162 is not a perfect square therefore you have to find the largest perfect square that can go into 162 which would be 81.
You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.
So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML
We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML
Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)
Since,
KL = 2.5 ML
Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)
Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]
In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5
Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5
So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]
Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9
Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.
So, we get the coordinates of point M which is (1,-1)
Answer:
C = π(6)
C = 6π
C = 18.84
Step-by-step explanation:
The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr or C = πd. The information given is the diameter so use C = πd by substituting d = 6.
C = π(6)
C = 6π
C = 18.84
Answer:
12 hours
Step-by-step explanation:
You have $12 in your bank and you need to get to $60 so
60-12= 48 , you need 48 dollars to reach to 60
48/4 = 12 hours. So if you get paid 4 dollars an hours, you only need to work 12 hours
Answer:
y = -3
Step-by-step explanation:
The y-axis is a vertical line, so the perpendicular line is a horizontal line. It is generally written in the form ...
y = constant
For the line to go through the point (-5, -3), the constant must match the y-coordinate of the point: -3
y = -3 . . . . your equation
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Such a line has a slope of 0, so could be written in "slope-intercept form" as ...
y = 0x -3
We generally omit terms that evaluate to zero.
