All categories

3 years ago

Given a point and a plane, how do you find a line that is parallel to the plane that passes through the point?

1 answer:

6 0

First we should solve the slope.
M1=M2 only if the lines are parallel...
and then we should take one point from our line and solve the equation with the standard line formula.

Y=m(x-X1) +Y1

You might be interested in

Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago

Find f(g(-4)) and g(f(-4)) using the functions below.<br><br> f(x) = 2x + 7<br> g(x) = x2 + 3x - 1

daser333 [38]

Answer:

f(g(-4)) = 13.

g(f(-4)) = -3.

Step-by-step explanation:

g(-4) = (-4)^2 + 3(-4) - 1

= 3.

so f(g(-4))

= f(3)

= 2(3) + 7

= 13.

f(-4) = 2(-4) + 7

= -1.

so g (f(-4))

= g(-1)

= (-1)^2 - 3 - 1

= -3.

8 0

4 years ago

Evaluate the expression for the given value of the variable -4b-8 + -1 b^2 + 2b^3 ; b= -2

Bad White [126]

-4b-8 + -1b^2 +2b^3
-4(-2)-8+-1(-2)^2+2(-2)^3
8-8+2^2-4^3
4-64
60

4 0

3 years ago

Read 2 more answers

What is the milone of fossils of the tribes <br><br>

Zanzabum

Try It First ! REMEBER PRACTICE MAKES PERFECT , AND MISTAKES MAKES LESSON

3 0

3 years ago

How many ways can a dozen books be placed on four distinguishable shelves if no two books are the same, and the positions of the

Jet001 [13]

Answer:

217945728000 ways

Step-by-step explanation:

Given

$Books = 12$ --- 1 dozen

$Shelf = 4$

The given condition implies that;

$Book\ 1 = 4$ ---- any of the 4 shelves

$Book\ 2 = 5$ --- any of the 4 shelves and either ways of book 1

$Book\ 3 = 6$ --- any of the 4 shelves and either ways of book 1 and 2

-----------------------

----------------

----------

So, the number of ways is:

$Ways = 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15$

$Ways = 217945728000$

5 0

3 years ago