You are choosing 3 of your 8 trophies and arranging them in a row on a shelf.

Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d

Stella [2.4K]

The answer is most likely A.

The integration interval [a, b] is split up into n subintervals of equal length (so each subinterval has width (b - a)/n, same as the coefficient of the sum of y terms) and approximated by the area of n rectangles with base (b - a)/n and height y.

n subintervals require n + 1 points, with

x₀ = a

x₁ = a + (b - a)/n

x₂ = a + 2(b - a)/n

and so on up to the last point x = b. The right endpoints are x₁, x₂, … etc. and the height of each rectangle are the corresponding y 's at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function G(x) continuous* over an interval [a, b] is equal to the slope of the secant line through x = a and x = b, i.e. the value of the difference quotient

(G(b) - G(a) ) / (b - a)

If G(x) happens to be the antiderivative of a function g(x), then this is the same as the average value of g(x) on the same interval,

$g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx$

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [a, b] into n subintervals of equal width (b - a)/n. Over the first subinterval, the area of a trapezoid with "bases" y₀ and y₁ and "height" (b - a)/n is

(y₀ + y₁) (b - a)/n

but y₀ is clearly missing in the sum, and also the next term in the sum would be

(y₁ + y₂) (b - a)/n

the sum of these two areas would reduce to

(b - a)/n = (y₀ + 2 y₁ + y₂)

which would mean all the terms in-between would need to be doubled as well to get

$\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)$

7 0

3 years ago

You plan to put anti-theft devices on each garment in your store. You have 1,320 garments, and it takes an employee 20 seconds t

makvit [3.9K]

Answer:

3 hours 40 minutes.

Step-by-step explanation:

We are told that we have 1320 garments and it takes an employee 20 seconds to tag a garment.

1 employee tags one garment in 20 seconds.

So garments tagged by 1 employees in 1 minute will be $\frac{60}{20} =3$ garments.

2 employees will tag 3*2=6 garments in 1 minute.

To find the total time it will take two employees to tag all the garments we will divide total number of garments by 6.

$\text{Time taken by two employees to tag 1320 garments}=\frac{1320}{6}$

$\text{Time taken by two employees to tag 1320 garments}=220$

Therefore, it will take 220 minutes or 3 hours and 40 minutes for 2 employees to tag 1320 garments.

6 0

3 years ago

Read 2 more answers

What is the closed linear form of the sequence of the negative even integers starting with -2?

Snowcat [4.5K]

Hello,

n=1,2,3,.... and not 0

Answer B a(n)=-2*n

4 0

3 years ago

Read 2 more answers

Liono4ka [1.6K]

Finding a price that is 30% lower than $2075 is the same as finding a price that is 70% of $2075.

That means all we need to do is calculate what is 70% of $2075.

Convert 70% into decimal form which is 0.70.

Next, multiply $2075 by 0.70.

$2075*0.70 = $1452.50

The price the travel agent found was $1452.50

Note: If you don't know how to multiply by decimals you can multiply $2075 by 7 than divide the result by 10 (move the decimal point one place to the left).

7 0

2 years ago

{5x+15}{8x-42} solve for angle CDE

Natalka [10]

The answer is 100 degrees

7 0

3 years ago