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horrorfan [7]
3 years ago
13

Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFr

action 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction
Mathematics
1 answer:
dybincka [34]3 years ago
3 0

Answer:

  \log{\dfrac{3\sqrt{x}(x^3+4)}{2}}

Step-by-step explanation:

\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}

__

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  log(a^b) = b·log(a)

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Answer:

Distance between A and B is 2672 km.

Step-by-step explanation:

Since one city B is having latitude of 23° and other town is having latitude of 47°.Radius of Earth has been given as 6380 km.

Therefore arc A from x-axis will be A = 2πr(∅/360) = 2×3.14×6380×(47/360)

= 5230.90 km

Now arc B from x-axis = 2πr(∅'/360) = 2×3.14×6380(23/360) = 2559.80 km

Therefore distance between them = 5230.9-2559.8 = 2671.9 ≅ 2672 km

Now we will rewrite the arc length formula in radians.

arc A = r×(∅×π/180)

arc A = 6380×(47×π/180) = 1665.9π

arc B = 6380×(23×π/180) = 815.22π    

Now the distance between A and B =  850.68π

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\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS
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=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr
=136\pi
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