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3 years ago

Find the value of x number on top is 6 and other is 9

Mathematics

1 answer:

faltersainse [42]3 years ago

5 0

Answer:

x = - 12, 3

Step-by-step explanation:

By tangent secant theorem:

$x(x + 9) = {6}^{2} \\ \\ {x}^{2} + 9x = 36 \\ \\ {x}^{2} + 9x - 36 = 0 \\ \\ {x}^{2} + 12x - 3x - 36 = 0 \\ \\ x(x + 12) - 3(x + 12) = 0 \\ \\ (x + 12)(x - 3) = 0 \\ \\ x + 12 = 0, \: \: x - 3 = 0 \\ \\ x = - 12, \: \: x = 3 \\ \\$

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A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal place

Andrej [43]

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

$P(t) = P(0)(1-r)^{t}$

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

$P(1) = 0.97P(0)$

Then

$P(t) = P(0)(1-r)^{t}$

$0.97P(0) = P(0)(1-r)^{0}$

$1 - r = 0.97$

$P(t) = P(0)(0.97t)^{t}$

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.5P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.5$

$\log{(0.97)^{t}} = \log{0.5}$

$t\log{0.97} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.97}}$

$t = 22.76$

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.85P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.85$

$\log{(0.97)^{t}} = \log{0.85}$

$t\log{0.97} = \log{0.85}$

$t = \frac{\log{0.85}}{\log{0.97}}$

$t = 5.34$

5.34 years for the sample to decay to 85% of its original amount

8 0

4 years ago

7x5 - 33x4 – 4x2 + 3x + 52 = 0

stepladder [879]

Hi there! Don’t forget your order of operations when doing problems like these. You can remember it by the phrase PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.

The answer I got was 53/3, or in standard for 3x=53z

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3 years ago

Please help I do anything just help

uranmaximum [27]

Answer:

i think it week 2

Step-by-step explanation:

hope this help

7 0

3 years ago

While on an 8.0 h trip, a car traveled for 3.5 h at an average speed of 90 km/h before stopping for 1.0 h. The car then traveled

Ede4ka [16]

Answer:

72.5 km/h

Step-by-step explanation:

Multiply the km/h by how many hours your going at that speed/total number of hours on trip.

(90x(3.5/8))+(80x(2/8))+(70x(1.5/8))

39.375+20.5+13.125

72.5km/h

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3 years ago

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Butoxors [25]

Answer:

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3 years ago