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3 years ago

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Misha’s family bought a large cattle farm. The number of acres of the cattle farm is the cube of the acres they used to own plus

10 acres. If a represents the number of acres the family used to own, which expression represents the number of acres they own now?

1 answer:

atroni [7]3 years ago

8 0

It should be axaxa +10. Or a to the third plus 10

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it is not going in any general direction

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A pebble is dropped into a deep well and 3s later the sound of a splash is heard as the pebble reaches the bottom of the well. T

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Answer:

$2.89\ \text{s}$

0.11 seconds

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Step-by-step explanation:

$t_1$ = Time taken by the pebble to hit the water

$t_2$ = Time taken by the sound to travel to the observer

$t_1+t_2$ = Time taken by the observer to listen to the splash after stone is thrown = 3 s

$t_1=3-t_2$

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The distance traveled by the pebble

$s=ut+\dfrac{1}{2}at_1^2\\\Rightarrow s=0+\dfrac{1}{2}\times9.81(3-t_2)^2\\\Rightarrow s=4.905(9+t_2^2-6t_2^2)$

Distance traveled by the sound

$s=u_st\\\Rightarrow s=340\times t_2$

The distance traveled by the sound and the pebble is equal

$4.905(9+t_2^2-6t_2)=340\times t_2\\\Rightarrow 9+t_2^2-6t_2=\dfrac{340}{4.905}t_2\\\Rightarrow 9+t_2^2-6t_2=69.32t_2\\\Rightarrow t_2^2-75.32t_2+9=0\\\Rightarrow t_2=\frac{-\left(-75.32\right)\pm \sqrt{\left(-75.32\right)^2-4\times \:1\times \:9}}{2\times \:1}\\\Rightarrow t_2=75.2,0.11$

Since $t_1+t_2=3$ the value of $t_2$ cannot be greater than 3.

So, time taken by the sound to reach the observer is 0.11 seconds.

Time taken by the pebble to hit the water is $t_1=3-t_2=3-0.11=2.89\ \text{s}$

Depth of the well is $s=340t_2=340\times 0.11=37.4\ \text{m}$

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