Answer:
The coordinate of point B is (4, 8.25)
Step-by-step explanation:
Here, we want to find the coordinates of point B
To do this, we are to use the section internal division formula as follows;
(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
In this case;
(x1,y1) = (2,6)
(x2,y2) = (5,9)
(m,n) = (3,1)
Substituting these values into the section formula, we have;
(x,y) = (1(1) + 3(5))/(1 + 3) , (1(6) + 3(9))/3 + 1)
(x,y) = (16/4, 33/4)
(x,y) = (4,8.25)
Answer: No answer
Step-by-step explanation:
You can calculate for x, because the equation isn't equal to anything.
60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2
abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.
d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.
Answer:
<em>y=0.10(t)+0.25 </em>
<em>27 minutes and 30 seconds </em>
Step-by-step explanation:
We know that you start with 25 cents as a service fee, this is for making the call. For each minute you talk, 10 cents are added. Multiply the number of minutes spent by 10 cents a minute for the cost based on the call. Then add the 25 cents service fee.
If you talked for 5 minutes:
y=0.10(5)+0.25
y=0.50+0.25
y=0.75
75 Cents
For three dollars, you would plug in 3 for y
3.00=0.10(t)+0.25
-0.25 -0.25
2.75=0.10(t)
divide both sides by 0.10 to get
27.5=t
You can talk for 27 minutes and 30 seconds
27 minutes
<u>Hope this helps :-)</u>
