Answer:
K (0,1)
L (-1,4)
M (-4,1)
N (-3,-2)
Step-by-step explanation:
When you rotate a figure 90 degrees counterclockwise about the origin, the points all change from (x,y) to (-y,x). Therefore the points would go from: (answers on right side)
K (1,0) ---> K (0,1)
L (4,1) ---> L (-1,4)
M (1,4) ---> M (-4,1)
N (-2,3) ---> N (-3,-2)
We're looking for the two values being subtracted here. One of these values is easy to find:
<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
The other value we find by taking a Left Riemann Sum, which means that we divide the interval [1,15] into the intervals listed above and find the area of rectangles over those regions:
</span><span>Each integral breaks down like so:
(3-1)*f(1)=4
(6-3)*f(3)=9
(10-6)*f(6)=16
(15-10)*f(10)=10.
So, the sum of all these integrals is 39, which means g(15)=39.
Then, g(15)-g(1)=39-0=39.
</span>
I hope my answer has come to your help. God bless and have a nice day ahead!
Answer:
a) 0.2
b) 0.2
c) 0.5
Step-by-step explanation:
Let 
be the event "the car stops at the signal.
In the attached figure you can see a tree describing all possible scenarios.
For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus
For the second one the blue path describes the situation
For the las situation the sum of the two green path will give us the answer
90(squared) + 90 (squared) = C (squared)
(we use 90 because the base path is 90 ft long since the diamond is a square that makes all sides 90 ft long)
8100 + 8100 = c(squared)
16200 = c(squared)
we will get the square root of 16200 to get the diagonal length
C=127.3 ft, and since it is the diagonal distance we will device it to 2, to get the distance from the pitcher ro the 2nd base.
127.3/2 = 67.7 ft.
67.7 ft is the distance from the pitcher<span> to the 2nd base.</span>
$118.00 - $9.00 - $84.25 + $95.00 is the correct order
