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avanturin [10]
3 years ago
12

A circle's radius is increased by 10%. By what percentage does its area increase

Mathematics
1 answer:
Vladimir79 [104]3 years ago
4 0
Answer: 21%

Explanation: Let the radius of the circle =R therefore area of the circle = [pi][R * R]
Radius of the circle after 10% increase =R+10% of R=R+R/10=11R/10
Therefore AREA of the circle with radius 11R/10 =[pi][11R/10*11R/10]=[pi][121R*R/100] Hence INCREASE in the AREA of the circle=[pi][121R*R/100]-[pi][R*R] =[pi] [R*R][121/100-1] =[pi][R*R][121-100]/100=[pi][R*R][21]/100 THEREFORE % increase in the area of the circle=[pi][R*R][21/100]/[pi][R*R] whole multiplied by 100=21 HENCE increase in the area of the circle =21% NOTE : pi is a constant whose value=22/7
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he​ half-life for a link on a social network website is 2.6 hours. Write an exponential function T that gives the percentage of
pychu [463]

Answer:

% Remaining= [1-(1/2)^{\frac{t}{2.6}}]x100

And replacing the value t =5.5 hours we got:

% Remaining= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%

Step-by-step explanation:

Previous concepts

The half-life is defined "as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not".

Solution to the problem

The half life model is given by the following expression:

A(t) = A_o (1/2)^{\frac{t}{h}}

Where A(t) represent the amount after t hours.

A_o represent the initial amount

t the number of hours

h=2.6 hours the half life

And we want to estimate the % after 5.5 hours. On this case we can begin finding the amount after 5.5 hours like this:

A(5.5) = A_o (1/2)^{\frac{5.5}{2.6}}

Now in order to find the percentage relative to the initial amount w can use the definition of relative change like this:

% Remaining = \frac{|A_o - A_o(1/2)^{\frac{5.5}{2.6}}|}{A_o} x100

We can take common factor A_o and we got:

% Remaining= [1-(1/2)^{\frac{t}{2.6}}]x100

And replacing the value t =5.5 hours we got:

% Remaining = [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%

5 0
3 years ago
What is the value of r2s for r=10 and ​s=2?
mezya [45]

Hey there!

<h2>10(2)(2) </h2><h2>10(2) = 20</h2><h2>20(2) = 40</h2><h2>Thus, your answer is: 40</h2>

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst

3 0
2 years ago
How many solution does 2x – 1 = 1 – 2x have?
ss7ja [257]

Answer:

1

Step-by-step explanation:

Hello,

2x – 1 = 1 – 2x

<=> 2x-1+2x=1

<=> 4x-1=1

<=> 4x = 1+1=2

<=> x = 2/4 = 1/2

Then there is only one solution.

Thanks

6 0
3 years ago
Read 2 more answers
Two planes that are traveling toward each other are 720 miles apart. One plane is traveling 40 miles per hour faster than the ot
natali 33 [55]

Answer:

y = 460 miles per hr

x = 500 miles per hr

Step-by-step explanation:

Let the planes be X any

Let their speeds be xmiles/hr and ymiles/hr respectively

x = y + 40 (assuming X is faster by 40miles/hr)

Distance travelled by X to meet Y = 0.75x

Distance travelled by Y to meet X = 0.75y

0.75x + 0.75y = 720 --------1

Put x = y + 40 in eqn 1

0.75(y+40) + 0.75y = 720

0.75y + 30 + 0.75y= 720

1.5y = 690

y = 460 miles per hr

x = 460 +40

= 500 miles per hr

7 0
2 years ago
If I went to break at 9:30 what time would be 30 mins after
bekas [8.4K]
10:00 would be the answer to that one.

3 0
3 years ago
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