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Yes, got 1/4m^2. You??

Here's the answer, but maybe not in a form you were looking for :

Let the above circle have its center at O, and let its radius = 1/2 m.

Then, AC is the diameter of the above circle = 1 m.  Now....  let D be a point on the circle such that OD is  perpendicular to AC and locate B at any point on the circle except at D.

Then let triangle ABC be inscribed in a circle such that its base is a diameter of 1.....and since angle ABC inscribes an arc of 180 degrees......it's measure is 1/2 of this arc = 90 degrees  and AC forms the hypotenuse of this right triangle = 1 m

So.....triangle ABC is a right triangle.......and it's clear that, if we move point B to D, the area of this right triangle ADC will be greater than any other right triangle ABC inscribed in the circle, because  even though their bases will be the same, the height of ADC  will always be greater than the height of any other right triangle ABC.

So the base of ADC = 1m  .....  and its height will be the radius of the circle = 1/2m....so the maximum area of such a triangle will be (1/2)bh = (1/2)(1m)(1/2 m)  = 1/4 m^2......

Have you done the one where it is asking to find the max area of a right triangle?

V=x^2y = 8 => 8/x^2

C= 1*x^2+4(4xy)

C= x^2+16xy

C(x)= x^2+16x* 8/x^2

C(x)= x^2+128/x

C'(x)= 2x-128/x = 0

2x = 128/x^2

2x^3=128

x^3=64

x=4

C''(x)= 2+256/x^3 >0, for all x>0

By the second derivative test for absolute min, cost is minimum when x=4, y= 1/2

thanks gretzu!

Stop being so nasty 

The least common denominator of 17 and 21 (the denominators above) is 357.

17 goes into 357 21 times, so you multiply 1 by 21 and get that you had 21/357.

21 goes into 357 17 times, so you multiply 7 by 17 abd get that your friend had 119/357.

Your friend had more.

think this. You have 0 cookies and you want to share it with o friends. It's impossible. And the cookie monster is sad you have no cookies. And your sad cuz you have no friends.

enough to buy the empire state building

Pretty sure its b, but don't hold me to that...

LOL. You are 100% correct on that one XD

NVM I got it

Solve the following system:

{y = x+3

y = 4 x+12

Substitute y = x+3 into the second equation:

{y = x+3

x+3 = 4 x+12

In the second equation, look to solve for x:

{y = x+3

x+3 = 4 x+12

Subtract 4 x+3 from both sides:

{y = x+3

-3 x = 9

Divide both sides by -3:

{y = x+3

x = -3

Substitute x = -3 into the first equation:

{y = 0

x = -3

Collect results in alphabetical order:

Answer: | x = -3             and                y=0

OK, you're welcome.....I don't know about being a life-saver.....I just know enough Geometry to be dangerous.....!!!!!

Thank you so much CPhill! You are a life saver! 

If BY = 24, then m<BAY  = 12   [ an inscribed angle measures 1/2 of its intercepted arc ]

And m<BAC = 90

And  m<BAC  = m<BAY  +  m< YAC

So

90 = 12 + m<YAC       subtract 12 from both sides

78 = m<YAC

"C" is correct

Let's prove Solveit's answer :

m<OBP  = m<OAP        tangents drawn to a circle meet radii at right angles

OB = OA                       radii in the same circle are congruent

PB = PA                        tangents drawn to a circle from a point are congruent

ΔBOP = ΔAOP              SAS

m<POB = m<POA          by definition of congruent triangles

m<POA = m<AOC         they are the same angle

m<POB = m<AOC  = 66       substitution

The answer is no number can be divided by 0.  Why this is,  is,  like,  You have 30 toys,  and you divide them by 0 people,  then,  that wouldn't make sense.  You can divide 0 by a number,  that is 0,  but no number can be divided by 0.

I am having trouble finding the answer for PV=29,669 n=78 and i=0.025. I cannot seem to get the PMT answer right

PMT=$868.25. This is on the assumption that your i=.025 matches the payment periods, n=78.

In financial calculations such as this one, you have to state your problem precisely. Otherwise, you will get a meaningless answer. So, here: what does n=78 represent? Is it: days, weeks, months, years....etc.

The interest rate must always MATCH the n periods. So, until you specify your problem precisely, you will NOT get the right answer.

\(\angle AOC=\angle POB=66 \)

X and y can be anything.  Plug in something for x,  and y comes out.  say x is 3.  Y=2*3+1  Y=7

Find the principal P that will generate the given future value A, where A=$10,000 at 6% compounded daily for 9 years.

PV=$5,827.74. The formula you use is this:

PV=$10,000*[1 + .06/365]^-(9*365)

(cos x)/(sec x - 1) - (cos x)/(sec x + 1) = 2 cos^3 x csc^2 x

Get a common denominator on the left, Shades....let's see what happens

[cosx(secx + 1) - cosx(sec - 1)] / [ (secx - 1) (secx + 1) ]

[cosxsecx + cosx - cosxsecx + cosx] / [tan^2x] =

[ 2cosx] / [tan^2x]  =

[2cosx[ / [ sin^2x/ cos^2x]  =

[2cosx] * [cos^2x /sin^2x] =

[2cos^3x] * [ 1 / sin^2x]  =

[2cos^3x] [csc^2x]

x-3/8=-5/8

x=-5/8 +3/8

x=-2/8=-1/4

The complete circumference is 2*pi*r where r is the length of the minute hand. 

One quarter of the circumference equals 15 cm  so:

2*pi*r/4 = 15

r = 2*15/pi   so r = 9.5 cm to 1dp

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