The population model given dP/dt â P or dP dt = kP (1)

Mathematics

1 answer:

Gnesinka [82]2 years ago

8 0

Answer:

Step-by-step explanation:

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The diameter of a circle is 14 m. Find its area to the nearest tenth.

SOVA2 [1]

Answer:

153.94cm squared

Step-by-step explanation:

π×7×7

=153.93804

=153.94cm squared

4 0

3 years ago

Find the area enclosed by x2=2y and y2=16x

jekas [21]

Answer: $\dfrac{32}{3}$

Step-by-step explanation:

Given

The parabolas are $x^2=2y$ and $y^2=16x$

Find the point of intersection of two parabolas

$\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4$

Obtain y using x

$(x,y)\rightarrow (0,0)\ \text{and }(4,8)$

Area enclosed between the two is

$\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}$