I need help on number 18

Mathematics

1 answer:

zloy xaker [14]2 years ago

7 0

Answer:

Volume = 35185.8 $km^{3}$

Step-by-step explanation:

Recall the formula for the volume of a cone: $Volume = \pi R^{2} \frac{h}{3}$

Where R is the radius of the cone's circular base (in your case half of 80 km,(that is 40 km)

And h stands for the height of the cone (in your case 21 km)

We replace such in the formula and calculate its final value:

$Volume = \pi 40^{2} \frac{21}{3} = \pi 1600 \frac{21}{3} = \pi 1600 (7) = 35185.83772...$

We round it to the number of decimals your problem request (let's say to one decimal) and also include the cubic units:

Volume = 35185.8 $km^{3}$

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The initial deceleration is 4 m/s^2, so this means that considering the first line segment, $\frac{V-100}{T}=-4 \implies V=100-4T$ .

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$400(100-4T)-\frac{1}{2}(4T)(5T)=4000\\\\40000-1600T-10T^2=4000\\\\10T^2 +1600T-36000=0\\\\T^2 +160T-3600=0\\\\(T+180)(T-20)=0\\\\T=20 (T > 0)\\\\\therefore V=100-4(20)=20$