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3 years ago

PLS HELP!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

REY [17]3 years ago

8 0

Answer:

pick the second one

Step-by-step explanation:

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

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3 years ago

Michael estimated his mass as 8 kilograms. Is his estimate reasonable. Justify your answer

saw5 [17]

No, a person weight on average anywhere from 40-80+kg depending on sex and build

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3 years ago

The record holder in eating chocolate ate 31.5 ounces of Chicago Chocolate Hearts in 7 minutes. How much chocolate did he eat pe

sasho [114]

Answer:

Step-by-step explanation:

This is a unit rate problem. If we want to find out how much chocolate was eaten in 1 minute, we divide 31.5 by 7. This gives us the number of ounces of chocolate eaten in 1 minute: 4.5 ounces per minute.

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3 years ago

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Create a list of steps, in order, that will solve the following equation.

AleksandrR [38]

Step-by-step explanation:

Add 1 to both sides

Multiply both sides by 4

Take the square root of both sides

Subtract 5 from both sides

(straight from khan academy hints)

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3 years ago

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diamong [38]

Step-by-step explanation:

<u>Initial value is the y-intercept:</u>

b = 1200

<u>Rate of change is the difference in the charge amount per year:</u>

m = (1350 - 1200) / (8 - 5) = 150 / 3 = 50

<u>The equation would be:</u>

y = 50x + 1200

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2 years ago

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