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Rzqust [24]
4 years ago
14

What is the next term of the geometric sequence? 40 20 10 27' 9'3'

Mathematics
1 answer:
krek1111 [17]4 years ago
4 0
40,20,10,5
27,9,3,1
On the first one, you’re taking half of the previous number. On the second one, you’re finding a third of the previous number.
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How much of a radioactive kind of thorium will be left after 14,680 years if you start with
babymother [125]

Answer:

8978 grams

Step-by-step explanation:

The equation to find the half-life is:

N(t)= N_{0}e^{-kt}

N(t) = amount after the time <em>t</em>

N_{0} = initial amount of substance

t = time

It is known that after a half-life there will be twice less of a substance than what it intially was. So, we can get a simplified equation that looks like this, in terms of half-lives.

N(t)= N_{0}e^{-\frac{ln(\frac{1}{2}) }{t_{h} } t} or more simply N(t)= N_{0}(\frac{1}{2})^{\frac{1}{t_{h} } }

t_{h} = time of the half-life

We know that N_{0} = 35,912, t = 14,680, and t_{h}=7,340

Plug these into the equation:

N(t) = 35912(\frac{1}{2})^{\frac{14680}{7340} }

Using a calculator we get:

N(t) = 8978

Therefore, after 14,680 years 8,978 grams of thorium will be left.

Hope this helps!! Ask questions if you need!!

8 0
2 years ago
Which equation has a graph that passes through the points at (0,5) and (-3,-4)?
Roman55 [17]

Answer:

y = 3x + 5

Step-by-step explanation:

We are asked the equation of the graph which passes through the points at (0,5) and (-3,-4).  

Now, we know that the equation of a straight line passing through the points (x_{1},y_{1}) and (x_{2},y_{2}) is given by

\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}.

So, in our case (x_{1},y_{1}) ≡ (0,5) and (x_{2},y_{2}) ≡ (-3,-4)

Therefore, the equation of the straight line will be  

\frac{y - 5}{5 - (- 4)} = \frac{x - 0}{0 - (- 3)}

⇒ y - 5 = \frac{9}{3}x

⇒y = 3x + 5 (Answer)

4 0
4 years ago
Find the volume of the prism
AlekseyPX

Answer:

80 units³

Step-by-step explanation:

→ State the formula

Length × Width × Height

→ Substitute in the values

8 × 2 × 5

→ Simplify

80 units³

6 0
2 years ago
Supply the missing numbers in the following sequences 4, 9, 14, _____, 24, 29, _____
Galina-37 [17]

Answer:

4,9,14,19,24,29,34

that the exact number

6 0
4 years ago
Please help me solve this
seropon [69]

9514 1404 393

Answer:

  103°

Step-by-step explanation:

The law of sines tells you ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin(c/a·sin(A)) = arcsin(37/19·sin(30°)) ≈ 180° -76.8° ≈ 103°

Obtuse angle C is about 103°.

5 0
3 years ago
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