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3 years ago

I need to know how to simplify these problems.

Mathematics

1 answer:

nalin [4]3 years ago

5 0

You need to factor the radicals into products of radicals, and when factoring you should keep in mind you want to obtain perfect square roots. So √125 = √5*√25 and squareroot 25 has a definite answer of 5, so ∛125=∛5×∛25=5×√5. You want to follow the general pattern of factoring perfect squares to obtain a number outside the radical which can be multiplied by the current coefficient

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If a man were to sell his T.V set for 7200, he would have lost 25%. For what price must he sell it to

vlabodo [156]

Answer:

Step-by-step explanation

S.P of a t.v = rs 7200

Loss % = 25%

Therefore, C.P = S.P (100/100-loss)

=7200(100/100-25)

=7200 x 100/75

=9600

So,now C.P = 9600

Profit% = 25%

Therefore, S.P = C.P (100+profit/100)

=9600(100+25/100)

=9600 x 125/100

=12000

So,the price he should sell to gain 25%

=12000

Hope it helps...!!!

3 0

3 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

PLEASE HELP DUE TODAY !

igor_vitrenko [27]

Answer:

let x be chips and y be sodas

8x + 4y = 5 ---> for the first hint

4x + 8y = 7------> second hint

0.25 cents is how much chips costs

and 0.75 cents is how much sodas costs

5 0

3 years ago

Read 2 more answers

Help me out please .

Marta_Voda [28]

I’m pretty sure it’s A but it could also me C
Hopes it right.

6 0

3 years ago

Read 2 more answers

Last month, 17 people showed up to help a local charity. This month, 55 people volunteered. What is the percentage increase?

astra-53 [7]

Step-by-step explanation:

The formula for percent change is

change/original.

So let's subtract 17 from 55 to find the change. 55-17=38

This is the change. Now we divide it by the original, 17.

38/17=2.235294

We're not done yet! We have to move the decimal point over to the right 2 spaces to make it a percentage. So, the percentage increase is

about 223.53 percent

6 0

3 years ago