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:
Apple = €0.20
Banana = €0.60
Step-by-step explanation:
Let A represent the price of an apple and B represent the price of a banana:
4A + B = €1.40
7A + B = €2.00 multiply first equation by -1 and then find the sum of the two equations:
-1 x (4A + B) = 1.40
-4A - B = -1.40
7A + B - 4A - B = 2.00 - 1.40
3A = 0.60 divide both sides by 3
A = 0.20 now we can use this information to calculate the price of a banana
4*0.20 + B = 1.40
0.80 + B = 1.40 subtract 0.80 from both sides
B = 0.60
Remark
Writing down the givens for these questions is almost a command. You must know which equation of the big 4 to use. The givens + what you want to find will determine the equation.
Givens
vi = 30.7 km/hr = 30.7 km/hr *[1000m/1km]*[1hr/3600sec] = 8.52m/sec
vf = 120 km/hr = 120 km/hr * [1000 m/1 km]*[1h/3600 sec] = 33.3 m/s
t = 4.9 seconds
d = ???
Formula
d = (vi + vf)*t/2
Solve
d = ( 33.3+8.52 )*4.9/2
d = (41.85333)*4.9/2
d = 205.02/2
d = 102.51 m<<<Answer
You first add all the angles together.
25 + 65 + 90 = 180°
The total angle measurement of a triangle is 180°. Therefore, it is possible to only make one triangle.
Answer:
It's 30 degrees. YSX and QSL are verticals so they are equal. Then QSL AND MLP are corresponding so they are too equal. So then yeah.
