Answer:
(6,0)
Step-by-step explanation:
The coordinates of the points dividing the line segment in ratio m:n can be calculated as:
Here x1, y1 are the coordinates of first point S (-2, -6) and x2, y2 are the coordinates of second point T(18, 9).
In this case m will be 2 and n will be 3 as the ratio is 2:3
Using all these values we can find the coordinates of point Q
Thus, the coordinates of point Q which divides the line segment ST in ratio of 2:3 are (6,0)
Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
For, A to be greatest ,
⇒
⇒
⇒
Therefore, from equation (3), k = 5 - h²
⇒
Hence,
Width = 2h =√10 and
Height =
Answer:
The range of is
.
Step-by-step explanation:
We must remember that range of function corresponds to the set of values of
in the graph (+y direction). Given that
is a stretched version of
, the range of
corresponds to the range of
multiplied by 4. Then,
The range of is
.