Question

A.Write an equation for each of the following statements.

1. V varies jointly as l,w and h.
2. The number of pechay plants n in a row varies inversaly as the space s between them.
3. The area A of a square varies directly as the square of its side s.
4. The electrical voltage V varies jointly as the current I and the resistance R.
5. The volume of a cylinder V varies jointly as its height h amd the square of raduis r.
6. P varies directly as x and inversely as s.
7. An enployee's salary S varies direcly as the number of days d he was worked.
8. The lenght L of a person's shadow at a given time varies directly as the height h of the person.
9. The base b of a triangle varies inversely as its attitude h.
10. The acceleration A of a moving object varies directly as the distance d it travel and inversely as the square of the time t it travels.



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Answer 1

SOLUTION

TO DETERMINE

An equation for each of the following statements.

1. V varies jointly as l,w and h.

2. The number of pechay plants n in a row varies inversely as the space s between them.

3. The area A of a square varies directly as the square of its side s.

4. The electrical voltage V varies jointly as the current I and the resistance R.

5. The volume of a cylinder V varies jointly as its height h amd the square of radius r.

6. P varies directly as x and inversely as s.

7. An employee's salary S varies directly as the number of days d he was worked.

8. The length L of a person's shadow at a given time varies directly as the height h of the person.

9. The base b of a triangle varies inversely as its attitude h.

10. The acceleration A of a moving object varies directly as the distance d it travel and inversely as the square of the time t it travels.

EVALUATION

1. V varies jointly as l,w and h.

$\sf{ \implies \: v \propto \: lwh}$

$\sf{ \implies \: v = k lwh}$

2. The number of pechay plants n in a row varies inversely as the space s between them.

$\displaystyle \sf{ \implies \: n \propto \: \frac{1}{s} }$

$\displaystyle \sf{ \implies \: n = \: \frac{k}{s} }$

3. The area A of a square varies directly as the square of its side s.

$\displaystyle \sf{ \implies \: A \propto \: {s}^{2} }$

$\displaystyle \sf{ \implies \: A = k {s}^{2} }$

4. The electrical voltage V varies jointly as the current I and the resistance R.

$\displaystyle \sf{ \implies \: V \propto \: IR }$

$\displaystyle \sf{ \implies \: V \: = k IR }$

5. The volume of a cylinder V varies jointly as its height h and the square of radius r.

$\displaystyle \sf{ \implies \: V \propto \: {r}^{2} h }$

$\displaystyle \sf{ \implies \: V = \: k{r}^{2} h }$

6. P varies directly as x and inversely as s.

$\displaystyle \sf{ \implies \: P \propto \: \frac{x}{s} }$

$\displaystyle \sf{ \implies \: P = k\frac{x}{s} }$

7. An employee's salary S varies directly as the number of days d he was worked.

$\displaystyle \sf{ \implies \: S \propto \: d}$

$\displaystyle \sf{ \implies \: S = \: kd}$

8. The length L of a person's shadow at a given time varies directly as the height h of the person.

$\displaystyle \sf{ \implies \: L \propto \: h}$

$\displaystyle \sf{ \implies \: L = \: kh}$

9. The base b of a triangle varies inversely as its attitude h.

$\displaystyle \sf{ \implies \: b \propto \: \frac{1}{h} }$

$\displaystyle \sf{ \implies \: b = \: \frac{k}{h} }$

10. The acceleration A of a moving object varies directly as the distance d it travel and inversely as the square of the time t it travels.

$\displaystyle \sf{ \implies \: A \propto \: \frac{d}{ {t}^{2} } }$

$\displaystyle \sf{ \implies \: A = \frac{kd}{ {t}^{2} } }$

In each of the above cases k is a variation constant

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