Solve:
"<span>twice the number minus three times the reciprocal of the number is equal to 1."
3(1)
Let the number be n. Then 2n - ------- = 1
n
Mult all 3 terms by n to elim. the fractions:
2n^2 - 3 = n. Rearranging this, we get 2n^2 - n - 3 = 0.
We need to find the roots (zeros or solutions) of this quadratic equation.
Here a=2, b= -1 and c= -3. Let's find the discriminant b^2-4ac first:
disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.
That's good, because 25 is a perfect square.
-(-1) plus or minus 5 1 plus or minus 5
Then x = ------------------------------ = --------------------------
2(2) 4
x could be 6/4 = 3/2, or -5/4.
You must check both answers in the original equation. If the equation is true for one or the other or for both, then you have found one or more solutions.</span>
<span>The graphs are identical and intersect at infinitely many points.
</span>
Step-by-step explanation:
Hello there!
Just double the given sides!
(18*2)+(12*2)=60 cm.
There you are!
:)
Given:
Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.
He is only allowed to work 13 hours total per week.
He wants to make at least 65 dollars.
To find:
The system of inequalities to represent this situation.
Solution:
Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.
He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.
He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.
Number of hours can not be negative.
.
Therefore, the required system of inequalities contains some equations, 
and 
.
In terms of its radius 
, the volume of the balloon is
The diameter 
is twice the radius, so that in terms of its diameters, the balloon's volume is given by
Differentiate both sides with respect to time 
:
The diameter increases at a rate of 
. When the diameter is 
, we have
or about 23,562 cc/min (where cc = cubic centimeters)
