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3 years ago

Identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 49

Mathematics

1 answer:

Paha777 [63]3 years ago

4 0

Answer:

The surface is a cylindrical surface with radius 7 units

Step-by-step explanation:

The equation is properly written as:

$\rho^{2} (sin^{2} \phi sin^{2} \theta + cos^{2} \phi) = 49$

The above equation takes the form $y^{2} + z^{2} = r^{2}$

Where $y^{2} = \rho^{2} sin^{2} \phi sin^{2} \theta$

$y = \rho sin \phi sin \theta$

and $z^{2} = \rho^{2}cos^{2} \phi$

$z = \rho cos \phi$

$r^{2} = 49$

r = 7 units

The surface is a cylindrical surface with radius 7 units

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Jamar drove 228 miles and used 6 gallons of gas.

Klio2033 [76]

Step-by-step explanation:

well, it is kind of written already :

228 miles and 6 gallons.

so, miles/gallon = 228/6 = 38 miles/gallon.

it is not mentioned, but I guess we have to assume that he got the same miles/gallon ratio on this trip as well.

so, again

38 miles/gallon

and he used 9 gallons.

so, he drove 38×9 = 342 miles

7 0

3 years ago

Find the slope of the line which is perpendicular to a line having a slope of 5/7

erica [24]

Answer:

-7/5

Step-by-step explanation:

5/7

= -7/5

3 0

3 years ago

The Slow Fix auto shop charges $28 for parts and $48 per hour of labor. The We Work Cheaper auto shop charges $59 for parts and

Sidana [21]

Answer: 10 hours

Step-by-step explanation:

Given

Slow fix auto charge $28 for parts and $48 per hour of labor

We work charge $59 for parts and $44.90 per hour of labor

Suppose both works for x hours

Cost of Slow fix= $\$(28+48x)$

Cost of We work= $\$(59+44.90x)$

When these costs are the same

$28+48x=59+44.90x\\3.1x=31\\x=10\ hours$

6 0

3 years ago

A rectangular school banner has a length of 36 inches and a width of 52 inches. A sign is made that is similar to the school ban

zalisa [80]

Answer:

4212 : 1573 is the ratio.

Step-by-step explanation:

Given:

Length of rectangular school banner is 36 inches and width is 52 inches.

And, the sign made is similar to banner.

The sign's length is 22 inches.

Now, we have to find the ratio of the area of the banner to the area of the sign.

So, we have dimensions of rectangular school banner:

Length = 36 inches.

Width = 52 inches.

But, we have only length of sign:

Length = 22 inches.

Now, we have to find the width of sign by using cross multiplication method:

Let the width of sign be $x.$

As, sign is similar to banner.

So, if 36 inches is equivalent to 52 inches.

Then, 22 inches is equivalent to $x.$

$\frac{36}{52} =\frac{22}{x}$

By cross multiplying we get:

$36x=1144$

Dividing both sides by 36 we get:

$x=31\frac{7}{9} .$

Hence, the width of sign is $31\frac{7}{9}$ inches.

Now, we find the area of banner and the area of sign by putting formula:

Area of banner = length × width.

$Area\ of\ banner=36\times 52$

$Area\ of\ banner=1872\ square\ inches.$

Now, area of sign:

$Area\ of\ sign=length\times width\\\\Area\ of\ sign=22\times 31\frac{7}{9} \\\\Area\ of\ sign=22\times \frac{286}{9} \\\\Area\ of\ sign=\frac{6292}{9} \ square\ inches.$

Now, to get the ratio of the area of the school banner to the area of the sign:

$1872:\frac{6292}{9}$

$=\frac{1872}{\frac{6292}{9} } \\\\=\frac{16848}{6292}$

On simplifying we get:

$=\frac{4212}{1573}$

$=4212:1573.$

Therefore, the ratio of the area of the school banner to the area of the sign is 4212:1573.

8 0

3 years ago

A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?

Alexxx [7]

Answer:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of larger square to smaller square is 9:1

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side of the small square is 2 units

so the are of the small square is $2^2$ = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=> $\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}$

=> $\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}$

=> $\sqrt{(3 +3)^2 +(-3 +3)^2}$

=> $\sqrt{(6)^2 +(0)^2}$

=> $\sqrt{36}$

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

$6^2$

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0

3 years ago