Answer: 1
1 Simplify \frac{3}\{4}\pi ra\times \frac{d}{m}\imath n
4
3
πra×
m
d
ın to \frac{3\pi rad\imath n}{4m}
4m
3πradın
.
w=\frac{3\pi rad\imath n}{4m}w=
4m
3πradın
2 Regroup terms.
w=\frac{3\pi \imath radn}{4m}w=
4m
3πıradn
3 Multiply both sides by 4m4m.
w\times 4m=3\pi \imath radnw×4m=3πıradn
4 Regroup terms.
4wm=3\pi \imath radn4wm=3πıradn
5 Divide both sides by 33.
\frac{4wm}{3}=\pi \imath radn
3
4wm
=πıradn
6 Divide both sides by \pi π.
\frac{\frac{4wm}{3}}{\pi }=\imath radn
π
3
4wm
=ıradn
7 Simplify \frac{\frac{4wm}{3}}{\pi }
π
3
4wm
to \frac{4wm}{3\pi }
3π
4wm
.
\frac{4wm}{3\pi }=\imath radn
3π
4wm
=ıradn
8 Divide both sides by \imath ı.
\frac{\frac{4wm}{3\pi }}{\imath }=radn
ı
3π
4wm
=radn
9 Simplify \frac{\frac{4wm}{3\pi }}{\imath }
ı
3π
4wm
to \frac{4wm}{3\pi \imath }
3πı
4wm
.
\frac{4wm}{3\pi \imath }=radn
3πı
4wm
=radn
10 Divide both sides by aa.
\frac{\frac{4wm}{3\pi \imath }}{a}=rdn
a
3πı
4wm
=rdn
11 Simplify \frac{\frac{4wm}{3\pi \imath }}{a}
a
3πı
4wm
to \frac{4wm}{3\pi \imath a}
3πıa
4wm
.
\frac{4wm}{3\pi \imath a}=rdn
3πıa
4wm
=rdn
12 Divide both sides by dd.
\frac{\frac{4wm}{3\pi \imath a}}{d}=rn
d
3πıa
4wm
=rn
13 Simplify \frac{\frac{4wm}{3\pi \imath a}}{d}
d
3πıa
4wm
to \frac{4wm}{3\pi \imath ad}
3πıad
4wm
.
\frac{4wm}{3\pi \imath ad}=rn
3πıad
4wm
=rn
14 Divide both sides by nn.
\frac{\frac{4wm}{3\pi \imath ad}}{n}=r
n
3πıad
4wm
=r
15 Simplify \frac{\frac{4wm}{3\pi \imath ad}}{n}
n
3πıad
4wm
to \frac{4wm}{3\pi \imath adn}
3πıadn
4wm
.
\frac{4wm}{3\pi \imath adn}=r
3πıadn
4wm
=r
16 Switch sides.
r=\frac{4wm}{3\pi \imath adn}r=
3πıadn
4wm
Explanation: 2
1 Simplify 24.8\times \frac{m}{s}24.8×
s
m
to \frac{24.8m}{s}
s
24.8m
.
r=\frac{24.8m}{s},120re\times \frac{v}{m}\imath nr=
s
24.8m
,120re×
m
v
ın
2 Simplify 120re\times \frac{v}{m}\imath n120re×
m
v
ın to \frac{120rev\imath n}{m}
m
120revın
.
r=\frac{24.8m}{s},\frac{120rev\imath n}{m}r=
s
24.8m
,
m
120revın
3 Regroup terms.
r=\frac{24.8m}{s},\frac{120e\imath rvn}{m}r=
s
24.8m
,
m
120eırvn
4 Break down the problem into these 2 equations.
r=\frac{24.8m}{s}r=
s
24.8m
r=\frac{120e\imath rvn}{m}r=
m
120eırvn
5 How?Solve the 1st equation: r=\frac{24.8m}{s}r=
s
24.8m
.
m=\frac{rs}{24.8}m=
24.8
rs
6 How?Solve the 2nd equation: r=\frac{120e\imath rvn}{m}r=
m
120eırvn
.
m=120e\imath vnm=120eıvn
7 Collect all solutions.
m=\frac{rs}{24.8},120e\imath vnm=
24.8
rs
,120eıvn
3
1 Simplify 256\imath \times \frac{n}{h}256ı×
h
n
to \frac{256\imath n}{h}
h
256ın
.
v=\frac{256\imath n}{h},0.5re\times \frac{v}{mi}nv=
h
256ın
,0.5re×
mi
v
n
2 Simplify 0.5re\times \frac{v}{mi}n0.5re×
mi
v
n to \frac{0.5revn}{mi}
mi
0.5revn
.
v=\frac{256\imath n}{h},\frac{0.5revn}{mi}v=
h
256ın
,
mi
0.5revn
3 Regroup terms.
v=\frac{256\imath n}{h},\frac{0.5ervn}{mi}v=
h
256ın
,
mi
0.5ervn
4 Break down the problem into these 2 equations.
v=\frac{256\imath n}{h}v=
h
256ın
v=\frac{0.5ervn}{mi}v=
mi
0.5ervn
5 How?Solve the 1st equation: v=\frac{256\imath n}{h}v=
h
256ın
.
n=\frac{vh}{256\imath }n=
256ı
vh
6 How?Solve the 2nd equation: v=\frac{0.5ervn}{mi}v=
mi
0.5ervn
.
n=\frac{mi}{0.5er}n=
0.5er
mi
7 Collect all solutions.
n=\frac{vh}{256\imath },\frac{mi}{0.5er}n=
256ı
vh
,
0.5er
mi