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3 years ago

If x = -3 calculate the value of: x3 + x

Mathematics

2 answers:

lisabon 2012 [21]3 years ago

7 0

3x+x=y
3(-3)+(-3)=y
-9-3=y
-12=y

Therefore the value of x3+x is -12

Serggg [28]3 years ago

6 0

$x^{3} + x$

x= -3

Plug the value of x into the equation. x = -3

After putting the value of x in it now looks like:

$-3^{3} + (-3)$

Now solve:
$-3^{3}$ is the same as: (-3) x (-3) x (-3)

(-3) x (-3) x (-3) = -27

Finish the equation by adding -3 to -27 (same thing as subtracting 3 from -27)
-27 + (-3) = -30

x = -30

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Write a proportion for this situation, and then solve.

AURORKA [14]

he could eat 250 hotdogs in an hour

50÷12=4.166

4.166×60=250

Answer 250

3 0

3 years ago

In a doctor's office, the receptionist's annual salary is $159,000 less than that of the doctor. Together, the doctor and the re

Ann [662]

Answer:

The salary of Doctor = $193,000

The salary of Receptionist = $34,000

Step-by-step explanation:

Given as,

Together ,the Doctor salary and the Receptionist salary = $ 227,000 per year

And the salary of Receptionist = The Doctor salary -$159,000 per year

Let the salary of Doctor = x

So, the Receptionist salary = x - $159,000 per year

And x + Receptionist salary = $ 227,000 per year

x + x - $159,000 per year = $ 227,000 per year

Or, 2x = $ 386,000 per year

Or, x = $ $\frac{386000}{2}$

Or, x = $ 193,000

And the salary of Receptionist = $193,000 - $159,000 = $34,000

Hence, The salary of Doctor = $193,000

And, The salary of Receptionist = $34,000

8 0

4 years ago

The population of a town is 15,000. If the population is growing by 5% per year, how long will it take for the population to rea

nikdorinn [45]

by 10 years it'll be 24439 but by 11 it'll be 25661 so it's technically 11 years

6 0

3 years ago

2. CHEMISTRY How many liters of 15% acid and

Wewaii [24]

Answer:

<h3> 26²/₃ liters of 15% acid and 13¹/₃ liters of 33% acid</h3>

Step-by-step explanation:

Concentration Amount of Amount

of Solution Solution (L) of Acid

15% x 0.15x

33% y 0.33y

21% 40 0.21•40

x + y = 40 ⇒ x = 40 - y

0.15x + 0.33y = 0.21•40

0.15(40 - y) + 0.33y = 0.21•40

6 - 0.15y + 0.33y = 8.4

0.18y = 2.4

y = 13¹/₃

x = 40 - 13¹/₃ = 26²/₃

8 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