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3 years ago

What is the equation of the plane that contains the triangle shown in the diagram?

Mathematics

2 answers:

Anastaziya [24]3 years ago

6 0

The first equation

2x + 3y + 6z = 12

kolezko [41]3 years ago

3 0

Answer:

Option A is correct.

$2x + 3y +z = 6$

Step-by-step explanation:

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

$\frac{x}{l}+\frac{y}{m} +\frac{z}{n} =1$ .....[1]

where

l is the intercept of x-axes

m is the intercept of y-axes and

n is the intercept of z-axes respectively;

From the given figure;

we have;

The intercepts of coordinates axes are;

$l = 3$

$m = 2$

$n = 6$

Substitute these values in the equation [1]; we have;

$\frac{x}{3}+\frac{y}{2} +\frac{z}{6} =1$

Taking LCM of 3, 2 and 6 is 6

$2x + 3y +z = 6$

therefore, the equation of plane that contains the triangle as shown in the diagram is, $2x + 3y +z = 6$

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3 years ago

What is 12 times13 without using a calculator

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. Let X and Y be random variables of possible percent returns (0%, 10%,

bazaltina [42]

(a) The marginal distribution of X is

Pr(X = x) = ∑ Pr(X = x, Y = y)

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That is, the first equality follows from the law of total probability, with the sum taken over y from {0, 5, 10, 15}. Each probability Pr(X = x, Y = y) is given in the table to be 0.0625.

Similarly, the marginal distribution of Y is

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(b) Yes, they're independent because

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and

Pr(X = x) Pr(Y = y) = 0.25 • 0.25 = 0.0625.

E[X] = ∑ x Pr(X = x)

… = 0.25 ∑ x

… = 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for Y,

E[Y] = 7.5

The variance of X is

V[X] = E[X^2] - E[X]^2

… = (∑ x^2 Pr(X = x)) - 7.5^2

… = 0.25 (∑ x^2) - 56.25

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3 years ago

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3 years ago

Two scuba divers are 30m apart below the surface of the water. They both spot a shark that is below them. The angle of depressio

Ostrovityanka [42]

Answer:

distance of diver 1 from the shark ≈ 18.88 m

Step-by-step explanation:

The illustration forms a triangle. The base of the triangle which is their distance apart is given as 30 m . The known angle of the triangle are 52° and 39°. To find the unknown side we subtract the sum of 52° and 39° from 180°. Note that the total angle in a triangle is 180°.

Therefore,

180 - (52 + 39) = 180 - 91 = 89 °. Now the three angle of the triangles are 52°, 39° and 89°.

Using the law of sine we can find the distance of the diver 1 from the shark.

let a = distance of the first diver to the shark.

a/sin 39° = 30/sin 89°

cross multiply

a sin 89° = 30 sin 39°

divide both sides by sin 89°

a = 30 sin 39°/sin 89°

a = 30 × 0.62932039105 /sin 89°

a = 18.8796117315 /0.99984769515

a = 18.8824876258

a ≈ 18.88 m

3 0

3 years ago