Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.

Answers

Answer 1

Answer: Hello,

Reminders:
$\sum_(i=1)^(n) i= (n(n+1))/(2)$
$\sum_(i=1)^(n) i^2= (n(n+1))/(2)$
$\sum_(i=1)^(n) i^3= (n^2(n+1)^2)/(4)$

$n=6\n x_(0)=0\n x_(n)=3\n \Delta= (x_n-x_0)/(n)=0.5\n$
$x_(i) =0+\Delta*i= (i)/(2)$

$\sum_(i=1)^(n)\ \Delta*f(x_(i))=\sum_(i=1)^(6)\ (i^3/8-6i)/(2)$
$$= (1)/(2)\sum_(i=1)^(6) ((i^3)/(8) -6i)=(1)/(16)*((6*7)^2)/(4)- (9*7)/(2)= -3.9575$

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Hich expression is rational? a. 4.121221222… b.square root of 36 c. square root of 21 d.1.192744502…

Answers

Answer: The correct option is (B) square root of 36.

Step-by-step explanation: We are given to select the correct number that is irrational.

RATIONAL NUMBER: The digits after the decimal are either terminating or repeating.

IRRATIONAL NUMBER: The digits after the decimal are non-repeating and non-terminating.

Option (A) is 4.121221222 . . .

Here, the digits after the decimal are non-repeating and non-terminating. So, the given number is irrational.

Option (B) is square root of 36, which is equal to 6.

6 = 6.00.

Here, the digits after the decimal are terminating. So, the given number is rational.

Option (C) is square root of 21.

We know √21 = 4.5825756 . . .

Here, the digits after the decimal are non-repeating and non-terminating. So, the given number is irrational.

Option (D) is 1.192744502 . . .

Here, the digits after the decimal are non-repeating and non-terminating. So, the given number is irrational.

Thus, the rational number is square root of 36.

Option (b) is correct.

A rational number is any number that can be expressed as the quotient of fraction of two integers.So the answer is b.square root of 36 = √36=6 because 6 is the quotient of 6/1

If two 6-sided number cubes are rolled, what is the probability that a 2 is rolled on the first cube and a 5 is rolled on the second cube?

Answers

There are 6 sides on the number cubes, numbered 1-6.

The odds of rolling a 2 are 1 in 6, or 1/6

P(2)=1/6

The odds of rolling a 5 are 1 in 6, or 1/6

P(5)=1/6

P(2)*P(5)=1/6*1/6=1/36

The odds of rolling a 2 and a 5 are 1/36

Answer=1/36

the answer is going to be 1/36

Change 161/4 to a mixed number

Answers

okay right off the bat, 161/4, so 16/4 is 4, plus the 1 is 40(forget the one).
So 40 1/4

the answer would be 40 and 1/4

For what values of k does the equation x^2 - (5k+1)x + 9k^2 = 0 have real roots?

Answers

K has a range from[ -1/11 to 1]

real roots occur when the determinant b^2-4ac >= 0

so substituting:-

(5k + 1)^2 - 4*1* (9k^2) >= 0
25k^2 + 10k + 1 - 36k^2 >= 0
-11k^2 +10k + 1 >= 0
11k^2 - 10k - 1 <= 0
(11k + 1)(k - 1) <= 0

the equation will have real roots for -1/11 =< k <= 1

How to round 0.125 to the nearest whole

Answers

In the number 0.125, there is:
0 in the ones place,
1 in the tenths place,
2 in the hundredths place, and
5 in the thousandths place.

We want to round to the hundredths place, which is 2.
To do this we must look to the next digit.
If it's less than 5, we round down.
If it's more than 5, we round up.

The next digit is 5, though! So what do we do then?
Well, we would look to the next digit again and decide from that.
There isn't really a next digit to decide from, though, is there?

In that case, we just round up.

and we get 0.13

The area of a rectangle is represented by 5x^2+19x+12. What is the length?

Answers

$5x^2+19x+12=5x^2+15x+4x+12=5x(x+3)+4(x+3)\n\n=(x+3)(5x+4)\n\nAnswer:x+3\ *\ 5x+4$

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