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3 years ago

20. A chef prepared five chocolate tortes for a dinner party. The guests consumed 2 5⁄16 tortes. How many tortes are left?

Mathematics

1 answer:

borishaifa [10]3 years ago

6 0

4 16/16 This is the same as 5.
-2 5/16
------------------
2 11/16

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Veronika [31]

The expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Given an integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ .

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

$\int\limits^b_a {f(x)} \, dx$ = $\lim_{n \to \infty}$ ∑f(a+iΔx)Δx ,here Δx=(b-a)/n

$\int\limits^5_1 {x/(2+x^{3}) } \, dx$ =f(x)= $x/2+x^{3}$

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)= $[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}$

$\lim_{n \to \infty}$ ∑f(a+iΔx)Δx=

$\lim_{n \to \infty}$ ∑ $n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n$

=4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$

Hence the expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

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5 0

2 years ago

A group of students and teachers are going on a field trip? One ninth of the group will fit on 1/3 of a school bus. How many bus

solniwko [45]

3/9 will fit on one bus so it will take 3 buses to fit 9/9 of the students, which 9/9 is the whole group.

6 0

3 years ago

Graph the data in the table below. Which kind of function best models the data? write an equation to model the data.

harina [27]

Answer:

A quadratic function.

$y=2.5x^{2}$

Step-by-step explanation:

If you plot the points given in the table, you obtain the graph shown in the figure attached.

As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.

By definition, the parent function of a quadratic function is:

$y=x^{2}$

You can compress or stretch it in the y-direction by multiplying the function by a constant $C$ :

$y=Cx^{2}$

If $0$ , then the function is compressed.

If $C>1$ , then the function is stretched.

You can find the constant of the function asked as following:

- Substitute x=1 into the parent function to obtain the y-coordinate:

$y=(1)^{2}=1$

Then the point is (1,1)

- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:

$C=2.5$

Then the function is:

$y=2.5x^{2}$

7 0

3 years ago

7 + (-2) is<br> units from 7, in the<br> direction.<br> 7+(-2) =

faltersainse [42]

I might be wrong.
7+(-2)= -9

3 0

3 years ago

Write one number that is a factor of 13

antiseptic1488 [7]

So, if we need to find 1 factor, let's just multiply 13 × 2.

13 x 2 = 26.

So, 26 is your answer.

Glad I could help, and good luck!

AnonymousGiantsFan

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4 0

3 years ago