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telo118 [61]
3 years ago
15

A circle with the radius of 1cm sits inside a 3cm×4cm rectangle. What is the area of the shaded region?

Mathematics
1 answer:
Tanya [424]3 years ago
8 0

Answer:

8.86

Step-by-step explanation:

Im guessing you want the rectangles area

Finding circle area do radius times radius times 3.14 so 1 x 1 = 1 x 3.14 = 3.14

Rectangle area is length times width so 3 x 4 = 12 - 3.14 = 8.86

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B is two fifths of c 4a = 3c work out the ratio a:b:c give your answer in its simplest form where a, b and c are integers
Alex17521 [72]

Answer:

a : b : c = 12 : 10 : 15

Step-by-step explanation:

Given that: b = \frac{2}{5} of c

 i.e             b = \frac{2c}{5} ............... 1

          2c = 5b

So that;

          c = \frac{5b}{2} .................... 2

Also,    

          4a = 3c

           a = \frac{3c}{4} ................ 3

⇒          a = \frac{3}{4} × (\frac{5b}{2})

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Comparing the derived equations:

From equations 2 and 3,

a:c = \frac{15b}{8}: \frac{5b}{2} = 4:5

From equations 1 and 2,

b:c = \frac{2c}{5} : \frac{5b}{2} = 2:3

But a common value of b = 15, gives;

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6 0
3 years ago
From a full 50-liter container of a 40% concentration of acid, x liters are removed and replaced with 100% acid. (A) Write the a
padilas [110]

Answer:

See explanation

Step-by-step explanation:

Given:

50 liter container

40% concentration of acid

x liters are removed and replaced with 100% acid

(A)

Acid in 50-liter container =  40% of 50 liters

                                          = (40/100) * 50

                                          = 0.4 * 50

                                          = 20

So there are 20 liters amount of acid in 50 liter container.

Now x liters are removed and replaced with 100% acid

The acid in x-liter

40% of x liters = (40/100) * x  = 0.4 * x

When x liters are removed then amount of acid that remained in container:

20 - 40% of x liters = 20 -  (40/100) * x  = 20 - 0.4 * x

This can also be written as:

(50-x) (40/100) =  (40*50/100) - (40*x/100) = 2000/100 - 40x/100 =  20 - 2x/5

Since x liters replaced with 100% acid so this becomes:

20 - 40% of x liters + 100% of x liters

= 20 -  (40/100) * x + 100/100 * x

= 20 - (40/100) x + (100/100)x

= 20 +  (100-40/100)x

= 20 + (60/100)x

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This can also be written as:

20 - 2x/5 + x = 20 + 3x/5 =  20 + 0.6 x

Hence the amount of acid in the final mixture as a function of x:

f(x) = 20 + 0.6 x

(B)

The value of x can not be greater than 50 liters and can not be lesser than 0 liters.  

so, range is [0, 50] where both 0 and 50 are inclusive.  

(C)

Since final mixture is 50% acid So

Acid = 50% of 50 litres =

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        = 1/2 * 50

         = 50/2

        = 25

Put 25 in the computed function of x

20 + 0.6 x = 25

0.6x = 25 - 20

0.6x = 5

x = 5/0.6

x = 8.333333

x = 8.3 liters

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