Mathematics, 24.04.2020 03:02 gabistock21

In a chemistry lab students use a filter paper cone to filter a liquid. The diameter of the cone is 11.5 cm and its height is 12 cm. How much liquid will the cone hold when it is full?

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Answer from: boxergirl2062

Volume of cone, $V=415.64\ cm^3$

Step-by-step explanation:

In a chemistry lab students use a filter paper cone to filter a liquid.

Diameter of the cone, d = 11.5 cm

Height of the cone, h = 12 cm

It is required to find the liquid that the cone can hold. It means we need to find the volume. The formula of the volume of cone is given by :

$V=\dfrac{1}{3}\pi r^2h$

r is radius of cone, r = 11.5/2

$V=\dfrac{1}{3}\times \dfrac{22}{7}\times (\dfrac{11.5}{2})^2\times 12\\\\V=415.64\ cm^3$

So, the filer paper cone can hold $415.64\ cm^3$ volume of liquid.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

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In a chemistry lab students use a filter paper cone to filter a liquid. The diameter of the cone is...