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SIZIF [17.4K]
1 year ago
5

?In the table below, y is a linear function of x.X-214710y09182736What is the y intercept of the function

Mathematics
1 answer:
Aleonysh [2.5K]1 year ago
7 0

y intercept : (0,6)

Explanation:

Use the formula:

. y = mx + b

Find m (the slope), using 2 random points of the graph: (-2,0) and (1,9)

. m = (y-y1) / (x-x1)

m = (0-9) / (-2-1)

m = -9 / -3

m = 3

Replace m in the equation:

. y = 3x + b

Find b by replacing y and x by a random point of the graph: (1,9)

. 9 = 3*1 + b

b = 9 - 3

b = 6

Replace b in the equation:

. y = 3x +6

To find the y-intercept replace x by 0 in the equation:

. y = 3*0 +6

y = 0+6

y = 6

=> y-intercept : (0,6)

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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
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Answer:

Given that,

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

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

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

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we get,

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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)}

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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=0.000585A=0.000585

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

4 0
1 year ago
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Answer:

\frac{1}{20}

Step-by-step explanation:

\frac{3}{60}=\frac{1}{20}

To get \frac{1}{20} you needed to divide the numerator and denominator by 3.

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