Answer:
A. FALSE
B. TRUE
C. FALSE
D. NOT POSSIBLE TO DETERMINE
Step-by-step explanation:
(A) FALSE. since the power series ∑ has radius of convergence |-4|=4 ans 7> 4 which is beyond its radius of convergence. thus by the theorem of power series, the series diverges at 10.
(B)TRUE. since the radius of convergence of the power series ∑ must be at least |-4| = 4 and 3 lies within this radius, thus it converges at x=3
(C)FALSE the series does not diverge at x=1, since 1 is within its radius of convergence |-4| = 4
(D)NOT POSSIBLE TO DETERMINE
At x=6, it is beyond its radius of convergence but has not attain its divergence point. thus it is not possible to determine.
Answer:
b
Step-by-step explanation:
First of all, lets ask ourselves how we are going to get Mary's marbles. In the problem, we can see that Joan has 15 times as many marbles as mary. So this means that Mary's marbles are multiplied to 15 in order to get Joan's marbles (which happens to be 45). So if we reverse the situation, then in order to get Mary's marbles, you are going to have to divide Joan's marbles by 15. Since we know that Joan has 45 marbles, we divide that by 15. The answer is 3. Mary has a total of 3 marbles.
Answer:
2,294.66 square inches
Step-by-step explanation:
The area of an octagon is given by the formula:
A = 2 * a² * ( 1 + √2 )
So, if we input the numbers we have:
A = 2 * 21.8² * ( 1 + √2 )
A = 2 * 475.24 * (2.4142)
A = 2,294.66 square inches
As you can see, if you double the side of an octagon, its area will quadruples, which is logic since the one variable in the calculation of the area is the side's length... that is squared. So, if you double it, that double factor is squared.
It's as if we had written
A = 2 * (10.9 * 2)² * ( 1 + √2 )
A = 2 * (10.9² * 2²) * ( 1 + √2 )
To simplify this expression we first need to apply the distributive property of the product. This means that we need to multiply the number outside of the parenthesis by each term of the sum inside the parenthesis. This is done below:
The simplified expression is "-20+12w".