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3 years ago

Which type of conic section has an eccentricity greater than one? a. an ellipse c. a hyperbola b. a parabola d. a circle

2 answers:

8 0

<span>circle has eccentricity 0
ellipse between 0 and 1
parabola has 1
hyperbolae have eccentricity greater than 1

so, a hyperbola

</span>

joja [24]3 years ago

7 0

Here are the figures you get with different values of eccentricity e.
e = 0: circle
0 < e < 1: ellipse
e = 1: parabola
e > 1: hyperbola

The conic section that has an eccentricity greater than 1 is ...
c. hyperbola

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A rectangular box is to have a square base and a volume of 72 ft3. If the material for the base costs $0.62/ft2, the material fo

Igoryamba

Answer:

a. length = 0.7211 ft

b. width = 0.7211 ft

c. height = 140.3846 ft

Step-by-step explanation:

This is an optimiztion with restriction problem.

We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.

As the cost for the sides is constant, we know that length and width are equal.

Then, we can express the volume as:

$V=x\cdot y\cdot z=x^2z=73$

being x: length and z: height

We can express the height in function of the length as:

$x^2z=73\\\\z=73x^{-2}$

Then, the cost of the box can be expressed as:

$C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}$

To optimize C, we derive and equal to zero

$\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211$

The height z is then

$z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846$

6 0

3 years ago

A rectangular garden has a walkway around it. The area of the garden is 6(5.5x + 2.5). The

Lorico [155]

Answer:The area of the walkway around is 26 x + 16 as the sum of two terms

Step-by-step explanation:

A rectangular garden has a walkway around it

1. The area of the garden is 4(4.5 x + 1.5)

2. The combined area of the garden and the walkway is 5.5(8 x + 4)

We need to find the area of the the walkway

To find the area of the walkway by subtracting the area of the

rectangle from the combined area

∵ The combined area = 5.5(8 x + 4) ⇒ simplify it

∴ The combined area = 5.5(8 x) + 5.5(4)

∴ The combined area = 44 x + 22

∵ The area of the garden = 4(4.5 x + 1.5) ⇒ simplify it

∴ The area of the garden = 4(4.5 x) + 4(1.5)

∴ The area of the garden = 18 x + 6

Now subtract the area of the garden from the combined area

∵ Area of the walkway = (44 x + 22) - (18 x + 6)

∴ Area of the walkway = 44x + 22 - 18 x - 6

- Add like terms

∴ Area of the walkway = (44 x - 18 x) + (22 - 6)

∴ Area of the walkway = 26 x + 16

The area of the walkway around is 26 x + 16 as the sum of two terms

Step-by-step explanation:

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3 years ago

What is 36/5 simplified by a whole number

goldfiish [28.3K]

Answer:

36/5 = 7 1/5

Step-by-step explanation: hope this help!

7 0

4 years ago

Read 2 more answers

Find the value and round to the nearest tenth<br> tan 56= 24/x

KatRina [158]

Hi :) ,

In degrees:

24
---- = tan 56 degrees
x

24
------- = x
tan 56 degrees

x = 16. 188

In radians:

24
---- = tan 56
x

24
----- = x
tan 56

x = -39.2623

hope that helps :)

8 0

3 years ago

Read 2 more answers

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VARVARA [1.3K]

Answer:

The four small cones combined will hold more ice cream than the big one.

Step-by-step explanation:

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3 years ago