Answer:
-175 or 175 along the x-axis in a negative direction
Step-by-step explanation:
The distance is the total length of the trajectory made by a moving object between two points. We need to find the total distance traveled by a particle over the time interval
, so:
Let:
![d_o=Distance\hspace{3}traveled\hspace{3}at\hspace{3}t=0\\d_f=Distance\hspace{3}traveled\hspace{3}at\hspace{3}t=7](https://tex.z-dn.net/?f=d_o%3DDistance%5Chspace%7B3%7Dtraveled%5Chspace%7B3%7Dat%5Chspace%7B3%7Dt%3D0%5C%5Cd_f%3DDistance%5Chspace%7B3%7Dtraveled%5Chspace%7B3%7Dat%5Chspace%7B3%7Dt%3D7)
Using the equation provided by the problem:
![x(t)=2t^3-9t^2-60t+4](https://tex.z-dn.net/?f=x%28t%29%3D2t%5E3-9t%5E2-60t%2B4)
For t=0
![x(0)=2*(0)^3-9*(0)^2-60*(0)+4=0-0-0+4=4](https://tex.z-dn.net/?f=x%280%29%3D2%2A%280%29%5E3-9%2A%280%29%5E2-60%2A%280%29%2B4%3D0-0-0%2B4%3D4)
For t=7
![x(7)=2*(7)^3-9*(7)^2-60*(7)+4=686-441-420+4=-171](https://tex.z-dn.net/?f=x%287%29%3D2%2A%287%29%5E3-9%2A%287%29%5E2-60%2A%287%29%2B4%3D686-441-420%2B4%3D-171)
Hence, the total distance traveled by the particle over the time interval 0≤t≤7 is:
![Total\hspace{3}distance\hspace{3}traveled=d_t=d_f-d_o=-171-4=-175](https://tex.z-dn.net/?f=Total%5Chspace%7B3%7Ddistance%5Chspace%7B3%7Dtraveled%3Dd_t%3Dd_f-d_o%3D-171-4%3D-175)
Answer:
A- Using real world problems to help students learn to solve them on their own
Explanation:
"Problem-based learning" is a teaching approach that centers on students. It allows the student to learn on their own or to solve problems on their own. This is also based on their own <em>"reasoning"</em> and <em>"reflection." </em> So, the role of the teacher here is to facilitate or guide the students. He doesn't need to provide direct instruction to the student. The goal here is "self-identified," so this means that the <u>students identity their own goals.</u> Real word problems are used in order for the students to learn how to solve them on their own.
So, this explains the answer.
Answer:
0.2460 is the required probability.
Step-by-step explanation:
We have been given binomial model
n is the total number of questions which is 10
x is the questions taken out to be which is 5
p is the probability of right answers which is :![\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
q is the probability of the false answers which is :![1-p=1-\frac{1}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=1-p%3D1-%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
We will use the model by substituting the values we get:
on substituting the values we get:
![P(x)=[\frac{`10!}{5!(5)!}]\frac({1}{2})^5\cdot \frac{1}{2}^{5}](https://tex.z-dn.net/?f=P%28x%29%3D%5B%5Cfrac%7B%6010%21%7D%7B5%21%285%29%21%7D%5D%5Cfrac%28%7B1%7D%7B2%7D%29%5E5%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5E%7B5%7D)
![P(x)=\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!(5\cdot4\cdot3\cdot2\cdot1)}\cdot\frac{1}{2}^5\cdot\frac{1}{2}^5](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%5Ccdot5%21%7D%7B5%21%285%5Ccdot4%5Ccdot3%5Ccdot2%5Ccdot1%29%7D%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5E5%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5E5)
Cancel out the common terms from numerator and denominator we get:
![\frac{10\cdot9\cdot8\cdot7\cdot6}{5\cdot4\cdot3\cdot2}\frac{1}{32}\cdot\frac{1}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%7D%7B5%5Ccdot4%5Ccdot3%5Ccdot2%7D%5Cfrac%7B1%7D%7B32%7D%5Ccdot%5Cfrac%7B1%7D%7B32%7D)
![\Rightarrow 14\cdot18\cdot\frac{1}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%2014%5Ccdot18%5Ccdot%5Cfrac%7B1%7D%7B1024%7D)
![\Rightarrow \frac{14\cdot18}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B14%5Ccdot18%7D%7B1024%7D)
![\Rightarrow \frac{252}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B252%7D%7B1024%7D)
![\Rightarrow 0.2460](https://tex.z-dn.net/?f=%5CRightarrow%200.2460)
4/5 x 3/4 is just 12/20, and then when you simplify that you get 3/4.
The interior angles of a triangle add up to 180 degrees, therefore:
40 + 40 + x-10 = 180
80 + x - 10 = 180
70 + x = 180
x = 110
< D = 110 - 10 = 100