A streamer goes down stream covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 2 km/hr, then find the speed of streamer in still water . PLEASE ANSWER IN ONE VARIABLE.
Answers
let we. take the speed be "x"
Distance covered in upstream=2(x-6)=2x-12
distance covered in downstream=2(x+5)=2x+10
2x-12=2x+10
2x-2x=10+12
0=22
0=22Answrr ......h
Answer:
4^x=8^2\quad :\quad x=34
x
=8
2
:x=3
Step-by-step explanation:
4^x=8^24
x
=8
2
\gray{\mathrm{Convert\:}4^x\mathrm{\:to\:base\:}2}Convert4
x
tobase2
\gray{4^x=(2^2)^x}4
x
=(2
2
)
x
(2^2)^x=8^2(2
2
)
x
=8
2
\gray{\mathrm{Convert\:}8^2\mathrm{\:to\:base\:}2}Convert8
2
tobase2
\gray{8^2=(2^3)^2}8
2
=(2
3
)
2
(2^2)^x=(2^3)^2(2
2
)
x
=(2
3
)
2
\gray{\mathrm{Apply\:exponent\:rule}:\quad (a^b)^c=a^{bc}}Applyexponentrule:(a
b
)
c
=a
bc
\gray{(2^2)^x=2^{2x},\:\space(2^3)^2=2^{3\cdot \:2}}(2
2
)
x
=2
2x
, (2
3
)
2
=2
3⋅2
2^{2x}=2^{3\cdot \:2}2
2x
=2
3⋅2
\gray{\mathrm{If\:}a^{f(x)}=a^{g(x)}\mathrm{,\:then\:}f(x)=g(x)}Ifa
f(x)
=a
g(x)
,thenf(x)=g(x)
2x=3\cdot \:22x=3⋅2
\gray{\mathrm{Simplify}}Simplify
2x=62x=6
\gray{\mathrm{Solve\:}\:2x=6}Solve2x=6
2x=62x=6
\gray{\mathrm{Divide\:both\:sides\:by\:}2}Dividebothsidesby2
\dfrac{2x}{2}=\dfrac{6}{2}
2
2x
=
2
6
\gray{\mathrm{Simplify}}Simplify
x=3x=3