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3 years ago

12

Billy found the slope of the line through the points (2,5) and (-2,-5) using the equation

2 answers:

Sav [38]3 years ago

7 0

Answer:

The slope of the line is the inverse of the answer he gave, 5/2.

Step-by-step explanation:

In this case, the slope equation for a line is:

$m\frac{y2-y1}{x2-x1}$

Analyzing the description, we can appreciate that Billy the x values by the y values, that is incorrect, because the equation is as shown before. So the slope of the line is the inverse of the answer he gave, 5/2.

Shkiper50 [21]3 years ago

3 0

Slope is calculated as the change in y over the change in x so you would need to do 5- (-5) which turns the negative sign to a positive making it 5+5=10 and the same thing with the 2s 2-(-2)=4 so the answer would be 10/4 or 5/2. Billy did the reciprocal.

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How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?

RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

$y = f(x)$

To find the area under the curve $y = f(x)$ between $x = a$ and $x = b$ , all we need is to integrate $y = f(x)$ between the limits of $a$ and $b$ .

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

$A=\int _a^b|f\left(x\right)|dx$

= $\int _{-2}^2\left|x^2-4\right|dx$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=\int _{-2}^2x^2dx-\int _{-2}^24dx$

solving

$\int _{-2}^2x^2dx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}$

$=\left[\frac{x^3}{3}\right]^2_{-2}$

computing the boundaries

$=\frac{16}{3}$

Thus,

$\int _{-2}^2x^2dx=\frac{16}{3}$

similarly solving

$\int _{-2}^24dx$

$\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax$

$=\left[4x\right]^2_{-2}$

computing the boundaries

$=16$

Thus,

$\int _{-2}^24dx=16$

Therefore, the expression becomes

$A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx$

$=\frac{16}{3}-16$

$=-\frac{32}{3}$

$=-10.67$ square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

6 0

3 years ago

Did I do this problem correctly??

DaniilM [7]

You're correct in the x parts where each is +3

You're incorrect in the y part

5 - 6 = -1

5 - 4 = 1

So the first one should be -6

From there, its +6

-1 + -6 = -7

-7 + -6 = -13

6 0

3 years ago

The graph of the portion I'll relationship contains the point with coordinates 3 and 12 what is the constant of proportionality

horsena [70]

Answer:

Step-by-step explanation:

I think it’s 8?

6 0

3 years ago

1. A rectangular field is 100 m long and 52.5 m broad. It has to be fenced to keep the cattle away. A) How much wire is needed f

Darina [25.2K]

Answer:

See the answers below

Step-by-step explanation:

Given data

Dimension of the field

Length = 100m

Width= 52.5m

A). Perimeter fencing= 2L+2W

P= 2*100+ 2*52.5

P= 100+ 105

P = 205m

B. Area= L*W

A= 100*52.5

A= 5250m^2

4 0

3 years ago

44 is what percent of 80

ra1l [238]

Answer:

it is 55% of 80

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers