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3 years ago

Find the volume of the ellipsoid x2+y2+4z2=100x2+y2+4z2=100.

1 answer:

kondor19780726 [428]3 years ago

3 0

Given the ellipsoid $x^2+y^2+4z^2=100$

For the radius in the x-dirextion, y = z = 0, and we have

$x^2=100 \\ \\ \Rightarrow x=\pm10$

For the radius in the y-dirextion, x = z = 0, and we have

$y^2=100 \\ \\ \Rightarrow y=\pm10$

For the radius in the z-dirextion, x = y = 0, and we have

$4z^2=100 \\ \\ \Rightarrow z^2=25 \\ \\ \Rightarrow z=\pm5$

Thus, the radius of the ellipsoid is given by

$Volume=4\pi r^3=4\pi\times10\times10\times5=500\pi$

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A restaurant serves custom-made omelets, where guests select meat, cheese, and vegetables to be added to their omelet. There are

FrozenT [24]

Answer:

15 possible combinations

Step-by-step explanation:

Given

$Vegetables = 6$

$Selection = 2$

Required

Determine the possible number of combinations

The question emphasizes on "selection" which means "combination".

So; To answer this question, we apply the following combination formula:

$^nC_r = \frac{n!}{(n-r)r!}$

In this case:

$n = 6$

$r = 2$

The formula becomes:

$^6C_2 = \frac{6!}{(6-2)!2!}$

$^6C_2 = \frac{6!}{4!2!}$

$^6C_2 = \frac{6*5*4!}{4!2*1}$

$^6C_2 = \frac{6*5}{2}$

$^6C_2 = \frac{30}{2}$

$^6C_2 = 15$

<em>Hence, there are 15 possible combinations</em>

7 0

3 years ago

What is the area of the 50ft by 100ft yard?

mario62 [17]

Answer: 4410 $ft^2$

Step-by-step explanation:

To find the area of a square or rectangle, all you need to do is multiply the length times the width:

L × W = A

The lengh is 100, and the width is 50

100 × 50 = 5000

However, in this problem, we also have other shapes in the rectangle. To find the area of JUST the green, we need to subtract the areas of the two circles and small blue rectangle.

First, let's get the two circles over with. To find the area of a circle, use this formula:

A = π $r^2$ r is the radius, which in this case, is 6

A = π $6^2$

A = 113 This isn't the exact answer, the exact answer would be 113.0973...

Now let's multiply the area of one of those circles by 2, since we have 2 circles:

113 × 2 = 226

Finally, we have to find the area of the blue rectangle. This is simple, just use the formula from the very beginning:

26 × 14 = 364

The last thing to do is to subtract the areas of the two circles and blue rectangle from the area of the entire thing:

5000 - (226 + 364) = 4410 $ft^2$

4 0

3 years ago

Read 2 more answers

The number of species of coastal dune plants in australia decreases as the latitude, in °s, increases. There are 34 species at 1

Bas_tet [7]

We have been given that the number of species of coastal dune plants in Australia decreases as the latitude, in °s, increases.

Further we know that there are 34 species at 11°s and 26 species at 44°s.

We can express the given information at two ordered pairs as shown below:

$(n,l)=(11,34)\text{ and }(n,l)=(44,26)$

Let us find slope of the line through these points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{26-34}{44-11}=\frac{-8}{33}=-0.2424$

Therefore, we can write the equation of line in slope intercept form as:

$n=-0.2424l+b$

Where b is the y intercept, and we can find its value using one of the two points.

$34=-0.2424(11)+b\\34=-2.67+b\\b=34+2.67=36.67$

Therefore, the required equation of the linear function is:

$n=-0.2424l+36.67$

4 0

3 years ago

2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work

Nostrana [21]

On this picture is shown a quadrilateral inscribed in a circle and by the Inscribed Quadrilateral Theorem the angles on the opposite vertices are supplementary, or in other words are equals to 180 degrees.

On this exercise it is asked to find the measure of angle B, First of all, you need to find the value of x. To so you have to select two opposite angles on this case angles A and C.

m<A+m<C=180 Substitute the given values for angles A and C
x+2+x-2=180 Combine like terms
2x=180 Divide by 2 in both sides to isolate x
x=90

Now, that the value of x is known you can substitute it in the expression representing angle D, and then subtract that number from 180 to find the measure of angle B.

m<D=x-10 Substitute the value of x
m<D=90-10 Combine like terms
m<D=80

m<B=180-m<D Substitute the value of angle D
m<B=180-80 Combine like terms
m<B=100

The measure of angle B is 100 degrees, and the value of x is 90.

7 0

3 years ago

14. A quadratic equation is graphed above.

IrinaVladis [17]

Answer:

Step-by-step explanation:

2=-2，3=-3

2²=-2²，3²=3²

3 0

3 years ago