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Mathematics

1 answer:

sasho [114]3 years ago

5 0

Answer: B

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Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gall

dalvyx [7]

Answer: a) $\frac{x^{2} }{2352.25 }$ + $\frac{y^{2} }{529}$ = 1

b) The distance of two foci is 85.4 feet

c) Area = 3502.67 square feet

Step-by-step explanation: a) An ellipse has the equation in the form of:

$\frac{x^{2} }{a^{2} }$ + $\frac{y^{2} }{b^{2} }$ = 1, where a is the horizontal axis and b is the vertical axis.

For the Statuary Hall, a = $\frac{97}{2}$ = 48.5 and b = $\frac{46}{2}$ = 23, so the equation will be

$\frac{x^{2} }{2352.25 }$ + $\frac{y^{2} }{529}$ = 1.

b) To determine the distance of the foci, we have to calculate 2c, where c is the distance between one focus and the center of the ellipse. To find c, as a, b and c create a triangle with a as hypotenuse:

$a^{2}$ = $b^{2} + c^{2}$

$c^{2} = a^{2} - b^{2}$

c = $\sqrt{48.5^{2} - 23^{2} }$

c = 42.7

The distance is 2c, so 2·42.7 = 85.4 feet.

The two foci are 85.4 feet apart.

c)The area of an ellipse is given by:

A = a.b.π

A = 48.5 · 23 · 3.14

A = 3502.67 ft²

The area of the floor room is 3502.67ft².

3 0

3 years ago

1. Determine whether the graphs of the given equation are Parallel, perpendicular, or neither.

Juliette [100K]

1. A. parallel, because when you get y by itself it is y=-2x+7, the two equations have the same slope which means they are parallel.

2. B. sometimes, in order for two lines to be parallel they have to have the same slope so, it is possible that two lines say with a slope of 3, those would be parallel BUT it doesn't always have to have a positive slope for it to be parallel like in question 1.

3. C. never, If they have the same slope they are parallel despite whatever the y-intercept is.

5 0

3 years ago

Read 2 more answers

How to do this and I need help pls

tatuchka [14]

Answer:

$9$