Answer:
y-intercept = 3
Step-by-step explanation:
value that's on the y - axis
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Answer:
Infinitely many solutions.
Step-by-step explanation:
12(x+3)=4(2x+9)+4x
12x+36=8x+36+4x
12x+36=12x+36
infinitely many solutions
Answer:
The town recreation department ordered 66 baseballs and 24 bats.
Step-by-step explanation:
Let the number of baseball be 'x'.
Also Let the number of bats be 'y'.
Given:
Total items bought = 100
Now we can say that;
Total items bought is equal to sum of number of baseball and number of bats.
Framing in equation form we get;

Also Given:
Cost of each baseball = $4.50
Cost of each bat = $20
Total purchase = $822
Now we can say that;
Total Purchase is equal to to sum of number of baseball multiplied by Cost of each baseball and number of bats multiplied by Cost of each bat.
framing in equation form we get;

Multiplying equation 1 by 4.5 we get;

Now Subtracting equation 3 from equation 2 we get;

Dividing both side by 15.5 we get;

Substituting the value of y in equation 1 we get;

Hence the town recreation department ordered 66 baseballs and 24 bats.
Answer is in the attachment.
note:
make a slight change in question 1;