Answer:
b = 15.75
Step-by-step explanation:
Lets find the interception points of the curves
36 x² = 25
x² = 25/36 = 0.69444
|x| = √(25/36) = 5/6
thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).
The area of the bounded region is given by the integral
The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.
125/18 = b^{1.5}/9
b = (62.5²)^{1/3} = 15.75
If a polygon has 5 sides, then it is a regular pentagon
False: regular pentagon = equiangular. There are pentagons that have 5 sides that are not equiangular
Answer:
Step-by-step explanation:
Let's first arrange it in ascending order :
340, 480, <u>560</u>, 680, 700
<u>560</u> is clearly the median.
Now add an additional score of 700 to the data :
340, 480, <u>560, 680</u>, 700 ,700
<u>560, 680</u> is separating both halves but is not the median
Median = (560+680)/2
= 1240 / 2
Median = 620
Since we are only dealing with integers, we do not need to worry about decimals. Therefore, finding the exact values of sqrt(19) and sqrt(77) is not important. We can just estimate.
19 is between 16 and 25 (which are 4^2 and 5^2), so the square root of 18 is some number between 4 and 5.
77 is between 64 and 81 (which are 8^2 and 9^2), so the square root of 77 is some number between 8 and 9.
So the integers (whole numbers) that are between our two sqaure roots are 5, 6, 7, and 8.
Add them up and we have our answer.
5+6+7+8 = 26
