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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.
