# Tag: Math

#### For the following equation, find the value of *x*.

Continue reading “Equations Involving One Variable| Algebra| ENGG10 LE3| Problem 3”

#### Solve for y in terms of the other symbols

Continue reading “Linear Equations| Algebra| ENGG10 LE3| Problem 2”

#### If a regular polygon of ten sides is inscribed in a circle of radius *r *units, then, if *s *units is the length of the side,

#### Solve this formula for *s *in terms of *r*.

Continue reading “Quadratic Equations| Algebra| ENGG10 LE3| Problem 1”

#### A right circular cylinder, radius of base x, height y, is inscribed in a right circular cone, radius of base r and a height h. Express y as a function of x (r and h are constants).

## Solution:

Refer to the figure below.

By ratio and proportion of two similar triangles ΔBCD and ΔACE, we have

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#### The stiffness of a beam of rectangular cross section is proportional to the breadth and the cube of the depth. If the breadth is 20 cm, express the stiffness as a function of the depth.

## Solution:

Let S=stiffness, b=breadth, and d=depth

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#### Express the area A of an equilateral triangle as a function of its side x.

## Solution:

From the formula of the area of a triangle, . Also, we know that an interior angle of an equilateral triangle is 60 degrees, and

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#### Express the distance D traveled in t hr by a car whose speed is 60 km/hr.

## Solution:

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#### If , find x as a function of y.

## Solution:

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#### If , find x as a function of y.

## Solution:

Solve for x using quadratic formula. We have

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