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3 years ago

Which transformations map the strip onto itself?

Mathematics

1 answer:

Pie3 years ago

4 0

Answer:

<h2>A horizontal translation and a 180° rotation only.</h2>

Step-by-step explanation:

Notice those shapes are positioned as a reflection.

So, one way to map them onto is self is by rotating 180° and a horizontal translation. Or it could work if we translate it horizontally, the we reflect it vertically. Those transformations would map the strip onto itself.

Therefore, the second choice is the best answer.

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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

Factor the expression below

Mazyrski [523]

Answer:

(2x² + 5x + 2) = (2x + 1)(x +2)

Step-by-step explanation:

Given expression is (2x² + 5x + 2).

We have to factorize the given expression.

(2x²+ 5x + 2) = 2x² + 4x + x + 2

= 2x(x + 2) + 1(x + 2)

= (2x + 1)(x + 2)

So the factored form of the given expression will be (2x + 1)(x + 2).

6 0

2 years ago

Korey runs every 3rd day and swims every 4th day. If he runs and swims today, how many days will it be before Korey runs and swi

hichkok12 [17]

Answer: 12 days

Step-by-step explanation:

Based on the question, we have to list the multiples of 3 and 4. This will be:

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.

The lowest common multiple is 12.

It will take 12 days before Korey runs and swims again on the same day.

5 0

3 years ago

Which phrase describes an unknown or changeable quantity?

Artist 52 [7]

B i think that because there’s no quantity

7 0

2 years ago

Car A travels 185 miles in 8 hours. Car B travels

svetoff [14.1K]

Car B because 334 divided by 5= 41 mph

8 0

3 years ago