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Fantom [35]
3 years ago
11

Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and

the plane?
Mathematics
1 answer:
Elenna [48]3 years ago
3 0

Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

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Answer:

Scale Factor - Finding Sides. L1S1. 3) Scale factor of S to T is 4 : 1. ; x = y = 4) Scale factor of G to H is 1 : 7. ; x = y = 20 yd. 10 yd. S. T.

Step-by-step explanation:

<em> A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.</em>

<em />

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<em>Hope this helps:) Have a great day! </em>

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6 0
2 years ago
1.. A train travels at a speed of 58 km/hr. If it goes from one station to the next in 1.6 hours, how far has it traveled?
wel

Answer:

92.8 km

Step-by-step explanation:

s=d/t

58=d/1.6

58*1.6=d

92.8=d

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3 years ago
Substitute (= 3 and 1-6 to determine if the two expressions are equivalent.
mezya [45]

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Step-by-step explanation:

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3 years ago
Plzzzz help me on this questions fast <br><br>This is Trigonometry​
Sladkaya [172]

Answer:

x ≈ 20.42, y ≈ 11.71

Step-by-step explanation:

Using the cosine ratio on the right triangle on the right, that is

cos20° = \frac{adjacent}{hypotenuse} = \frac{11}{y}

Multiply both sides by y

y × cos20° = 11 ( divide both sides by cos20° )

y = \frac{11}{cos20} ≈ 11.71

Using the sine ratio on the right triangle on the left, that is

sin35° = \frac{opposite}{hypotenuse} = \frac{y}{x} = \frac{11.71}{x}

Multiply both sides by x

x × sin35° = 11.71 ( divide both sides by sin35° )

x = \frac{11.71}{sin35} ≈ 20.42

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