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2 years ago

Find the slope of the line passing through the points (7, -2) and (3, - 7).

Mathematics

1 answer:

professor190 [17]2 years ago

3 0

Answer:

m = $\frac{5}{4}$

Step-by-step explanation:

To find the slope, we have to use the slope formula:

m = $\frac{y_2 -y_1}{x_2 - x_1}$ .

Let $(x_1,y_1) = (7, -2)$ and $(x_2,y_2) = (3, -7)$ . Then

m = $\frac{(-7)-(-2)}{3-7} = \frac{-5}{-4} = \frac{5}{4}$

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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

How to simplify fraction to its lowest terms

tatuchka [14]

5/15 = 1/3
6/15 = 2/5
6/8 = 3/4
2/4 = 1/2

6 0

3 years ago

Read 2 more answers

What is the the value of m in the equation 1/2m-3/4n=16, when n=8

Norma-Jean [14]

Answer: m=44

explanation:
1/2m-3/4(8)=16
just fill substitute the n for 8 and then find the value of m

3 0

1 year ago

Square root of 2x squared - 7 -1=4

Snowcat [4.5K]

The answer is probably x=3. I am great at math so it should be the answer!

7 0

3 years ago

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Which expression represents these words?

Daniel [21]

Answer:

(32 ÷4) +8

Step-by-step explanation:

More than means it comes after

quotient of 32 and 4

32÷ 4

8 more than

(32 ÷4) +8

7 0

3 years ago