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2 years ago

Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?

Mathematics

1 answer:

kvasek [131]2 years ago

3 0

Answer: Determine whether (–x)3 + 5(–x) + 1 is equivalent to x3 + 5x + 1.

To determine if a function is even, we need to check if f(-x)=f(x).

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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

A. Original Price: $16.20

Tom [10]

Answer:

The final price is $ 22.68 And Proportional constant is 1.4

Step-by-step explanation:

Given as :

The Original price = $ 16.20

The rate of increase = 40%

Let The final price = x

Now,

Final price after increase = initial price × ( 1 + $\frac{\textrm Rate}{100}$

Or. Final price after increase = $ 16.20 × ( 1 + $\frac{\textrm 40}{100}$

Or, Final price after increase = $ 16.20 × ( 1.4 )

∴ Final price after increase = $ 22.68

Now , Proportional constant = $\frac{22.68}{16.20}$

I.e Proportional constant = 1.4

Hence The final price is $ 22.68 And Proportional constant is 1.4 Answer

4 0

3 years ago

2+2y = -10 6х +8y = -48 help please

irina1246 [14]

Answer:

x = 0 and y = -6

5 0

3 years ago

Natasha can type 30 words a minute. How many words can be typed in 7.5 minutes?

julia-pushkina [17]

225. I think. However its not clear if total words typed are asked for Natasha or in General.

3 0

4 years ago

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What is the area of this circle in terms of pi? Radius=4cm

Dmitriy789 [7]

Answer:

A≈50.27cm²

Step-by-step explanation:

4 0

3 years ago

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