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Gekata [30.6K]
3 years ago
10

Branliest offered

Mathematics
1 answer:
blsea [12.9K]3 years ago
7 0
The circumference can be obtained fairly easily by simply substituting the d in c = πd for the colony's given diameter of 12 mm. Performing that calculation using the approximation of π ≈ 3.14, we obtain a circumference of 12 x 3.14 = 37.68 mm.

To find the radius, remember how the diameter and radius of a circle are defined. The radius is a length extending from the center of a circle to a point on its circumference, and a diameter is a line extending from one point on the circle's circumference to an opposite point, passing through the circle's center along the way. The diameter can, in this way, be defined as twice the length of the radius, which means we can find the radius of a circle by taking half of its diameter. In this case, our diameter is 12 mm, so our radius would be 6 mm.
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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...
katovenus [111]

Answer:

  • a_{12}=-244140625

Step-by-step explanation:

Considering the geometric sequence

5,-25,\:125,\:...

a_1=5

As the common ratio 'r' between consecutive terms is constant.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

r=\frac{-25}{5}=-5

r=\frac{125}{-25}=-5

The general term of a geometric sequence is given by the formula:  

a_n=a_1\cdot \:r^{n-1}

where a_1 is the initial term and r the common ratio.

Putting n = 12 , r = -5 and a_1=5 in the general term of a geometric sequence to determine the 12th term of the sequence.

a_n=a_1\cdot \:r^{n-1}

a_n=5\left(-5\right)^{n-1}

a_{12}=5\left(-5\right)^{12-1}

      =5\left(-5^{11}\right)

\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a

       =-5\cdot \:5^{11}

\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

        =-5^{1+11}     ∵ 5\cdot \:5^{11}=\:5^{1+11}

        =-244140625

Therefore,

  • a_{12}=-244140625
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Step-by-step explanation:

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Marta_Voda [28]

Answer:

1:23

Step-by-step explanation:

20 / 460

= 1 / 23

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Answer:

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Step-by-step explanation:

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