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Nimfa-mama [501]

3 years ago

15

The equation above can be used to calculate the volume V, of a sphere with radius r. If the volume of a sphere is 288πcm3, what

is the radius of the sphere in centimeters? Select one: A. 13 B. 9 C. 16 D. 6

1 answer:

ella [17]3 years ago

8 0

Answer:

Step-by-step explanation:

V=4/3πr^3

288πcm^3=4/3×π×r^3

288π×3cm^3=4πr^3

864π=4πr^3

r^3=216

r=6cm

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Solve the inequality 42<-6d

pentagon [3]

Answer:

d < - 7

Step-by-step explanation:

given

42 < - 6d ( divide both sides by - 6 )

Remembering to reverse the inequality symbol as a consequence

- 7 > d ⇒ d < - 7

6 0

3 years ago

Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14

PilotLPTM [1.2K]

Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

$N(t)=N_{0}e^{-\lambda t}$

Where:

No = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

$\lambda$ = The decay constant.

One important parameter related to radioactive decay is the half-life:

$\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }$

If we know the value of the half-life, we can calculate the decay constant:

$\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}$

Carbon-14 has a half-life of 5,730 years, thus:

$\displaystyle \lambda=\frac {\ln(2)}{ 5,730}$

$\lambda=0.00012097$

The equation of the remaining quantity of Carbon-14 is:

$N(t)=N_{0}e^{-0.00012097\cdot t}$

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

$0.10N_o=N_{0}e^{-0.00012097\cdot t}$

Simplifying:

$0.10=e^{-0.00012097\cdot t}$

Taking logarithms:

$ln 0.10=-0.00012097\cdot t$

Solving for t:

$\displaystyle t=\frac{log 0.10}{-0.00012097}$

$t\approx 19,035\ years$

Carbon-14 will take 19,035 years to decay to 10 percent.

6 0

3 years ago

Read 2 more answers

Suppose that 10 people, including you and a friend, line up for a group picture. How many ways can the photographer rearrange th

slamgirl [31]

Answer:

483 840 ways

Step-by-step explanation:

Let you and your friend be A and B.

With three people always between you two,, we have

Case 1: AxxxBxxxxx

Case 2: xAxxxBxxxx

Case 3: xxAxxxBxxx

Case 4: xxxAxxxBxx

Case 5: xxxxAxxxBx

Case 6: xxxxxAxxxB

So there is 6 ways of arranging you two through the line and for each of the six cases,

If you two remained in your positions, the rest can be arranged in 8! ways

Also for each case, you two can interchange your positions in 2! ways

Therefore,

The photographer can rearranged the line keep three people between you an your friend in

8! * 2! * 6 = 483 840 ways

7 0

3 years ago

A student spends the same amount each week for bus fare. In 6 weeks, he spends $81. Which equation shows this relationship? Let

Pavel [41]

Answer:

The answer is 13.50x

Step-by-step explanation:

81 / 6=13.5 per week

8 0

3 years ago

Read 2 more answers

HELP ME PLEASEEE ILL GIVE BRAINLIEST ITS DUE TODAY

nikdorinn [45]

Dang… I wish I can help.

6 0

3 years ago