

<u>Event X = 4</u> means basically the first player has won all the battles i.e, he has got the greatest number. Hence

P(X=4)=\frac{1}{5}

7 0
3 years ago
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