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3 years ago

Write a function describing the relationship of the given variables.

Mathematics

1 answer:

Oliga [24]3 years ago

3 0

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

variables that can be expressed by an equation in which one

variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

constant of variation

* Now lets solve the problem

# V is varies directly with the square of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

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Answer:

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Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is $=\frac{diameter}{2}$

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= 7 cm.

The volume of the cone is $= \frac13 \pi r^2 h$

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Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is $= \frac43 \pi(R^3-r^3)$

$=\frac43 \pi (5^3-r^3) \ cm^3$

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

$\frac43 \pi (5^3-r^3) =\frac{392}{3}\pi$

$\Rightarrow 4(5^3-r^3)= 392$

$\Rightarrow 5^3-r^3=\frac{392}{4}$

$\Rightarrow 5^3-r^3=98$

$\Rightarrow -r^3=98-125$

$\Rightarrow-r^3= -27$

⇒r= 3

The internal radius of the sphere is = 3 cm.

The internal diameter of the given sphere is = (2×3) cm =6 cm.

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