Can anybody give me hand here please?

[Adrenaline]

hello, i am a really poor math student who trying to pass but...as you probably guessed it..i have not natural math genius brain or any sorts. but i really love maths and want to continue it...but i really can't understand the current topics.......now i have an this question i have to do and i can't even do it. if anyone can please help me out here, i would be so grateful thank you.

2) 4cos2(theta)-14sin(theta)=7 for 0<=(theta)<=2pi^c

3)An engineer is asked to build a table in the shape of two circles C1 and C2 which intersect each other.

the equations of C1 and C2 are x^2+y^2+4x+6y-3=0 and x^2+y^2+4x+2y-7=0 respectively.
the leg of the table is attached to each of the points Q and R where the circles intersect. Determine the position of the legs on the tables.
ATTACHMENTS

this is the diagram of the intersecting circles with A and B being equal to points Q and Rcirlce.jpg (5.78 KiB) Not viewed yet

So what i have done is for no.2 - i tried converting 4cos2(theta) = 2cos^2 2(theta) - 14sin (theta) -7=0
then i tried converting then and go to 2sin^2 2(theta)-14sin(theta)-7=0

im i going alright?

for the other one, i honestly do not know how and where to start.....i havent even done this yet. please someone help please.

 

[stapel]

i really can't understand the current topics.......now i have an this question i have to do and i can't even do it.

If you "really [don't] understand the current topics", then you likely need private tutoring in order to help you get caught up. Because all we can do is provide hints and helps; your use of that assistance requires that you have at least some basic comprehension of the topics at hand. A simple forum posting can't fix this problem, so I hope you're exaggerating a bit...?

2) 4cos2(theta)-14sin(theta)=7 for 0<=(theta)<=2pi^c

So what i have done is for no.2 - i tried converting 4cos2(theta) = 2cos^2 2(theta) - 14sin (theta) -7=0
then i tried converting then and go to 2sin^2 2(theta)-14sin(theta)-7=0

I don't follow your steps...? How did the first term of the left-hand side of the original equation become equal to that big expression, and then become equal to zero? Are you maybe conflating a bunch of different steps?

A good start might be to show your steps separately, so your reasoning becomes clear (to yourself, as well as to others). For this particular exercise, I would suggest converting the squared cosine into a squared sine, using the Pythagorean Identity, and then solving the resulting quadratic equation in sine. You'll factor, and then solve the two trig factors for their solutions.

By the way, what is meant by "2pi^c"?

3)An engineer is asked to build a table in the shape of two circles C1 and C2 which intersect each other.

the equations of C1 and C2 are x^2+y^2+4x+6y-3=0 and x^2+y^2+4x+2y-7=0 respectively.
the leg of the table is attached to each of the points Q and R where the circles intersect. Determine the position of the legs on the tables.

this is the diagram of the intersecting circles with A and B being equal to points Q and R

What is meant by "determining the position of the legs on the tables"? There is only the one table, according to the exercise, and the legs, of which there are, bizarrely, only two, are denoted as being the two marked intersection points. Are you maybe actually supposed to find the coordinates of those intersection points?

 

[Deleted member 4993]

hello, i am a really poor math student who trying to pass but...as you probably guessed it..i have not natural math genius brain or any sorts. but i really love maths and want to continue it...but i really can't understand the current topics.......now i have an this question i have to do and i can't even do it. if anyone can please help me out here, i would be so grateful thank you.

2) 4cos2(theta)-14sin(theta)=7 for 0<=(theta)<=2pi^c

3)An engineer is asked to build a table in the shape of two circles C1 and C2 which intersect each other.

the equations of C1 and C2 are x^2+y^2+4x+6y-3=0 and x^2+y^2+4x+2y-7=0 respectively.
the leg of the table is attached to each of the points Q and R where the circles intersect. Determine the position of the legs on the tables.
ATTACHMENTS

this is the diagram of the intersecting circles with A and B being equal to points Q and Rcirlce.jpg (5.78 KiB) Not viewed yet

So what i have done is for no.2 - i tried converting 4cos2(theta) = 2cos^2 2(theta) - 14sin (theta) -7=0
then i tried converting then and go to 2sin^2 2(theta)-14sin(theta)-7=0

im i going alright?

for the other one, i honestly do not know how and where to start.....i havent even done this yet. please someone help please.

To find the location of intersection in problem 1- set

x^2+y^2+4x+6y-3 = x^2+y^2+4x+2y-7

Now solve for x and y.

However, I see you got your answers at another website