A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Closed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0question b) the area of the right triangle, is: \[\Large \frac{{AC \cdot BC}}{2} = \frac{{B{C^2}}}{2}\] Using the theorem of Pitagora, we have this: \[\Large r = \frac{{BC}}{{\sqrt 2 }}\] where \( r \) is the radius of the halfcircumference. So the requested area is: \[\Large \begin{gathered} A =  \frac{{B{C^2}}}{2} + \frac{{\pi {r^2}}}{2} =  \frac{{B{C^2}}}{2} + \frac{{\pi B{C^2}}}{4} = \hfill \\ \hfill \\ = \frac{{B{C^2}}}{2}\left( {\frac{\pi }{2}  1} \right) \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0oops... I have made a typo: \[\Large \frac{{AB \cdot BC}}{2} = \frac{{B{C^2}}}{2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have to write the equation of your line, in order to do that, we can apply this equation: \[\Large \frac{{y  {y_1}}}{{{y_2}  {y_1}}} = \frac{{x  {x_1}}}{{{x_2}  {x_1}}}\] what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please try, you have to substitute the coordinates of your points into my formula above: (x1,y1)=(4,6), and (x2, y2) = (8,3)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0x, and y are the variables, you have only to susbstitute x1, x2, y1, y2 with the coordinates of your points

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I got this: \[\Large y =  \frac{3}{4}x + 3\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0by substitution int my formula: \[\Large \frac{{y  6}}{{  3  6}} = \frac{{x  \left( {  4} \right)}}{{8  \left( {  4} \right)}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lemme solve plz .. 1 min..

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please wait there is a sign error

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the slope of your equation is 3/4 which is positive, whereas the slope of the requested line has to be negative

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0anyway: the requested distance, is: \[\Large \begin{gathered} d = \sqrt {{{\left( {{x_2}  {x_1}} \right)}^2} + {{\left( {{y_2}  {y_1}} \right)}^2}} = \hfill \\ \hfill \\ = \sqrt {{{\left( {8  \left( {  4} \right)} \right)}^2} + {{\left( {  3  6} \right)}^2}} = \hfill \\ \hfill \\ = \sqrt {{{12}^2} + {9^2}} = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the equation of the yaxis is \( \Large x=0 \), so the requested intersection point is given by the solution of this algebraic system: \[\Large \left\{ \begin{gathered} y =  \frac{3}{4}x + 3 \hfill \\ \hfill \\ x = 0 \hfill \\ \end{gathered} \right.\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0yes! it is the point (0,3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://prntscr.com/8cxltt how did you gte that formula *get

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0it is a standard formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0never learnt of it. Can you give me details about the same??

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0ok! the equation of the line which passes at point (x1,y1) is: \[\Large y  {y_1} = m\left( {x  {x_1}} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0where m is the slope of our line

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0next I require that line has to pass at point (x2,y2) too, so I can write this: \[{y_2}  {y_1} = m\left( {{x_2}  {x_1}} \right) \qquad \qquad (*)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we equate them , right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0not exactly, I solve equation (*) for m, so I get: \[\Large m = \frac{{{y_2}  {y_1}}}{{{x_2}  {x_1}}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0then I substitute such expression for m into the first equation: \[\Large y  {y_1} = \left( {\frac{{{y_2}  {y_1}}}{{{x_2}  {x_1}}}} \right)\left( {x  {x_1}} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have finished, since we got the standard formula

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0here is the situation of your exercise: dw:1441473727673:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0next we have to compute the subsequent distances: \[\Large \begin{gathered} d(A,C) = \sqrt {{{\left( {  4  0} \right)}^2} + {{\left( {6  3} \right)}^2}} = \sqrt {{4^2} + {3^2}} = ...? \hfill \\ \hfill \\ d(B,C) = \sqrt {{{\left( {8  0} \right)}^2} + {{\left( {  3  3} \right)}^2}} = \sqrt {{8^2} + {6^2}} = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \begin{gathered} d(A,C) = \sqrt {{{\left( {  4  0} \right)}^2} + {{\left( {6  3} \right)}^2}} = \sqrt {{4^2} + {3^2}} = ...? \hfill \\ \hfill \\ d(B,C) = \sqrt {{{\left( {8  0} \right)}^2} + {{\left( {  3  3} \right)}^2}} = \sqrt {{8^2} + {6^2}} = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the requested ratio, part (i), is given by the subsequent expression: \[\Large r = \frac{{d(A,C)}}{{d(B,C)}}\] or by the subsequent ratio: \[\Large {r_1} = \frac{{d(B,C)}}{{d(A,C)}} = \frac{1}{r}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.