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bearhunter [10]

2 years ago

7

Please help !

1 answer:

nadya68 [22]2 years ago

6 0

Answer:

r(-2)= -5

r(0)= -7

r(5)= -12

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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.

5 0

3 years ago

Solve the following inequality for x (nearest tenth):<br> -4<-17.03-7x

Mila [183]

Answer:

x<-1303/700

Step-by-step explanation:

8 0

4 years ago

HELP ME PLEASEEEE! Thank you

Sergio039 [100]

Answer:

A. Yes

B. Yes

C. No

Step-by-step explanation:

We can substitute each value in to the equation and see if the sides match up. Let's start with a.

$4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5$

So, n = 2 works for equation a. Let's try B.

$9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11$

So, m = $\frac{10}{3}$ works for B. Now let's try C.

$3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54$

So y = 30 doesn't work for C.

Hope this helped!

6 0

4 years ago

Find the axis of symmetry for this parabola:

lara31 [8.8K]

Answer:

x = - 1

Step-by-step explanation:

The equation of the axis of symmetry for a parabola in standard form

y = ax² + bx + c : a ≠ 0 is found using

x = - $\frac{b}{2a}$

y = - x² - 2x - 5 ← is in standard form

with a = - 1 and b = - 2, thus equation of axis of symmetry is

x = - $\frac{-2}{-2}$ = - 1

Equation of axis of symmetry is x = - 1

6 0

3 years ago

Grade low in math help if you can :) Geometry

mestny [16]

Answer:

C) 10 inches

Step-by-step explanation:

I think the simplest way to do this is as follows:

divide 75 by 15 to get how many times you need to multiply 2in by

75/15=5

since 15(5)=75 or the actual size of the airplane,

2(5)=10 which is the size of the model airplane

5 0

3 years ago