Peter piper picked a pepper
Answer:
363.22
Step-by-step explanation:
<u>Method 1: </u>
You could find the whole figure surface area than divided by 1/2
<u>Method 2:</u> (the one I'm going to personally be doing)
Break the figure into two rectangular figures
Formula for surface area of rectangular prism:
A = 2(width x length + height x length + height x width)
Figure 1:
A = 2(width x length + height x length + height x width)
height = 3.8 yd
length = 10.1 yd
width = 4.3 yd
A = 2((4.3) x (10.1) + (3.8) x (10.1) + (3.8) x (4.3))
A = 2(98.15)
A = 196.3
Figure 2:
A = 2(width x length + height x length + height x width)
height = 8.4 yd
length = 10.1 yd
width = 2 yd
A = 2((2) x (10.1) + (8.4) x (10.1) + (8.4) x (2))
A = 2(121.84)
A = 243.68
There is overlapping surface area that shouldnt be include so we need to subtract it...
<u>For one face of figure 1</u>
3.8 x 10.1 = 38.38
Total:
Figure 1 + Figure 2 - 2(one face)
196.3 - 38.38 = 157.92
243.68 - 38.38 = 205.3
205.3 + 157.92 = 363.22
It would be zero because you can’t raise 0 to any positive power.
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)
Coming from a 6th grader but I hope this is right!
Polynomials of degree greater than 2 can have more than one max or min value. The largest possible number of minimum or maximum points is one less than the degree of the polynomial. The following examples illustrate several possibilities.
since the degree is 4
number of possible extreme values = 4 -1 = 3
