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miss Akunina [59]
3 years ago
11

Consider the ellipse 25xsquared plus 4y squared equals 1 in the​ xy-plane. a. If this ellipse is revolved about the​ x-axis, wha

t is the equation of the resulting​ ellipsoid? b. If this ellipse is revolved about the​ y-axis, what is the equation of the resulting​ ellipsoid?
Mathematics
1 answer:
BaLLatris [955]3 years ago
5 0

Answer:

  • about x: 25x² +4y² + 4z² = 1
  • about y: 25x² +4y² +25z² = 1

Step-by-step explanation:

When the figure is revolved around the x-axis, its extent in the z-direction will match its extent in the y-direction. So, the z-term will have the same coefficient as the y-term. 25x² +4y² +4z² = 1

Similarly, when the figure is revolved around the y-axis, its extent in the z-direction will match its extent in the x-direction. Then the z-term will have the same coefficient as the x-term. 25x² +4y² +25z² = 1

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Given that 5W = 2P + 3R find the value of P when W = 4 and R = −4
Olenka [21]

Answer:

P = 16

Step-by-step explanation:

Given

5W = 2P + 3R ← substitute W = 4 and R = - 4 into the equation

5(4) = 2P + 3(- 4), that is

20 = 2P - 12 ( add 12 to both sides )

32 = 2P ( divide both sides by 2 )

16 = P

5 0
3 years ago
What is the value of y in the sequence below?<br> 2,y,18, -54,162,
snow_lady [41]

First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

<u>A</u><u>r</u><u>i</u><u>t</u><u>h</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>

\displaystyle \large{a_{n + 1} - a_n = d}

d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.

<u>G</u><u>e</u><u>o</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>

\displaystyle \large{ \frac{a_{n + 1}}{a_n}  = r}

r stands for a common ratio.

To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

We have:

  • 2,y,18,-54,162,...

Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

\displaystyle \large{ \frac{ - 54}{18}  = - 3 } \\  \displaystyle \large{ \frac{ 162}{ - 54}  = - 3}

Hence, the sequence is geometric.

Because the common ratio is -3. Let these be the following:

\displaystyle \large{ a_{n + 1} = y } \\  \displaystyle \large{ a_n = 2 } \\  \displaystyle \large{ r =  - 3 }

From the:

\displaystyle \large{ \frac{a_{n + 1}}{a_n}  = r}

Substitute the values in.

\displaystyle \large{ \frac{y}{2}  =  - 3}

Multiply the whole equation by 2 to isolate y.

\displaystyle \large{ \frac{y}{2} \times 2  =  - 3 \times 2} \\  \displaystyle \large{ y =  - 6}

Therefore, the value of y is -6.

7 0
2 years ago
How do you solve thsi
VLD [36.1K]
You multiply the length of the model car by the meters from the actual car. It’s easier to convert one unit of measurement to match with the other. I found it easier to convert 18.2 cm to meters which is 0.182 m. Now we multiply 0.182m by 0.3m to get the length of the actual car.

The answer would be 0.0546m. Or if you prefer centimeters, then the answer would be 5.46 cm. Either way is fine.

Hope this helped, please let me know if I was correct. :D
5 0
3 years ago
The angle bisector of
klemol [59]
A is correct. Hope my answer helped u :)
6 0
3 years ago
please help I'm really frustrated at this - A baseball diamond is a square with sides of 90 feet. What is the shortest distance,
ioda

The distance from third base to first base is 127.3 feet.

5 0
3 years ago
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