2/9 is 32/144 in simplest form
This is the worksheet I’m doing https://www.manhassetschools.org/cms/lib8/NY01913789/Centricity/Domain/710/Aim%2082%20Pd%209%20KEY.pdf
Answer:
Since b^2 -4ac = 256 we have 2 real distinct root roots
Step-by-step explanation:
4x^2+12x=7
We need to subtract 7 to get it in the proper form
4x^2+12x-7=7-7
4x^2+12x-7=0
The discriminant is b^2 -4ac
when the equation is ax^2 +bx+c
so a =4 b=12 and c=-7
(12)^2 - 4(4)(-7)
144 +112
256
If b^2 -4ac > 0 we have 2 real distinct roots
If b^2 -4ac = 0 we have one real root
If b^2 -4ac < 0 we have two complex root
Since b^2 -4ac = 256 we have 2 real distinct root roots
Answer:
80 feet
Step-by-step explanation:
Given:
Initial speed of the car (
) = 40 ft/sec
Deceleration of the car (
) = -10 ft/sec²
Final speed of the car (
) = 0 ft/sec
Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.
Now, deceleration means rate of decrease of velocity.
So, 
Negative sign means the velocity is decreasing with time.
Now, 
using chain rule of differentiation. Therefore,
Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,
![\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft](https://tex.z-dn.net/?f=%5Cint%5Climits%5E0_%7B40%7D%20%7Bv%7D%20%5C%2C%20dv%3D%5Cint%5Climits%5Ex_0%20%7B-10%7D%20%5C%2C%20dx%5C%5C%5C%5C%5Cleft%20%5B%20%5Cfrac%7Bv%5E2%7D%7B2%7D%20%5Cright%20%5D_%7B40%7D%5E%7B0%7D%3D-10x%5C%5C%5C%5C-10x%3D%5Cfrac%7B0%7D%7B2%7D-%5Cfrac%7B1600%7D%7B2%7D%5C%5C%5C%5C10x%3D800%5C%5C%5C%5Cx%3D%5Cfrac%7B800%7D%7B10%7D%3D80%5C%20ft)
Therefore, the car travels a distance of 80 feet before stopping.
To avoid multiplying the two numbers and then finding the cube root, find the cube root of each number first. the cube root of 27 is 3x3x3, so you can take out the three to outside of the sqrt, to get 3 cube root 18. eighteen does not have a cube root, so that's all you have to do. the answer would be 3 (cube root) 18.
