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3 days ago

What is the volume of the cylinder below?

15.9

Detailed explanation:

$\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9$

5 0

2 months ago

Before the last school year began, it was estimated that the average discretionary personal expenses each school year for a stud

tester [12383]

Answer:

M=2,179.29

The average exceeds the estimate

Her expenses would need to be $1,625.00

Step-by-step explanation:

1.) What is the mean of her friends' personal expenses?

The mean is defined as the average expense value, calculated as follows:

$M=\frac{2,800+1,990+2,005+2,400+1,860+2,200+2,000}{7}\\M=2,179.29$

2.) Is the average higher or lower than the estimate?

Given the estimate of $2,110, the average is indeed higher than this estimate.

3.)What amount of personal expenses would Ashley need to maintain a combined average of $2,110 with her friends' amounts for that school year?

$M= 2,110=\frac{7*2,179.29+x}{8} \\x=2,110*8 - 15,255\\x=1,625$

Her needed amount of expenses would be $1,625.00.

4 0

2 months 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

PIT_PIT [12445]

Answer:

The tangent plane equation for the hyperboloid

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

Step-by-step explanation:

We have

The ellipsoid's equation is

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

The equation for the 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 hyperboloid's equation is

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

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 tangent plane equation 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 tangent plane equation for the hyperboloid is

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

The tangent plane equation

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

Hence, the required tangent plane equation for the hyperboloid is

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

7 0

3 months ago

Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d =

AnnZ [12381]

Answer:

The distance from the point (0,1,1) to the specified line is zero.

Step-by-step explanation:

Considering the parametric equations of the line,

x=2t, y=5-2t, z=1+t

In order to calculate the distance from (0,1,1), we must remove t from the equations above, such that

$y=5-2t=5-x\implies x+y=5=4+1=4+z-t=4+z-\frac{1}{2}x$

$\implies 3x+2y-2z-8=0\hfill (1)$

whose direction ratios are (l,m,n)=(3,2,-2) and the distance from point (a,b,c)=(0,1,1) is defined as

$\frac{al+bm+cn}{\sqrt{l62+m^2+n^2}}=\frac{(3\times 0)+(2\times 1)+(-2)(1)}{\sqrt{3^2+2^2+(-2)^2}}=\frac{0+2-2}{\sqrt{17}}=0$

The distance between the point (0,1,1) and (1) amounts to zero. Therefore, the point (0,1,1) is located on the line (1).

8 0

2 months ago

He dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-week period

babunello [11817]

In the seventh-grade data, the left side appears similar to the right side, unlike in the fifth-grade data. In seventh grade, we can divide the dots into two equal segments, one ranging from 0 to 3 and the other from 4 to 7. The distribution in the first segment is {2, 2, 3, 5}, while the second segment has {5, 3, 3, 1}. These sides mirror each other. When attempting a comparable division in the fifth-grade data, we find one segment from 1 to 4 with a distribution of {2, 3, 1, 4}, and another from 5 to 8 with a distribution of {5, 5, 2, 2}. In this case, the left side does not reflect the right side, indicating a lack of symmetry.

7 0

1 month ago