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3 years ago

Which set of ordered pairs represents a function?

Mathematics

1 answer:

jasenka [17]3 years ago

8 0

Answer:

The final set of ordered pairs represents a function.

Step-by-step explanation:

Each X value corresponds to exactly one y- value. Essentially, none of the x values are the same in the final set.

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2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA

professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

$A=45e^{-0.0045(t)}$

a) To find the initial amount of this substance

At t=0, we get

$A=45e^{-0.0045(0)}$ $A=45e^0$

We know that e^0=1 ( anything to the power zero is 1)

we get,

$A=45$

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

$\frac{45}{2}=45e^{-0.0045(t)}$

$\frac{1}{2}=e^{-0.0045(t)}$

Taking natural logarithm on both sides we get,

$\ln (\frac{1}{2})=-0.0045(t)^{}$ $(-1)\ln (\frac{1}{2})=0.0045(t)$ $\ln (\frac{1}{2})^{-1}=0.0045(t)$ $\ln (2)=0.0045(t)$ $0.6931=0.0045(t)$ $t=\frac{0.6931}{0.0045}$ $t=154.02$

Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

$A=45e^{-0.0045(2500)}$ $A=45e^{-11.25}$ $A=45\times0.000013=0.000585$ $A=0.000585$

The amount of substance will be present around in 2500 years is 0.000585 grams

4 0

1 year ago

Michelle has a $100. She wants to purchase paper pins ($20) and file covers ($20) and paper weights. each paper weight costs $10

MatroZZZ [7]

$1000 - ($20 + $20) = $60
$60 / $10 = 6 paper weights

4 0

3 years ago

This famous clock tower has a clock face with a diameter of 23 feet. What is the approximate area of this clock face

pashok25 [27]

Answer:

Therefore the approximate area of this clock face is 415.3 feet².

Step-by-step explanation:

Given:

Clock is of Circular Shape,

Diameter = 23 feet

$Radius =r =\dfrac{diameter}{2}=\dfrac{23}{2}=11.5\ feet$

To Find :

Area of Clock Face = ?

Solution:

Area of Circle having Radius 'r' is given as,

$\textrm{Area of Circle}=\pi r^{2}$

Substituting the values we get

$\textrm{Area of Clock Face}=3.14\times (11.5)^{2}=415.265=415.3\ feet^{2}$

Therefore the approximate area of this clock face is 415.3 feet².

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3 years ago

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SOVA2 [1]

Answer:

I dont know sorry

Step-by-step explanation:

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3 years ago

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Jlenok [28]

Answer:

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Step-by-step explanation:

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3 years ago