Complete the number sentence:

How can you solve problems by ordering rational numbers from least to greatest?

Mariana [72]

Answer:

B same form

Step-by-step explanation:

By using them for fractions or decimals. You can compare fractions by having them from least to greatest and it helps in getting the same denominator for fractions.

6 0

3 years ago

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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

Which one is right triangle angle a. 45, 55 and 35 b. 52, 48 and 20

Gemiola [76]

<h2>option b. 52, 48 and 20</h2>

Step-by-step explanation:

let's solve:-

To test whether given this triangle is right triangle or not, we can use the Pythagorean Theorem .

soo

Pythagorean Theorem=

$\bold \green{(leg1)^{2} +(leg2)^{2} =(hypotenuse)^{2} }$

Here:-

$\bold \blue{leg \: 1 = 48} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold \blue{ leg2 = 20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold\blue{hypotenuse = 52}$

Putting values:-

${48}^{2} + {20}^{2} = {52}^{2} \: \: \: \: \: \: \\ \\ 2304 + 400 = 2704 \\ \\ 2704 = 2704 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

4 0

3 years ago

What is the area of this figure?

Hunter-Best [27]

Answer:

just a guess I would say 70cm squared.

4 0

3 years ago

Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow

AlekseyPX

For this case we are going to assume the following:
m: whole number greater than zero.
n: integer greater than zero.
Where,
n> m
According to these assumptions, the percentage of growth is given by the following formula:
$(n / m) * 100 - 100$
Answer:
the number of students did grow by:
$(n / m) * 100 - 100$

4 0

4 years ago

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