Ask question

Ask question

All categories

4 years ago

7

Change in the radius of the circle as the area increases from 3 square feet to 7 square feet ??? Help please

1 answer:

leva [86]4 years ago

3 0

Answer:

The radius will change from 0.977 feet to 1.49 feet.

Step-by-step explanation:

The area of a circle with radius r is given by πr².

If the are of the circle is 3 square feet, then πr² = 3, ⇒ r²= $\frac{3}{\pi }$

⇒ r² =0.9545, ⇒ r=0.977 feet.

If the area of the circle changes to 7 square feet, then its radius will change to r²= $\frac{7}{\pi }$ =2.228, ⇒ r =1.49 feet.

Therefore, the radius will change from 0.977 feet to 1.49 feet. (Answer)

You might be interested in

What is the value of the function at x=−2?

adell [148]

x = -2

function value at x = -2 is intersection of the x value and graph

which is, 3

Hope it is clear:)

5 0

3 years ago

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 for h. -117 = -9h

leva [86]

H= 13
This is because -117/ -9 equals 13

5 0

3 years ago

Read 2 more answers

Plz help me I will mark u brainiest

Likurg_2 [28]

Answer:

quadrant one

Hope this helps

5 0

4 years ago

Does this graph represent a function?

taurus [48]

Yeas it does represent a function

8 0

3 years ago