Let $v_0$ be the cat's speed just as it leaves the edge of the table. Then taking the point 1.3 m below the edge of the table to be the origin, the cat's horizontal position at time $t$ is given by

$x(t)=v_0t$

and its height is

$y(t)=1.3\,\mathrm m-gt^2$

where $g$ is 9.8 m/s^2, the magnitude of the acceleration due to gravity.

The time it takes for the cat to hit the ground is $t$ with

$0=1.3\,\mathrm m-gt^2\implies t=\sqrt{\dfrac{1.3\,\rm m}g}\approx0.36\,\mathrm s$

(Unfortunately, this doesn't match any of the given options...)

The cat lands 0.75 m away (horizontally) from the edge of the table, so that its speed $v_0$ was

$0.75\,\mathrm m=v_0(0.36\,\mathrm s)\implies v_0\approx2.08\dfrac{\rm m}{\rm s}$

(Again, not one of the answer choices...)

I'm guessing there's either a typo in the question or answers.

6 0

3 years ago

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

taurus [48]

The numbers are: 36 and 11 .
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Explanation:
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Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .
__________________________________________
     x + y = 47 .

     y − x = 25.
__________________________________________
Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
_____________________________________________
   y − x + x = 25 + x ;

to get:

   y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

    x = 11 ;
______________________________________________
x + y = 47<span> ;

</span>Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

            y = 36 .
___________________________________________
So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
______________________________________________
The numbers are: 36 and 11 .
______________________________________________

5 0

3 years ago

Help with this please ​

Help with this please