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2 years ago

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Latanya was asked to determine if (375,4) lies on the circle with radius 7 centered at (0.-2). what is her error?

1 answer:

Vilka [71]2 years ago

6 0

The point (3/5,4) would lie on the circle if it makes the equation of the circle to be true

Latansha's equation of the circle is wrong

<h3>How to determine her error?</h3>

The given parameters are:

Center = (a,b) = (0,-2)

Radius, r = 7

The equation of a circle is:

$(x - a)^2 + (y - b)^2 = 0$

This gives

$(x - 0)^2 + (y + 2)^2 = 0$

Rewrite as:

$x^2 + (y + 2)^2 = 0$

In Latanya's first step, we have:

$x^2 + (y - 2)^2 = 0$

By comparing her first step with x^2 + (y + 2)^2 = 0, we can see that her equation is wrong

Hence, Latansha's error is that she determine the equation of the circle, wrongly.

Read more about circle equations at:

brainly.com/question/1559324

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Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest ten

serg [7]

Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

$\frac {dN}{dt}\propto -N$

$\Rightarrow \R\frac {dN}{dt}=-\lambda N$

$\Rightarrow \frac {dN}N=-\lambda dt$

Integrating both sides

$\Rightarrow \int \frac {dN}N=\int-\lambda dt$

$\Rightarrow ln|N|=-\lambda t+c$

When t=0, N= $N_0$ = initial amount

$ln|N_0|=-\lambda .0+c$

$\Rightarrow c=ln|N_0|$

$ln|N|=-\lambda t+ln|N_0|$

$\Rightarrow ln|N|-ln|N_0|=-\lambda t$

$\Rightarrow ln|\frac{N}{N_0}|=-\lambda t$

Decay equation:

$ln|\frac{N}{N_0}|=-\lambda t$

Given that, the half life of of element X is 11 minutes.

For half life, $N=\frac12 N_0$ , t= 11 min.

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11$

$\Rightarrow ln|\frac12}|=-\lambda . 11$

$\Rightarrow -\lambda . 11=ln|\frac12}|$

$\Rightarrow \lambda =\frac{ln|\frac12|}{-11}$

$\Rightarrow \lambda =\frac{ln|2|}{11}$ [ $ln|\frac12|=ln|1|-ln|2|=-ln|2|$ , since ln|1|=0]

N=154 grams, $N_0$ = 870 grams, t=?

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t$

$\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}$

=27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

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Help please this is due I don’t understand <br> !!!!!

Dmitrij [34]

Answer:

B

Lemme explain rq.

If a number has a fractional exponent, that bottom part of the fraction goes the to root side when it is turned into a root.

Step-by-step explanation:

For example, 4 to the power of 2/3 becomes cube root of 4 to the power of 2.

When an exponent to a number also has a power

For example:

4 to the power of 2 to the power of 3

$(4^{2} )^{3} = 4^{2 * 3}$

So B because B is the only one where the two powers are multiplied.

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3 years ago

Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) a

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Answer:

$log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1$

Step-by-step explanation:

Given

$log_3(\frac{21}{5})$

Required

Express in terms of $log_3(5)$ and $log_3(7)$

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Apply law of logarithm

$log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)$

$log_3(3) = 1$ . So, we have:

$log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)$

Rewrite:

$log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1$

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