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mart [117]
3 years ago
15

Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

Mathematics
1 answer:
Gnesinka [82]3 years ago
3 0

Answer:

Step-by-step explanation:

Suppose we a point P(x,y,z) such that its distance from either the point A(3,4,-5) or B(-2,1,4) is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}

AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}

similarly, we can find the distance BP

BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}

since both distances are exactly the same we can equate them

AP = BP

\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

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3 years ago
How do i calculate the height?
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Answer:

3

Step-by-step explanation:

YS = DI = 6

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4 0
2 years ago
PLEASE HELP!!!!!
Ad libitum [116K]
X+5=3 is the answer.
8 0
3 years ago
3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie
allsm [11]

Answer:

<em>The building is 61.5 m tall</em>

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x  = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}

\displaystyle \tan 53^\circ=\frac{150-x}{h}

\displaystyle \tan 48^\circ=\frac{x}{h}

From the last equation:

x=h.\tan 48^\circ

Substituting into the first equation:

\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}

Operating on the right side:

\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ

Rearranging:

\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}

Solving for h:

\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}

Calculating:

h = 61.5 m

The building is 61.5 m tall

5 0
3 years ago
X=4<br> what is the domain and what is the range and is it a function?
marusya05 [52]
The domain is the numbers you can use for x

so the domain is 4

the range is the possible y values we get from that domain
we get all real numbers because it goes up and down infinitey


domain is 4
range is all real numbers
7 0
3 years ago
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