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2 years ago

15

How many variables are displayed in a scatterplot?

1 answer:

vampirchik [111]2 years ago

5 0

One along the X-axis and one along the y- axis

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Write the following coordinates where they belong in the line segments below. (5 1/2, -4 1/4) _______ (3 3/4, -1 1/4)

Ket [755]

ANSWER

$(4 \frac{5}{8} , - 2\frac{3}{4} )$

EXPLANATION

The end points of the segment are:

$(5 \frac{1}{2} ,-4 \frac{1}{4} )$

and

$(3 \frac{3}{4} ,-1 \frac{1}{4} )$

The box represents the midpoint of the two points.

Using the midpoint formula;

$( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

We substitute the end points of the line segment to obtain,

$( \frac{5 \frac{1}{2} +3 \frac{3}{4} }{2} , \frac{ - 4 \frac{1}{?} + - 1 \frac{1}{4} }{2} )$

This simplifies to:

$( \frac{37}{8} , - \frac{11}{4} )$

We convert back to mixed numbers to get,

$(4 \frac{5}{8} , - 2\frac{3}{4} )$

The correct choice is B

3 0

2 years ago

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

2 years ago

Identify the area of the trapezoid.

Vlad1618 [11]

Option B: The area of the trapezoid is 157.5 m²

Explanation:

We need to determine the area of the trapezoid.

The area of the trapezoid can be determined by the formula,

$Area=\frac{h}{2} (a+b)$

where h is the height, a and b are the base of the trapezoid.

From the figure, it is obvious that $a=14$ , $b=7$ and $h=15$

Substituting these values in the formula, we have,

$Area=\frac{15}{2} (14+7)$

Simplifying the terms, we have,

$Area=\frac{15}{2} (21)$

Multiplying the terms in the numerator, we have,

$Area=\frac{315}{2}$

Dividing, we get,

$Area= 157.5 \ m^2$

Thus, the area of the trapezoid is 157.5 m²

Hence, Option B is the correct answer.

4 0

3 years ago

The width of a DNA molecule is about 2.5 nanometers. A nanometer is 0.000000001 meter. Write the width of a DNA molecule in scie

Molodets [167]

Hey there!!

Scientific notation of 0.000000001 :

0.1 ⁻⁷

Hope it helps!

8 0

3 years ago

Read 2 more answers

What's one fifth of 45

pishuonlain [190]

1 /5 = 0 . 2
45 * . 2 = 9
Hope this helped :)

3 0

3 years ago

Read 2 more answers