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what is the next 3 terms in this geometric sequence?... 32, 48, 72, 108

Geometric Sequence ... 32, 48, 72, 108, ...

The common ratio r is 1.5

\(r = 1.5\\ r = \frac{48}{32} = \frac{72}{48} = \frac{108}{72}\)

The  geometric sequence is \(a,\ a\cdot r,\ a\cdot r^2,\ a\cdot r^3,\ a\cdot r^4,\ \dots\)

\(\begin{array}{rcll} a_{n+1} &=& a_n \cdot r \\ \end{array}\)

32,

32*1.5 = 48

48 *1.5 = 72

72 * 1.5 = 108

108 * 1.5 = 162

162 * 1.5 = 243

243 * 1.5 = 364.5

The next 3 terms in this geometric sequence 162, 243, 364.5

9.296e+7 i need this writen out with zeros

\(\begin{array}{rcll} 9.296\cdot 10^7 &=& 92960000 \end{array} \)

what is 5/16 - 1/16

\(\begin{array}{rcll} \frac{5}{16} - \frac{1}{16} &=& \frac{5-1}{16} \\ &=& \frac{4}{16} \\ &=& \frac{4}{4\cdot 4} \\ &=& \frac{\not{4}}{\not{4}\cdot 4} \\ &=& \frac{1}{4} \\ \end{array}\)

What is square root of 583

The square root of 583 is 24.1453929353

(4^3X^6YZ^3)(5^2X^2Y^3Z^2)

\(\begin{array}{rcll} (4^3x^6yz^3)\cdot (5^2x^2y^3z^2) &=& 4^3x^6yz^3 5^2x^2y^3z^2 \\ &=& 4^35^2x^6x^2yy^3z^3z^2\\ &=& 4^35^2x^{6+2}y^{1+3}z^{3+2}\\ &=& 4^35^2x^{8}y^{4}z^{5}\\ \end{array}\)

908

Find the mass of Planet X, given that its radius is 3.39e6m and that the acceleration due to gravity on its surface is 3.73m/s2.

\(\begin{array}{rcll} \text{ The mass of Planet X } &=& M \\ r &=& 3.39\cdot 10^6\ m \\ a &=& 3.73\cdot \frac{m}{s^2} \\\\ \text{Newton }\\ F &=& G \cdot \frac{ M\cdot m }{r^2} \qquad & G = 6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}\\ F &=& m \cdot a \\\\ F = G \cdot \frac{ M\cdot m }{r^2} &=& m \cdot a \\ G \cdot \frac{ M\cdot m }{r^2} &=& m \cdot a \\ G \cdot \frac{ M }{r^2} &=& a \\ \mathbf{M} &\mathbf{=}& \mathbf{\frac {a\cdot r^2}{G} } \\\\ M & =& \frac { 3.73\cdot \frac{m}{s^2}\cdot (3.39\cdot 10^6\ m)^2}{6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}} \\ M & =& \frac { 3.73\cdot \frac{m}{s^2}\cdot 3.39^2\cdot 10^{12}\ m^2}{6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}} \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{12} }{6.67\cdot 10^{-11} } \cdot \frac{m\cdot m^2\cdot kg\cdot s^2}{m^3\cdot s^2} \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{12}\cdot 10^{11} }{6.67} \cdot \ kg \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{23} }{6.67} \cdot \ kg \\ \mathbf{M} &\mathbf{=}& \mathbf{6.42661664168\cdot 10^{23} \cdot \ kg }\\ \end{array}\)

48/32 = 1.5 = r 
108/72 = 1.5 = r 
Success ! r, the ratio, is 1.5,

answer 32 48 72 108 162 243 364.5 546.75 etc 

Find the circumcenter of a triangle that has these points

A=(4,5)

B=(-8,-6)

C=(4,-6)

find the midd point between A and B

The circumcenter of a right triangle is the midd point between A and B (Thales' theorem).

M is the midd point between A and B.

\(\begin{array}{rcll} \vec{M} &=& \frac12\cdot \left[ \vec{A} + \vec{B} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4}{5} + \binom{-8}{-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4-8}{5-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{-4}{-1}\right]\\ \vec{M} &=& \dbinom{ -\frac{4}{2} } {-\frac{1}{2} }\\ \vec{M} &=& \binom{-2}{-0.5} \\ \end{array}\)

The circumcenter of a right triangle is (-2, -0.5)

1/4

Jim bought a round picnic table. The diameter of this table is 12.

What is the area and circumference of Jim’s picnic table?

\(\begin{array}{rcll} \text{diameter }~ d &=& 12 \\\\ \text{radius } ~r &=& \frac{d}{2} \\ r &=& \frac{12}{2} \\ r &=& 6\\\\ \text{area } ~ a &=& \pi\cdot r^2 \\ a &=& \pi\cdot 6^2 \\ a &=& \pi\cdot 36 \\\\ \text{circumference } ~ c &=& 2\cdot \pi\cdot r \\ c &=& 2\cdot \pi\cdot 6 \\ c &=& \pi\cdot 12 \\\\ a &=& 36\cdot \pi \\ a &=& 36\cdot 3.14159265359\\ \mathbf{a} &\mathbf{=}& \mathbf{113.097335529} \\\\ c &=& 12\cdot \pi \\ c &=& 12\cdot 3.14159265359\\ \mathbf{c} &\mathbf{=}& \mathbf{37.6991118431} \end{array}\)

(9/4)x=--16 multiply both sides by 4/9

x=-16 X 4/9

x=-64/9=-7 1/9, OR IF

9 / (4x) = -16 cross multiply

9 =-64x divide both sides by -64

x = -64/9 = -7 1/9

what is the next 3 terms in this geometric sequence?... 32, 48, 72, 108

32, 48, 72, 108, 162, 243, 364.5, 546.75..........and so on. You multiply each term by 1.5.

Thanks guys

circumference=2radius x pi (3.1415...)

Factor the following:
3 a^4-75 a^2+432

Factor 3 out of 3 a^4-75 a^2+432:
3 (a^4-25 a^2+144)

a^4-25 a^2+144 = (a^2)^2-25 a^2+144:
3 (a^2)^2-25 a^2+144

The factors of 144 that sum to -25 are -9 and -16. So, (a^2)^2-25 a^2+144 = (a^2-9) (a^2-16):
3 (a^2-9) (a^2-16)

a^2-16 = a^2-4^2:
3 (a^2-9) (a^2-4^2)

Factor the difference of two squares. a^2-4^2 = (a-4) (a+4):
3 (a-4) (a+4) (a^2-9)

a^2-9 = a^2-3^2:
3 (a^2-3^2) (a-4) (a+4)

Factor the difference of two squares. a^2-3^2 = (a-3) (a+3):
Answer: | 3 (a-3) (a+3) (a-4) (a+4)

b. it makes me enter a longer answer, so the answer is 52

Drew Voldemort. XD lol

Idk why.