Splitting up the interval of integration into
subintervals gives the partition
![\left[0,\dfrac1n\right],\left[\dfrac1n,\dfrac2n\right],\ldots,\left[\dfrac{n-1}n,1\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac1n%5Cright%5D%2C%5Cleft%5B%5Cdfrac1n%2C%5Cdfrac2n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7Bn-1%7Dn%2C1%5Cright%5D)
Each subinterval has length
. The right endpoints of each subinterval follow the sequence

with
. Then the left-endpoint Riemann sum that approximates the definite integral is

and taking the limit as
gives the area exactly. We have

Answer: 9.19 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the opposite side (x) is distance between the top of the ladder and the ground.
Replacing with the values given:
Sin 45 = x/ 13
Solving for x
sin45 (13) =x
x= 9.19 ft
Feel free to ask for more if needed or if you did not understand something.
Answer:
Mr Blake's science class
Step-by-step explanation:
The standard deviation is a measure of variation.
It tells us how far each of the data set in the distribution are far from the mean of the distribution.
The average score of students in Mr. Blake's science class was 73 with a standard deviation of 11, while the average score of students in Mrs. Arnold's class was 75 with a standard deviation of 10.
Since 11>10, Mr Blake's science class is more variable than Mrs. Arnold's class.
Answer:
A
Step-by-step explanation:
Take a look at the graph starting from the left. You’ll see that on the horizontal line, the graph starts at -4 then starts to go downward until it gets to -2 and it starts going up after that so your first interval is (-4, -2). The line increases from -2 to 2 and then it starts sliding downward again from 2 to 4 so your second decreasing interval is (2, 4).