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3 years ago

Which expression represents the greatest value?

Mathematics

1 answer:

Luden [163]3 years ago

4 0

Answer:

"-2" is the same in all expressions, and it's just plus or minus. so let's ignore the "-2" and look only at the rest

+1 is the greatest then

so -2+1 is the greatest

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figure a is a scale image of figure b the scale image that maps figure a onto figure b is 1:7 1/4 enter the value of x

skad [1K]

Answer: $x=21.75$

Step-by-step explanation:

You need to convert from mixed number to decimal number.

In order to do this, you can follow the steps shown below:

1. You must divide the numerator of the fraction by the denominator of the fraction.

2. Now you must add the quotient obtained to the Whole number part.

Then, you get:

$7\frac{1}{4}=7+0.25=7.25$

Then, the scale image that maps "Figure A" onto "Figure B" is:

$1:7.25$

Finally, in order to find the value of "x", you need to multiply the given length of the corresponding side of "Figure A" by $7.25$ .

Therefore, the result is:

$x=(3)(7.25)\\\\x=21.75$

3 0

3 years ago

A car can be rented for $75 per week plus $0.35 per mile. How many miles can be driven if you have at most $110 to spend for wee

sergey [27]

After you subtract the fixed cost of $75 from your budget of $110, you have $35 to spend on miles. At $0.35 per mile, you can afford 100 of them.

You can drive up to 100 miles for $110 or less.

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

John wants to buy a new bike that cost 337 and he already has saved 103. Estimate to find about how much more John needs to save

Ede4ka [16]

We can round numbers to estimate.

337 is approximately 340.
103 is approximately 100.

340 - 100 = 240

John needs to save around $240 more in order to be able to afford the bike.

Hope this helps!

8 0

3 years ago

What is the value of x? Leave your answer in simplest radical form.

OleMash [197]

Step-by-step explanation:

By using Pythagoras theoram,

x²= (6)²+(4)²

${x}^{2} = 36 + 16$