Is it possible for two planes to intersect in exactly one point

Mathematics

1 answer:

Strike441 [17]4 years ago

8 0

Two planes intersect at a line. Not a point.

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On the coordinate line, point A from point B (4) is 3 units away from point C point -6. Question: What can be the distance betwe

NISA [10]

Answer:

is 3 units away from c

Step-by-step explanation:

4 0

3 years ago

RS=5y+5, ST=3y+7, and RT=12y-20 what is the value of y?

marta [7]

Since S is a point on the line RT, therefore:
RS+ST = RT
5y+5+3y+7 = 12y-20
separate the variables and solve to get thevalue of y as follows:
5+7+20 = 12y-3y-5y
32=4y
y = 8

substitute in the equation of each line to get its length as follows:
RS = 5y+5 = 5(8)+5 = 45
ST = 3y+7 = 3(8)+7 = 31
RT = 12y-20 = 12(8)-20 = 76

7 0

4 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$