Answer:
P(5, 1)
Step-by-step explanation:
Segment AB is to be partitioned in a ratio of 5:3. That means the ratio of the lengths of AP to PB is 5:3. We need to find the ratio of the lengths of AP to AB.
AP/PB = 5/3
By algebra:
PB/AP = 3/5
By a rule of proportions:
(PB + AP)/AP = (3 + 5)/5
PB + AP = AP + PB = AB
AB/AP = 8/5
AP/AB = 5/8
The first part of the segment is 5/8 of the length of the segment, and the second part of the segment has length of 3/8 of the length of segment AB.
Point P is located 5/8 of the distance from point A to point B. The x-coordinate of point P is 5/8 of the difference in x-coordinates added to the x-coordinate of point A. The y-coordinate of point P is 5/8 of the difference in y-coordinates added to the y-coordinate of point A.
x-coordinate:
difference in coordinates: |14 - (-10)| = |14 + 10| = 24
5/8 of 24 = 5/8 * 24 = 15
Add 15 to the x-coordinate of point A: -10 + 15 = 5
x-coordinate of point P: 5
y-coordinate:
difference in coordinates: |4 - (-4)| = |4 + 4| = 8
5/8 of 8 = 5/8 * 8 = 5
Add 5 to the y-coordinate of point A: -4 + 5 = 1
y-coordinate of point P: 1
Answer: P(5, 1)
Answer:
3/5
Step-by-step explanation:
Soh Cah Toa
In some trigonometry classes, this acronym is very important to solving questions like this.
Why?
It tells us the right triangle-definition of these trigonometry functions.
We have that cosine of an angle is equal to tge side that is adjacent to it over the hypotenuse.
So here we are asked to find cos(B).
Lets look at triangle respect to the angle B
The measurement of the side that is opposite is 64.
The measurement of the side that is adjacent is 48.
The measurement of the hypotenuse is 80.
So cos(B)=48/80.
Let's reduce. 48 and 80 have a common factor of 8 so divide numerator and dexter by 8. This gives us:
cos(B)=6/10.
One more step in reducing. Both factors are even so cos(B)=3/5.
Just add the two equations together.
2b = 18
b = 18/2
b = 9
9 = k + 10
9 - 10 = k
k = - 1
Given:
x and y are both differentiable functions of t.


To find:
The value of
.
Solution:
We have,
...(i)
At x=-1,




Divide both sides by 3.

Taking cube root on both sides.

So, y=2 at x=-1.
Differentiate (i) with respect to t.

Putting x=-1, y=2 and
, we get



Divide both sides by -8.


Therefore, the value of
is 36.
Answer:
first one
Step-by-step explanation:
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