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3 years ago

If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

1 answer:

3 0

True.

Let p1 and p2 be the two parallel planes. Let n1 be the normal vector of plane p1 (which is a vector perpendicular to the plane). If p2 is parallel to p1, then n1 is also a normal vector for p2.

Let p3 be the third secant plane, and n3 be its normal vector.

The direction vector of the intersection line of two planes is given by the cross products of their normal vectors (this is due to the fact that the cross product of two vectors is orthogonal two both of them, and that the direction vector of the intersection must be orthogonal two both normal vectors). So, the direction vectors of the two lines are:

v1 = n1 × n3
v2 = n1 × n3

The are equal. Hence, the lines are parallel.

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3 years ago

Read 2 more answers

Preeta watches an ant and beetle crawl in a hole in the ground. the beetle is 3/4 inch below ground level. the beetle climbs 1/3

Alex_Xolod [135]

Answer:

1a: $\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

1b: See below

1c: $2\frac{3}{4}$ inches between the beetle and ant

Step-by-step explanation:

1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.

So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:

$\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

1b. Solve the equation written above from 1a.

$\frac{3}{4}$ + $\frac{1}{3}x$ = $2\frac{1}{2}$

-3/4 -3/4 [subtract 3/4 to start the process of getting x by itself]

$\frac{1}{3}x$ = 1 $\frac{3}{4}$

*3/1 *3/1 [Multiply Reciprocal to get X by itself]

x= $5\frac{1}{4}$

1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them

5 1/4 - 2 1/2 = $2\frac{3}{4}$

4 0

2 years ago

Which graph represents the solution set of the system of inequalities?

vivado [14]

Solve first for the solution of the inequalities. This can be done by replacing first the inequalities sign with the equal sign.

x + y = 1
2y = x - 4

The values of x and y from the system of linear equation are 2 and -1. This means that the intersection of the lines should be at point (2, -1).

Substitute 3 to x and determine the value of y from the second inequality.
2y ≥ x - 4

Substituting,
2y ≥ 3 - 4, y ≥ -1/2

Hence, the solution to this item should be the fourth one.

6 0

3 years ago

Hi boys!!!! Can u answer my question pls!!!!

erma4kov [3.2K]

Answer:

The quality control facility operates for 10 hours each day.

Step-by-step explanation:

The given function models the number of cars that are put through a quality control test each hour at a car production factory.

The given function is

We need to find the number of hours does the quality control facility operate each day.

Rewrite the given function it factored form.

Taking out the common factors from each parenthesis.

The factored form of given function is c(t)=-(t-10)(t+2).

Equate the function equal to 0 to find the x-intercept.

Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.

4 0

4 years ago