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3 years ago

A médium-sized paper cone has a diameter of 8 centimeters and a height of 10 centimeters. What is the volume of the cone?

Mathematics

1 answer:

lubasha [3.4K]3 years ago

5 0

Answer:

40/3 pi

Step-by-step explanation:

Volume of a cone = 1/3 *pi*h*r^2 , where h = height, and r = radius.

diameter = 2 radius, so radius = 8/2 = 4

The height = 10, so plug these values into the equation:

1/3 * pi * 10 * 4 =

40/3 pi

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Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

5 0

3 years ago

ava pours 3 gallons of paint equally into 5 cans. how many gallon of paint will there be in each can?

IrinaK [193]

Answer:

15 gallons of paint

Step-by-step explanation:

5 x 3 = 15

equal groups !

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2 years ago

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Fiesta28 [93]

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3 years ago

4.875 = d - 2.125 <br><br>what do I do here?

spayn [35]

Answer:

d=7

Step-by-step explanation:

7-2.125= 4.875

7 is your answer as it balances both sides of the equation.

i got seven by adding 2.125. to 4.875

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Step-by-step explanation:

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