Question

I need help on a project, I understand some of it but I need some help please :)

Answer 1

1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.
2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.
4.A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.
5.Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.

Answer 2

I know one and two but I am not sure on the rest

Answer 3

Hi there!
Welcome To OpenStudy :-)
I am unsure of these questions as I have not learned them yet however a better way to get help might be to post the questions one by one that way users don't feel intimitated by all the words :P I'll tag users who might know this stuff :)

@mathmate @zepdrix

Answer 4

@jim_thompson5910

Answer 5

@skullpatrol :P

Answer 6

thank you so much! I just wanted them to have all the info on that problems :D

Answer 7

It's alright :) trying to see if people will help :P hopefully someone will come by

Answer 8

I hope so ! I have been stuck on this for a while :(

Answer 9

`1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.`

Let's say we have a triangle ABC
A = first angle
B = second angle
C = third angle
opposite of angle A is side 'a'
opposite of angle B is side 'b'
opposite of angle C is side 'c'

If we know two sides (say a and b) and the angle between them (angle C), then we must use the law of cosines to find side c. The law of cosines applies to SAS triangles

If we know 2 angles, then we can easily find that missing angle. We would also need to know at least 1 side. With this collective info, we can use the law of sines. The law of sines is handy for AAS or ASA triangles. However, be careful that you may get trouble dealing with SSA triangles

Answer 10

with the SSA case, 3 possibilities could occur

* one triangle is possible

* two triangles are possible

* no triangles are possible

Answer 11

oh thank you so much but I got number one already haha but thanky uo

Answer 12

I need help with 3-5

Answer 13

just for future reference, you should post each question as a separate thread. One problem per post. This is to avoid clutter and lag and such

Answer 14

`3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.`

if the two foci are (3,0) and (-3,0) then what is the center? Do you know how to find the center?

Answer 15

again im so sorry I just wanted everyone to know the whole thing.

Answer 16

I understand. It's just a lot to go through. Especially since each problem is pretty lengthy on its on.

Answer 17

b^2=a^2-c^2 ?

Answer 18

hint: the center is the midpoint of the foci

Answer 19

wait no midpoint formula!

Answer 20

do you know the midpoint formula?

Answer 21

not by heart but I can look it up

Answer 22

x1 + x2, y1+y2 both over 2

Answer 23

correct

Answer 24

basically you add up the corresponding coordinates, then divide by 2

Answer 25

so the midpoint is 0

Answer 26

you should get (0,0)

Answer 27

yes I did woohoo!

Answer 28

so I just have to plot those on a graph?

Answer 29

yeah and an ellipse and hyperbola as well

Answer 30

your teacher also wants the equations of the ellipse and hyperbola

Answer 31

do you mind helping me with those I am sorry

Answer 32

where do you want the vertex point to be? pick any point on the x axis that is to the right of (3,0)

Answer 33

1,2?

Answer 34

any point on the x axis is of the form (x,0)

Answer 35

ohh im dumb I sorry how about 2,0

Answer 36

pick something to the right of (3,0)

Answer 37

oh sorry 4,0

Answer 38

the two foci are (-3,0) and (3,0)
the center is (0,0)
the vertex you picked is (4,0)

Answer 39

how far is it from the center to the vertex?

Answer 40

4,0

Answer 41

a distance is a single number

Answer 42

oh so 4?

Answer 43

yes

Answer 44

ok so the ellipse is wider than it is tall, which means that the co-vertex will be some point on the y axis that is closer than 4 units to the center

let's say the co-vertex is (0,2)

Answer 45

the two foci are (-3,0) and (3,0)
the center is (0,0)
vertices (4,0) and (-4,0)
co-vertices (0,2) and (0,-2)

Answer 46

are you able to take that info and form an equation for the ellipse?

Answer 47

yes!

Answer 48

ok great

Answer 49

x^ over a^ + y^2 over b^2 =1 correct?

Answer 50

Did you mean this?

\[\Large \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]

Answer 51

General equation of an ellipse
\[\Large \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]
(h,k) is the center
'a' determines how wide the ellipse is
'b' determine how tall the ellipse is

Answer 52

yes:)

Answer 53

In this case, the center is (0,0) so the 'h' and 'k' will effectively go away

Answer 54

making
\[\Large \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]
turn into
\[\Large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]
now you just need to figure out what 'a' and 'b' are

Answer 55

So what do I do D:

Answer 56

In this case, the distance from the center (0,0) and the vertex (4,0) is 4 units

so a = 4

Answer 57

the distance from center to focus is 3 units so c = 3

Answer 58

ohhhhhh okay

Answer 59

so now b

Answer 60

http://www.mathwords.com/f/foci_ellipse.htm

a^2 = b^2 + c^2
b^2 = a^2 - c^2
b^2 = 4^2 - 3^2
b^2 = ???

Answer 61

btw we don't need to find the value of b, we can stop at b^2

Answer 62

sorry my computers lagging so I cant open the link

Answer 63

so I just put that as the answer to the ellipse?

Answer 64

you should find that b^2 = 7

Answer 65

a = 4 ---> a^2 = 16
b^2 = 7
so
\[\Large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]
becomes
\[\Large \frac{x^2}{16} + \frac{y^2}{7} = 1\]
which is the equation of the ellipse with these properties

* center at (0,0)
* foci at (-3,0) and (3,0)
* vertices at (4,0) and (-4,0)

Answer 66

I am so sorry I am so confused

Answer 67

where are you stuck?

Answer 68

from right after I said so now b

Answer 69

did you see the attachment where I have a screenshot of the formulas needed? in this case, we use a^2 = b^2 + c^2

Answer 70

ohhh is that the ellipse formula?

Answer 71

it will help figure out the ellipse equation. It's not the actual ellipse equation

Answer 72

I'll be right back

Answer 73

ohhhh I see thank you! I just didn't know how you got that