Find the area and the circumference of a circle with the radius of 5 cm use the value 3.14 and do not round your answer

How do I determine which is y=-1/3x+2?

Jlenok [28]

Step-by-step explanation:

This is a linear equation in slope intercept form which is

$y = mx + b$

where m is the slope and b is the y intercept.

The equation

$y = - \frac{1}{3} x + 2$

Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.

In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.

6 0

3 years ago

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

Select the two values of x that are roots of this equation. 2x2 + 7x + 6 = 0

Anna007 [38]

Answer:

x = -3/2, -2

Step-by-step explanation:

2x^2 + 7x + 6 = 0

(2x + 3)(x + 2) = 0

(2x + 3)

2x = -3

x = -3/2

(x + 2)

x = -2

7 0

2 years ago

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In 1963, the United States Postal Service started using ZIP (Zone Improvement Plan) codes. Each ZIP code is a sequence of five d

bija089 [108]

Here is how you find the number of possible U.S Zip codes.
Take note of this: There are 10 1 digit numbers: 0,1,2,3,4,5,6,7,8,9.
And we have 5 slots. So in each slot, there can be 10 possible numbers.
So let's put 10 in each blank slot.
10, 10, 10, 10, 10.
Therefore, the final answer would be 100,000. There are 100,000 possibilities of different U.S zip codes. Hope this answer helps.

5 0

3 years ago

You have 108 seats, there are 12 times as many seats as rows, how many rows

nignag [31]

Im pretty sure you just multiply 12 by 108, in that case there would be 2160 rows

6 0

3 years ago

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