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## If r varies directly as sand inversely as the square

**Ask: ** If r varies directly as sand inversely as the square of u, and r = 2 when s = 18 and u = 2,

find:

a. r when u = 3 and s = 27.

b. s when u = 2 and r=4.

c. u when r = 1 and s = 36.

## Problem:

*If r varies directly as s and inversely as the square of u, and r = 2 when s = 18 and u = 2, find:*

a. r when u = 3 and s = 27.

b. s when u = 2 and r=4.

c. u when r = 1 and s = 36.

## Solution:

r = ks/u²

2 = k(18)/2²

2 = k(18)/4

2(4) = k(18)

8 = 18k

k = 8/18

k = 4/9

*a. r when u = 3 and s = 27*

r = ks/u²

r = (4/9)(27)/3²

r = (108/9)/9

r = 12/9

r = 4/3

*b. s when u = 2 and r = 4*

r = ks/u²

ru² = ks

s = ru²/k

s = 4(2²)/(4/9)

s = 4(4)/(4/9)

s = 16/(4/9)

s = 16(9/4)

s = 144/4

s = 36

*c. u when r = 1 and s = 36.*

r = ks/u²

ru² = ks

u² = ks/r

[tex][begin{array}{l}u = sqrt {frac{{ks}}{r}} \\u = sqrt {frac{{frac{4}{9}(36)}}{1}} \\u = sqrt {frac{{144}}{9}} \\u = sqrt {16} \\u = 4end{array}][/tex]

*#CarryOnLearning*

## If r varies directly as s and inversely as the

**Ask: **If r varies directly as s and inversely as the square of u and r=2 when s=18and u=2

Find:

r when u=3 and s=27

s when u=2 and r=4

u when r=1 and s=36

**Answer:**

1.3

2.1

3.1/6

**Step-by-step explanation:**

## C. Solve the following1. Ifr varies directly as s and

**Ask: **C. Solve the following

1. Ifr varies directly as s and inversely as the square u, and r=2 when s=18 and u=2, find:

a r when u=3 and s=27

b. s when u=2 and r=4

c. u when r=1 and s=36

## COMBINED VARIATION

### ==============================

» Solve the following:

[tex] : : implies sf large r = frac{ks}{ {u}^{2} } \ [/tex]

[tex]large tt red{given} begin{cases} sf : r = 2 \ sf : s = 18 \ sf : u = 2end{cases}[/tex]

» Find the constant (k).

[tex] implies sf large 2 = frac{k(18)}{ {2}^{2} } \ [/tex]

[tex]implies sf large 2 = frac{k(18)}{ 4 } \ [/tex]

[tex]implies sf large 2 times frac{4}{18} = frac{k(18)}{ 4 } times frac{4}{18} \ [/tex]

[tex]implies sf large frac{8}{18} = frac{k( cancel{72})}{ cancel{72} } \ [/tex]

[tex]implies sf large k = frac{8 div 2}{18 div 2} \ [/tex]

[tex]implies sf large k = frac{4}{ {9} } \ [/tex]

» The constant of the variation is 4/9, Solve the following questions:

**›› A. r when u = 3 and s = 27**

[tex]implies sf large r = frac{ frac{4}{9} (27)}{ {3}^{2} } \ [/tex]

[tex]implies sf large r = frac{ frac{4}{9} (27)}{9 } \ [/tex]

[tex]implies sf large r = frac{ frac{108}{ 9}}{9 } \ [/tex]

[tex]implies sf large r = frac{108}{81} \ [/tex]

[tex]implies sf large r = frac{108 div 27}{81 div 27} \ [/tex]

[tex] tt huge » : purple{ frac{4}{3}} : : or : : purple{1 frac{1}{3} }[/tex]

**»**** ****B****. s when u**** ****=**** ****2 and r**** ****=**** ****4**

[tex]implies sf large 4 = frac{ frac{4}{9} s}{ {2}^{2} } \ [/tex]

[tex]implies sf large 4 = frac{ frac{4}{9} s}{ 4} \ [/tex]

[tex]implies sf large 4 = frac{4s}{36} \ [/tex]

[tex]implies sf large 4 times frac{36}{4} = frac{4s}{36} times frac{36}{4} \ [/tex]

[tex]implies sf large cancel4 times frac{36}{ cancel4} = frac{ cancel{144}s}{ cancel{144}} \ [/tex]

[tex]tt huge » : purple{36} [/tex]

**»**** ****C****. u when r**** ****=**** ****1 and s**** ****=**** ****36**

[tex] implies sf large 1 = frac{ frac{4}{9} (36)}{ {u}^{2} } \ [/tex]

[tex] implies sf large 1 = frac{144}{ 9{u}^{2} } \ [/tex]

[tex]implies sf large 1 times frac{9}{144} = frac{144}{ 9{u}^{2} } times frac{9}{144} \ [/tex]

[tex]implies sf large frac{9 div 9}{144 div 9} = frac{ cancel{1296}}{ cancel{1296}{u}^{2} } \ [/tex]

[tex]implies sf large frac{1}{16} = {u}^{2} \ [/tex]

[tex]implies sf large sqrt{ frac{1}{16} } = sqrt{ {u}^{2} } \ [/tex]

[tex]tt huge » : purple{ frac{1}{4} } [/tex]

### ==============================

**#CarryOnLearning**

(ノ^_^)ノ

## Find u, when r=1 and s=36

**Ask: **Find u, when r=1 and s=36

firstly r is ewuivalent to one because whenever u divide itself is itself too

## 1. If r varies directly as s and inversely as

**Ask: **1. If r varies directly as s and inversely as the square of u, then r = 2 when s=18 and u=2 find:

a. r when u=3 and s=27

b.s when u=2 and r=4

c u when r=1 and s=36

**Answer:**

a po para sa akin correct po yn

## If r varies directly as s and inversely as the

**Ask: **If r varies directly as s and inversely as the square of u, and r=2 when s=18 and u=2, find

a. r when u=3 and s=27

b. s when u=2 and r=4

c/ u when r=1 and s=36

**Answer:**

A. R WHEN U=3 AND S=7 PA BRAINLEST PO

## Solve the following: if r varies directly as s and

**Ask: **Solve the following:

if r varies directly as s and inversely as the square of u, and r=2 when s=18, and u=2, find:

a.) r when u=3 and s=27

b.) s when u=2 and r=4

c.) u when r=1 and s=36

EQUATION: r = ks/u²

2 = k (18)/(2)²

2 = k 18/4 ÷ 2/2

2 = k 9/2

2 ÷ 9/2 = k 9/2 ÷ 9/2

4/9 = k

a. r = (4/9)(27) / (3)²

r = 12 / 9

r = 4/3

ANSWER: r = 4/3

b. 4 = (4/9)s / (2)²

4 = 1/9s

4 ÷ 1/9 = 1/9s ÷ 1/9

36 = s

ANSWER: s = 36

c. 1 = (4/9)(36) / u²

1 = 16 / u²

√16 = √u²

±4 = u

ANSWER: u = ±4

## -If r varies directly as s and inversely as the

**Ask: **–

If r varies directly as s and inversely as the square of u, and r = 2 whead

s=18 and u=2, find the following:

4. r, when u = 3 and s = 27

5. S, when u = 2 and r = 4

6.u, when r= 1 and s = 36

## Problem:

*If r varies directly as s and inversely as the square of u, and r = 2 when s = 18 and u = 2, find:*

a. r when u = 3 and s = 27.

b. s when u = 2 and r = 4.

c. u when r = 1 and s = 36.

## Solution:

r = ks/u²

2 = k(18)/2²

2 = k(18)/4

2(4) = k(18)

8 = 18k

k = 8/18

k = 4/9

*4. r when u = 3 and s = 27*

r = ks/u²

r = (4/9)(27)/3²

r = (108/9)/9

r = 12/9

r = 4/3

*5. s when u = 2 and r = 4*

r = ks/u²

ru² = ks

s = ru²/k

s = 4(2²)/(4/9)

s = 4(4)/(4/9)

s = 16/(4/9)

s = 16(9/4)

s = 144/4

s = 36

*6. u when r = 1 and s = 36.*

r = ks/u²

ru² = ks

u² = ks/r

[tex][begin{array}{l}u = sqrt {frac{{ks}}{r}} \\u = sqrt {frac{{frac{4}{9}(36)}}{1}} \\u = sqrt {frac{{144}}{9}} \\u = sqrt {16} \\u = 4end{array}][/tex]

*#CarryOnLearning*

## if r varies directly as s and inversely as the

**Ask: **if r varies directly as s and inversely as the squre of u and r=2 when s=18 and u=2 a.find r when u=3 and s=27 b.find s when u=2 r=4 c.find u when r=1 s=36

r=[tex] frac{ks}{u^{2} } [/tex] 2=[tex] frac{k18}{2^{2} } [/tex] 2=[tex] frac{k18}{4 } [tex] frac{8}{18} [/tex]=[tex] frac{18}{18} [/tex] k=[tex] frac{8}{18} [/tex] k=**[tex] frac{4}{9} [/tex] a. **r=[tex] frac{ks}{u^{2} } r=[tex] frac{ frac{4}{9}27 }{3 ^{2} } [/tex] [tex] frac{ frac{4}{9}27 }{6 } [/tex] [tex] frac{12}{6} [/tex] r=2

## If r varies directly as s and inversely as the

**Ask: **If r varies directly as s and inversely as the square of u, and r = 2 when s= 18 and u = 2 find:

a. r when u = 3 and s= 27. 3 .

b. s when u = 2 and r=4.

c. u when r = 1 and s= 36

ANSWER:

*b. s when u = 2 and r=4. FOR SURE*

**Answer:**

C

**Step-by-step explanation:**

sana makatulong kung ayaw ede wag

Not only you can get the answer of **u when r=1 and s=36**, you could also find the answers of If r varies, -If r varies, if r varies, C. Solve the, and If r varies.