The weight of 100 identical samples of a substance is 0.1 pound. What is the weight of 10 samples?

Triangle TRI has a base of m centimeters and a height of n centimeters. Rectangle RECT has a length of n centimeters and a width

hram777 [196]

The area of the triangle is
a=( m x n) /2 in cm² , implies 2xa = m xn
the area of the rectanglle
A= n x m in cm²
but we know <span> 2xa = m xn = A, </span>
that means the surface of the rectangle is 2 times of the area of the triangle

7 0

4 years ago

Read 2 more answers

The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful ene

madreJ [45]

Answer:

d. H0: $(\mu_e - \mu_g) = 0$ vs. $Ha: (\mu_e - \mu_g) \neq 0$

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the Management try to determine if there is a difference in the average investment/quad between using electricity and using gas. So this needs to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.

Null hypothesis : $\mu_e = \mu_g$

Alternative hypothesis: $\mu_e \neq \mu_g$

Or equivalently:

Null hypothesis : $\mu_e - \mu_g = 0$

Alternative hypothesis: $\mu_e - \mu_g \neq 0$

Other important thing is that on the alternative hypothesis we never can have the symbol equal.

So on this case the best options is:

d. H0: $(\mu_e - \mu_g) = 0$ vs. $Ha: (\mu_e - \mu_g) \neq 0$

7 0

3 years ago

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

7 0

3 years ago

Whats the height of the rectangular prism

garri49 [273]

Answer:

length l = 32.25 m

width w = 8223.75 m

height h = 12.5 m

diagonal d = 8223.82273 m

total surface area Stot = 736831.875 m2

lateral surface area Slat = 206400 m2

top surface area Stop = 265215.938 m2

bottom surface area Sbot = 265215.938 m2

volume V = 3315199.22 m3

Step-by-step explanation:

5 0

2 years ago

0.0176165803 is estimated to what

bezimeni [28]

It most common to round to the hundredths place, this is two spaces after the decimal.

So look two spaces right - 0.17. If the third digit (in this case 6) is higher than 5 you round the number up if its not, keep it the same.

"6" is greater than five, so round it to about (or approximately) 0.18.

5 0

3 years ago