Help with this please. I’d appreciate if you showed the steps and the answer. Thanks!

Mathematics

1 answer:

melisa1 [442]3 years ago

8 0

Answer:

Diagonal=11.3m

Area of square (A) =1/2*d^2

=1/2*(11.3)^2

=63.845m^2

We know,

Area of square A= l^2

63.845=l^2

$\sqrt{63.845 }$

L=7.99m

Now,

Perimeter of square =4l

=4*7.99

=31.96m

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A circular oil slick is expanding at a rate of 3m/min. How fast is the area of the oil slick changing when the diameter is 48 me

olga55 [171]

Answer:

$48\pi \:m/min$

Step-by-step explanation:

Diameter = 48 m

Therefore radius r = 48/2 = 24 m

$Area \: of \: circular \: oil \: slick \\ A = \pi {r}^{2} \\ differentiating \: w \: r \: to \: t \: on \: \\ both \: sides \\ \\ \frac{dA}{dt} = \frac{d}{dt} (\pi {r}^{2} )\\ \\ \frac{dA}{dt} =\pi \frac{d}{dt} {r}^{2} \\ \\ \frac{dA}{dt} =\pi \times 2{r}\\ \\ \frac{dA}{dt} =2\pi {r} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =2\pi \times {24} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =48\pi \: m \: per \: min$