1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artist 52 [7]
3 years ago
7

Ineed help help me please

Mathematics
1 answer:
melamori03 [73]3 years ago
8 0
The symbol ₁₂P₉ represents the permutations of 9  quantities out of 12.
By definition,
_{12}P_{9} =  \frac{12!}{(12-9)!} = \frac{12!}{3!}

From the calculator,
12! = 479,001,600
3! = 6

Therefore
₁₂P₉ = 479001600/6 = 79,833,600

Answer: 79,833,600
You might be interested in
The price of paper increases by a lot. Book producers respond by supplying ____ books.
lubasha [3.4K]
If the price of paper increases by a lot, then book producers would respond by supplying less books.
5 0
2 years ago
Alma is changing the shape of her backyard from 150 feet long by 62 feet wide to a square that has the same area. What is the pe
umka2103 [35]
Hey there!
Here's your answer: the perimeter of the redone yard would be ~193 feet

Hope this helps!
6 0
2 years ago
Jordan is picking berries. The number of blueberries he
inna [77]
D. x/3 - 5
--------------
4 0
3 years ago
Please help just say A,B,C, Or D if you don’t feel like giving examples. Thank you
Mashcka [7]

D. is the correct anser

7 0
2 years ago
Read 2 more answers
Can someone give me an example on a Riemann Sum and like how to work through it ? I want to learn but I don’t understand it when
Georgia [21]

Explanation:

A Riemann Sum is the sum of areas under a curve. It approximates an integral. There are various ways the area under a curve can be approximated, and the different ways give rise to different descriptions of the sum.

A Riemann Sum is often specified in terms of the overall interval of "integration," the number of divisions of that interval to use, and the method of combining function values.

<u>Example Problem</u>

For the example attached, we are finding the area under the sine curve on the interval [1, 4] using 6 subintervals. We are using a rectangle whose height matches the function at the left side of the rectangle. We say this is a <em>left sum</em>.

When rectangles are used, other choices often seen are <em>right sum</em>, or <em>midpoint sum</em> (where the midpoint of the rectangle matches the function value at that point).

Each term of the sum is the area of the rectangle. That is the product of the rectangle's height and its width. We have chosen the width of the rectangle (the "subinterval") to be 1/6 of the width of the interval [1, 4], so each rectangle is (4-1)/6 = 1/2 unit wide.

The height of each rectangle is the function value at its left edge. In the example, we have defined the function x₁(j) to give us the x-value at the left edge of subinterval j. Then the height of the rectangle is f(x₁(j)).

We have factored the rectangle width out of the sum, so our sum is simply the heights of the left edges of the 6 subintervals. Multiplying that sum by the subinterval width gives our left sum r₁. (It is not a very good approximation of the integral.)

The second and third attachments show a <em>right sum</em> (r₂) and a <em>midpoint sum</em> (r₃). The latter is the best of these approximations.

_____

<u>Other Rules</u>

Described above and shown in the graphics are the use of <em>rectangles</em> for elements of the summation. Another choice is the use of <em>trapezoids</em>. For this, the corners of the trapezoid match the function value on both the left and right edges of the subinterval.

Suppose the n subinterval boundaries are at x0, x1, x2, ..., xn, so that the function values at those boundaries are f(x0), f(x1), f(x2), ..., f(xn). Using trapezoids, the area of the first trapezoid would be ...

  a1 = (f(x0) +f(x1))/2·∆x . . . . where ∆x is the subinterval width

  a2 = (f(x1) +f(x2))/2·∆x

We can see that in computing these two terms, we have evaluated f(x1) twice. We also see that f(x1)/2 contributes twice to the overall sum.

If we collapse the sum a1+a2+...+an, we find it is ...

  ∆x·(f(x0)/2 + f(x1) +f(x2) + ... +f(x_n-1) + f(xn)/2)

That is, each function value except the first and last contributes fully to the sum. When we compute the sum this way, we say we are using the <em>trapezoidal rule</em>.

If the function values are used to create an <em>approximating parabola</em>, a different formula emerges. That formula is called <em>Simpson's rule</em>. That rule has different weights for alternate function values and for the end values. The formulas are readily available elsewhere, and are beyond the scope of this answer.

_____

<em>Comment on mechanics</em>

As you can tell from the attachments, it is convenient to let a graphing calculator or spreadsheet compute the sum. If you need to see the interval boundaries and the function values, a spreadsheet may be preferred.

8 0
3 years ago
Other questions:
  • How do you plot a linear graph​
    11·1 answer
  • A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. the process is repeated
    14·1 answer
  • What is the decimal for -2 and 4/5ths
    13·1 answer
  • Two lines intersecting at a right angle form
    13·2 answers
  • Sadie set her watch 2 seconds behind, and it falls behind another 2 seconds every day. Write an equation that shows the relation
    8·1 answer
  • 65000÷9330
    15·1 answer
  • Solve the system by the addition method.
    14·1 answer
  • HELP PLEASE WILL MARK RIGHT ANSWER BRAINLIEST
    12·1 answer
  • Which of the following triangles has a circle inscribed?
    5·2 answers
  • PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!