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Mice21 [21]
3 years ago
14

Ratio of two volume cylinders (Geometry)

Mathematics
2 answers:
Kazeer [188]3 years ago
5 0
V1 = π* ( r1)^2 * 75;
V2 = π* ( r2)^2 * 25;

V1/V2 = (r1/r2)^2 * 3.

Masteriza [31]3 years ago
3 0
The ratio of the lengths is 75 : 25 or 3 : 1 

The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)

The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)

Hopefully this explains it

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Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).
Serjik [45]

Answer:

\displaystyle f(x)=x^2+2x+2

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

\displaystyle f(x)=ax^2+bx+c

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

\displaystyle f(-1)=a(-1)^2+b(-1)+c

\displaystyle f(-1)=a-b+c

\displaystyle a-b+c=1.....[eq\ 1]

Now we use the second condition f(1)=5

\displaystyle f(1)=a(1)^2+b(1)+c

\displaystyle f(1)=a+b+c

\displaystyle a+b+c=5.......[eq\ 2]

Finally, we use the third condition f(2)=10

\displaystyle f(2)=a(2)^2+b(2)+c

\displaystyle f(2)=4a+2b+c

\displaystyle 4a+2b+c=10....[eq\ 3]

We put together eq 1, eq 2, and eq 3 to form the system

\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.

Adding the first two equations we have

\displaystyle 2a+2c=6

\displaystyle a+c=3

And also

\displaystyle b=2

Using the above equation and the value of b in the third equation, we have

\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.

Subtracting the first equation from the second

\displaystyle 3a=3

\displaystyle a=1

And therefore

\displaystyle c=2

Now we have all the values, the quadratic function is

\displaystyle \boxed{f(x)=x^2+2x+2}

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nevsk [136]

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3

Step-by-step explanation:

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