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3 years ago

Which is bigger 40% of 180 or 1/4 of 320

Mathematics

2 answers:

prohojiy [21]3 years ago

5 0

40% of 180
2/5 * 180
360/5
72

1/4 of 320
320/4
80

Therefore 1/4 of 320 is bigger.

Hope this helps :)

Veronika [31]3 years ago

3 0

40% of 180 is 72
1/4 of 320 is 80

therefore 1/4 of 320 is bigger

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When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population gr

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(a) The population after 15 years is 2678.

(b)Therefore the population P(t) at any time t>0 is

$P(t)= 45t+30 {t^{\frac32}}+260$

Step-by-step explanation:

Given that,

The population grew at a rate of

$P'(t)=45(1+\sqrt t)$

Integrating both sides

$\int P'(t) dt=\int 45(1+\sqrt t)dt$

$\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt$

$\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt$

$\Rightarrow P(t)= 45t+45\ \frac{t^{\frac12+1}}{\frac12+1}+c$ [ c is integration constant]

$\Rightarrow P(t)= 45t+45\ \frac{t^{\frac32}}{\frac32}+c$

$\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c$

$\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c$

When t=0 , P(0)= 260

$\therefore 260= 45\times0+30\times {0^{\frac32}}+c$

$\Rightarrow c=260$

$\therefore P(t)= 45t+30 {t^{\frac32}}+260$

Therefore the population P(t) at any time t>0 is

$P(t)= 45t+30 {t^{\frac32}}+260$

To find the population after 15 years, we need to plug t=15 in the above expression.

$P(15)=( 45\times 15)+30( {15^{\frac32}})+260$

≈2678

The population after 15 years is 2678.

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3 years ago