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3 years ago

Justify the last two steps of the proof.

Mathematics

1 answer:

Georgia [21]3 years ago

3 0

Statement 3:

NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself).

Statement 4:

Shape MNO and shape PON are congruent by side-side-side since:

side PN = side MO
side MN = side PO
side NO = side ON

Answer: Fourth option

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The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

svetlana [45]

Answer:

The equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

Given

The equation of ellipsoid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation of tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ ( Given)

The equation of hyperboloid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The equation of tangent plane at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The equation of tangent plane to the hyperboloid

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The equation of tangent plane

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

3 years ago

Need help for this one!

WARRIOR [948]

I THINK IT'S ASA OR SSS ..

6 0

2 years ago

What is the slope of the line that contains these points?

Novosadov [1.4K]

Answer:

-2/5

Step-by-step explanation:

We can find the slope of a line by using

m = (y2-y1)/ (x2-x1)

= (6-4)/(41-46)

= 2/-5

= -2/5

8 0

3 years ago

Read 2 more answers

tony said that the school playground was 3,600 inches long. Explain how you could write 3,600 inches in a way that might be easi

kirill115 [55]

Well I would change it to feet to make it easier. There are 12 I inches in a foot so I would divide by 12. 3,600÷12=300 so the playground would be 300feet long. Which is easier than 3,600 inches. ANSWER:300 feet

7 0

3 years ago

Derek uses a 136 cm flat steel bar that weighs 4 kg to make rack in the garage. Determine the weight of a 170 cm steel bar

Bumek [7]

The weight of a 170 cm steel bar will be 5 Kg

Step-by-step explanation:

Derek uses a 136 cm flat steel bar that weighs 4 kg to make rack in the garage.

1 kg = 1000 gm

So the weight of 1 cm steel bar will be $\frac{4 }{136}$ kg