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4 years ago

The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?

1 answer:

7 0

It's the Geometric Sequence.

The n-th term of a geometric sequence with initial value a and common ratio r is given by:

$a_n=a_1\cdot r^{n-1}\ for\ n\in\mathbb{N^+}$

We have:

$a_1=-2;\ r=3;\ n=6$

Substitute:

$a_6=-2\cdot3^{6-1}=-2\cdot3^5=-2\cdot243=-486$

Answer: The sixth term is equal -486.

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Element X decays radioactively with a half life of 13 minutes. If there are 110 grams of Element X, how long, to the nearest ten

Vaselesa [24]

Answer : The time taken by the element to decay to 2 grams is, 75.2 minutes

Step-by-step explanation:

Half-life = 13 min

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{13\text{ min}}$

$k=0.0533\text{ min}^{-1}$

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $0.0533\text{ min}^{-1}$

t = time passed by the sample = ?

a = initial amount of the reactant = 110 g

a - x = amount left after decay process = 2 g

Now put all the given values in above equation, we get

$t=\frac{2.303}{0.0533}\log\frac{110}{2}$

$t=75.2\text{ min}$

Therefore, the time taken by the element to decay to 2 grams is, 75.2 minutes

7 0

4 years ago

Determine the value of each unknown variable

Oksi-84 [34.3K]

X=18 and y=10 because they are both 90degree angles therefore all you have to do is solve the equations: 5x=90 and 9y=90.

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3 years ago

How do you do four Column solving

Luba_88 [7]

Arrange the first row arbitrarily: 1 2 3 4.
Then there is only one option to begin the next row: 3.
The remaining row must be 4 1 2.
This leaves no options for beginning the third row (1 and 3 are in the same column, and 2 and 4 share the diagonal).

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3 years ago

Read 2 more answers

(10 points)What is the sum of the first ten terms of the sequence 4,-12, 36, -144...

vova2212 [387]

Answer:

Step-by-step explanation:

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3 years ago

The function y - 3 = 4(x + 2) is in point-slope form. Select the equivalent equation in slope-intercept form

Phoenix [80]

<h2>Answer:</h2>