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160/400 x 100% = 40% are late....so far

Congratulations on figuring out some latex!!   

Where is the problem

It would be easier for me if you had typed the question in.

I just say this for your future reference.

\(x^2+y^2=50 \qquad \text{Tangent at (1,7)} \)

\(x^2+y^2=50\\ \text{top semicircle}\\ y=(50-x^2)^{0.5}\\ \frac{dy}{dx}=0.5(50-x^2)^{-0.5}*-2x\\ \frac{dy}{dx}=-x(50-x^2)^{-0.5}\\ \text{when x=1}\\ \frac{dy}{dx}=\frac{-1}{7}\\ \)

The gradient of the line is -1/7  and it passses through  (1,7)

After checking what i have already done, you can:

1) find the equation of the line.

2) Find the x and y intercepts

2) determine the area of the triangle.

If you do not understand something then you can ask.

I RESPECTFULLY REQUEST that no one else jumps in and finishes this.  

It is Homework and the asker will learn more if they have to do some of it themself.

It's been okay so far.  Had a sausage mcmuffin from McDonalds for breakfast.  Tonight will be a different story, though.  The forecast is for snow, so I'll be outside with a shovel. 

May has 16 odd-numbered days so Dave ran (16)(15)   = 240 minutes

May has 15 even-numbered days so Dave ran (15)(44)  = 660 minutes

Dave ran a total of 900 minutes.  Divide by 60 min/hr  =  15 hours

THANK YOU!! This all helped so much

The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3

The y coordinate of the focus is > the y value of the directrix....thus this opens upward

Vertex    ( 0, (-3 +   -2) /2 )   =   ( 0,  -5/2)   =  (h, k)

"p"  =   l  -5/2 - - 2 l  =  l  - 5/2 + 2 l  =   l -5/2 + 4/2 l  =  l -1/2  l = 1/2

The form is

4p ( y - k) = ( x - h)^2

4(1/2) ( y -  - 5/2) = (x - 0)^2

2(y + 5/2) = x^2        multiply both sides by  1/2

y + 5/2  =  (1/2)x^2

y = (1/2)x^2  - 5/2

oh okay I see where I made my mistake, I have to watch out for whether it goes downward or upward

If you can check this last one since I am worried because I did not get that other one correct

The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3

.

What is the equation of the parabola?

y=−1/2x^2−52

y=1/2x^2−52

y=1/4x^2−2

y=−1/4x^2+2

i think it would be option B

24 +  7  =   31

The directrix of a parabola is the line y=7 . The focus of the parabola is (2,3)

Remember jenny....if the y coordinate of the focus is less than the directrix....the parabola turns downward

Vertex     ( 2,  (3+7)/2)  = (2, 10/2) = ( 2, 5)  = (h, k)

"p"  =  l  5 - 3 l = l 2 l = 2

We have the form

-4p(y - k) = (x - h)^2

-4(2) ( y - 5) = ( x - 2)^2

-8 ( y - 5) = ( x - 2)^2        divide both sides by -1/8

y - 5 =  (-1/8)( x - 2)^2

y = -(1/8) ( x - 2)^2 + 5

I have this one and jsut 1  more if can double check for me I understand if you cant

The directrix of a parabola is the line y=7 . The focus of the parabola is (2,3)

.

What is the equation of the parabola?

y=−1/8(x−2)^2−5

y=−1/8(x−2)^2+5

y=1/8(x−2)^2+5

y=1/8(x−2)^2−5

i think it is option c

Second one.....the dirctrix is below the focus....this turns upward

Vertex    ( -2 ,  (-6 - 8)/2 )  = (-6, -14/2)  = (-2, -7)    = (h, k)

"p" =  l -7 - - 6 l =   l -1 l   =   1

We have the form

4p(y - h ) =  (x - k)^2

4(1) ( y - - 7) =  ( x - - 2)^2

4 (y + 7) = ( x + 2)^2            multiply both sides by 1/4

y + 7 =  (1/4) ( x + 2)^2       subtract 7 from both sides

y =  (1/4)(x + 2)^2 - 7

Looks good  !!!

The one above is the steps I took as well thank you .

The one where you went over each step more in depth

OK....

From your explantation in the other question it really helped ! Thank you

this one if you can also

The directrix of a parabola is y=−8 . The focus of the parabola is  (−2,−6)

.

What is the equation of the parabola?

y=−1/8(x+2)^2+7

y=1/4(x+2)^2−7

y=1/8(x−2)^2−7

y=−1/4(x−2)^2−7

i think it is option 2

The y coordinate of the focus is below the directrix.....thus....this turns downward

Find the vertex =  ( -3 , (-5 + 2)/2 ) =  (-3, -3/2)

Find p  ..... l -3/2 -  - 5 l  = l  5 - 3/2 l  = [ 10/2 - 3/2 l  =  7/2

So.....we have the form

-4p(y - k) = (x - h)^2

-4(7/2)(y - -3/2) = (x - - 3)^2      simplify

-14 ( y + 3/2) = (x + 3)^2             mutiply both sides by -1/14

y + 3/2 = -(1/14) ( x + 3)^2        subtract 3/2 from both sides

y =  -(1/14)(x + 3)^2 - 3/2

Looks like you are correct, jenny  !!!

Its okay