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vovangra [49]
3 years ago
10

What is the equation of the plane that contains the triangle shown in the diagram *answers in question*

Mathematics
2 answers:
natulia [17]3 years ago
6 0
Consider, pls, the offered option:
1. knowing points on the graph (2;0;0), (0;5;0) and (0;0;4) it is possible to check an equation.
2. only equation 10x+4y+5z=20 is right if to substitute coordinates in it.
Answer: 10x+4y+5z=20
LiRa [457]3 years ago
5 0

Answer:

Option C is correct.

10x+4y+5z =20

Step-by-step explanation:

The intercept form of the equation of plane is given by:

\frac{x}{a}+\frac{y}{b} +\frac{z}{c} = 1    .....[1]

where

a is the intercept of x-axes

b is the intercept of y-axes and

c is the intercept of z-axes

From the given diagram:

a = 2

b = 5

c = 4

Substitute these in equation [1] we have;

\frac{x}{2}+\frac{y}{5} +\frac{z}{4} = 1

LCM of 2, 5 and 4 is 20

\frac{10x+4y+5z}{20} = 1

Multiply equation 20 both sides we get;

10x+4y+5z =20

Therefore, the equation of plane that contains the given triangle is, 10x+4y+5z =20


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6 0
3 years ago
A series of three? separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers. Each
Nadya [2.5K]

Answer:

312.5\pi \text{ km}^3\approx 981.75\text{ km}^3

Step-by-step explanation:

We have been given that a series of 3 separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers.

Each of the three tunnels is shaped like a half-cylinder with a radius of 5 meters.

Since we know that volume of a semicircular or a half cylinder is half the volume of a circular cylinder.

\text{Volume of a semicircular cylinder}=\frac{\pi r^2h}{2}, where,

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h = height of the cylinder.

Upon substituting our given values in volume formula we will get,

\text{Volume of a semicircular cylinder}=\frac{\pi (5\text{ km})^2*25\text{ km}}{2}

\text{Volume of a semicircular cylinder}=\frac{\pi*25\text{ km}^2*25\text{ km}}{2}

\text{Volume of a semicircular cylinder}=\frac{\pi*625\text{ km}^3}{2}

\text{Volume of a semicircular cylinder}=\pi*312.5\text{ km}^3

\text{Volume of a semicircular cylinder}=\pi*312.5\text{ km}^3

\text{Volume of a semicircular cylinder}=981.74770\text{ km}^3

Therefore, the volume of earth removed to build the three tunnels is 312.5\pi \text{ km}^3\approx 981.75\text{ km}^3.


4 0
3 years ago
If UPT=48°, what is the measure of RPU?
Xelga [282]

Answer:

132

Step-by-step explanation:

TPR = 180

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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3 0
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