Factor 3x^2+11x-4=0 as the product of two linear expressions

The formula to find the period of orbit of a satellite around a planet is T^2=(4pi^2/GM)r^3 where r is the orbit's mean radius,

Natalija [7]

The answer is $r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$

$T^{2} = \frac{4 \pi^{2}}{GM} r^{3}$

Move $\frac{4 \pi^{2} }{GM}$ to the other side of the equation:
$T^{2} /\frac{4 \pi^{2} }{GM} = r^{3} \\ 
T^{2} *\frac{GM}{4 \pi^{2} } = r^{3}$

Rearrange:
$r^{3} = T^{2} *\frac{GM}{4 \pi^{2} } \\ 
r^{3}= \frac{T^{2} *GM}{4 \pi^{2} } \\ 
r^{3}= \frac{GMT^{2}}{4 \pi^{2} } \\ 
r^{3} = GMT^{2}/4 \pi^{2}$

Since $x^{3}= \sqrt[3]{x}$ , then
$r^{3} = GMT^{2}/4 \pi^{2} \\ 
r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$

3 0

3 years ago

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Your drawer has 5 pairs of black socks, 4 pairs of gray socks, 2 pairs of white socks, 1 pair of brown socks, and 1 pair of blue

Sergeeva-Olga [200]

5 pairs of black socks*2 because it’s a pair= 10 socks
4 pairs of grey socks*2=8
2 pairs of white socks*2=4
1 pair of brown socks*2=2
1 pair of blue socks*2=2
10 socks+8 socks+4 socks+2 socks+ 2 socks=26 socks in total
26/2=13+1 because you need to be sure you get one pair of socks. The smallest amount of socks you would have to grab to get at least one matching pair is 14 socks.

7 0

3 years ago

In parallelogram QRST if RT=16 find RU. R S U Q T

padilas [110]

Answer:

I think it's 8

Step-by-step explanation:

Because it's half of it, you can tell by the image. RT is 16 and RU is 8

8 0

3 years ago

Adjacent angles have no common interior points. A.)Always. B.)Sometimes. C.)Never

irina [24]

The actual answer is "always", as adjacent angles have no common interior points under any circumstances. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that you were looking for and it has come to your help.

6 0

3 years ago

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What is the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 )?

vlada-n [284]

Answer:

y = -x² + 4

Step-by-step explanation:

The equation of the parabola in the vertex form is:

y = a (x-h)² + k

Where: (h,k) the coordinates of the vertex & a is a multiplier

The parabola has a vertex at ( 0,4 )

So, h = 0 , k = 4

∴ y = a (x-0)² + 4

∴ y = a x² + 4

The parabola passes through points ( 2,0 )

∴ 0 = a 2² + 4

∴ 4 a = -4 ⇒ a = -4/4 = -1

∴ y = -x² + 4

So, the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 ) is y = -x² + 4

See the attached figure.

4 0

3 years ago