Determine if the lines r1(t) = <3, 0, 2> + t <1, 2, −2> and r2(s) = <0, 1, −1> + s <4, 1, 1> intersect,
1 answer:
Answer:
Yes lines are intersecting, point of intersection is <4,2,0>.
Step-by-step explanation:
Given parametric equations of line are:
If lines are intersecting then parametric coordinates of (1) are equal to (2)
Considering A and B to find values of t and s
From A
t=4s-3---(D)
Putting in (B)
2(4s-3)=1+s
8s-6=1+s
7s=7
s=1
Then
t=4-3
t=1
If lines are intersecting then these values of s and t must satisfy (C)
2-2(1)=1-1
0=0
This shows lines are intersecting.
At this value of t, (1) becomes
Putting s=1 in (2)
Point of intersection is <4,2,0>.
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When you roll a number cube, there is a possibility of a number from 1 to 6 appearing. i.e. 1, 2, 3, 4, 5, or 6 can appear.
The same goes for the second number cube.
The table below presents the possible outcomes of rolling two number cubes with the sum written as exponent.
![\begin{center} \begin{tabular} {| c || c | c | c | c | c | c |} & 1 & 2 & 3 & 4 & 5 & 6 \\ [1ex] 1 & \{1,1\}^2 & \{1,2\}^3 & \{1,3\}^4 & \{1,4\}^5 & \{1,5\}^6 & \{1,6\}^7 \\ 2 & \{2,1\}^3 & \{2,2\}^4 & \{2,3\}^5 & \{2,4\}^6 & \{2,5\}^7 & \{2,6\}^8 \\ 3& \{3,1\}^4 & \{3,2\}^5 & \{3,3\}^6 & \{3,4\}^7 & \{3,5\}^8 & \{3,6\}^9 \\ 4 & \{4,1\}^5 & \{4,2\}^6 & \{4,3\}^7 & \{4,4\}^8 & \{4,5\}^9 & \{4,6\}^{10} \\ \end{tabular} \end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%0A%5Cbegin%7Btabular%7D%20%7B%7C%20c%20%7C%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%0A%26%201%20%26%202%20%26%203%20%26%204%20%26%205%20%26%206%20%5C%5C%20%5B1ex%5D%0A1%20%26%20%5C%7B1%2C1%5C%7D%5E2%20%26%20%5C%7B1%2C2%5C%7D%5E3%20%26%20%5C%7B1%2C3%5C%7D%5E4%20%26%20%5C%7B1%2C4%5C%7D%5E5%20%26%20%5C%7B1%2C5%5C%7D%5E6%20%26%20%5C%7B1%2C6%5C%7D%5E7%20%5C%5C%20%0A2%20%26%20%5C%7B2%2C1%5C%7D%5E3%20%26%20%5C%7B2%2C2%5C%7D%5E4%20%26%20%5C%7B2%2C3%5C%7D%5E5%20%26%20%5C%7B2%2C4%5C%7D%5E6%20%26%20%5C%7B2%2C5%5C%7D%5E7%20%26%20%5C%7B2%2C6%5C%7D%5E8%20%5C%5C%20%0A3%26%20%5C%7B3%2C1%5C%7D%5E4%20%26%20%5C%7B3%2C2%5C%7D%5E5%20%26%20%5C%7B3%2C3%5C%7D%5E6%20%26%20%5C%7B3%2C4%5C%7D%5E7%20%26%20%5C%7B3%2C5%5C%7D%5E8%20%26%20%5C%7B3%2C6%5C%7D%5E9%20%5C%5C%20%0A4%20%26%20%5C%7B4%2C1%5C%7D%5E5%20%26%20%5C%7B4%2C2%5C%7D%5E6%20%26%20%5C%7B4%2C3%5C%7D%5E7%20%26%20%5C%7B4%2C4%5C%7D%5E8%20%26%20%5C%7B4%2C5%5C%7D%5E9%20%26%20%5C%7B4%2C6%5C%7D%5E%7B10%7D%20%5C%5C%20%0A%5Cend%7Btabular%7D%0A%5Cend%7Bcenter%7D)
From the table it can be seen that the sums: 2 and 12 appeared only once and hence will represent the shortest bars if the distribution is represented in a bar chart.
Therefore, the <span>two sums that are represented by the shortest bars on a bar graph of this distribution</span> are 2 and 12.
The same goes for the second number cube.
The table below presents the possible outcomes of rolling two number cubes with the sum written as exponent.
From the table it can be seen that the sums: 2 and 12 appeared only once and hence will represent the shortest bars if the distribution is represented in a bar chart.
Therefore, the <span>two sums that are represented by the shortest bars on a bar graph of this distribution</span> are 2 and 12.
First we write down this expression:
We notice that 36 is a square of 6 so we write:
Now, square root we imply on each of factors (g^6 and 6 ^2)
we get.
6*|g^3|
The reason for absolute value is because of variable g.
Answer is C.
We notice that 36 is a square of 6 so we write:
Now, square root we imply on each of factors (g^6 and 6 ^2)
we get.
6*|g^3|
The reason for absolute value is because of variable g.
Answer is C.