The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
![t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Substituting:
![\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81-4%282%29%28-18%29%7D%7D%7B2%282%29%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81%2B144%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B225%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm15%7D%7B4%7D%20%5Cend%7Bgathered%7D)
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Answer:
53
reason:
substitute a with -7 and b with -37
this makes the equation (-7)3 - (-37)2, which equals 53
if the figures perimeter is 18 units, and the width of the figure is 5 units. I am guessing the figure is a rectangle
where the width is 5 units, and 2 of the sides have 2 be the same 2 be a rectangle, than the width on each side is 10 units all together
18-10= 8
if the figure is a rectangle then that means there are 2 sides left of equal length so if we divide our current number (8) by 2 then we will have the length of each side (4)
8 divided by 2= 4
width= 5
length= 4
3
multiply by 4
12
add 12
24
divide by 2
12
subtract 6
6
number 6 : 6(4) = 24... + 12 = 36...36/2 = 18.....- 6 = 12
number 8 : 8(4) = 32....+ 12 = 44...44/2 = 22....- 6 = 16
number 12: 12(4) = 48....+ 12 = 60...60/2 = 30....-6 = 24
well...by following these steps, it appears the original number doubles as a result.
You need 9 grams of sodium chloride per 1 liter of water
or
1 teaspoon of sodium chloride per cup of water (1 cup = 8 Fluid ounces)
