3 years ago

Select the function that represents a geometric sequence.

Mathematics

1 answer:

steposvetlana [31]3 years ago

6 0

Answer is A(n)=P(1+i)n-1 where n is a positive integer

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3 years ago

Simplify each expression (2a^4)^-3,a does not =0

Masja [62]

Answer:

3rd option.) 1/8a^12

Step-by-step explanation:

(2a⁴)^-3

=1/(2a⁴)³

=1/8a^12

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2 years ago

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

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3 years ago

A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle for

katovenus [111]

Answer: 15

Step-by-step explanation: its 15

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3 years ago

A jar holds 42 yellow and 14 purple crayons. A crayon is pulled out of the jar at random and then placed back in the jar.

noname [10]

The purple crayons take up 1/4 of the crayons in the jar. To get the answer:
140/4 = 35

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2 years ago

Read 2 more answers