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3 years ago

How many different pairs of classmates can you choose from six classmates?

Mathematics

1 answer:

il63 [147K]3 years ago

4 0

Answer:

15 pairs

Step-by-step explanation:

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Find the value of x in the following triangle

ozzi

Answer:

x = 124°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

x = 180° - (32 + 24)° = 180° - 56° = 124°

4 0

3 years ago

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

How many hours is 4,480 minutes.

zysi [14]

Answer:74.67

Step-by-step explanation:There ya go :>

7 0

3 years ago

-2(3x-1)<8 on a number line

Veronika [31]

Answer:

Checkout the image below the explanation.

Step-by-step explanation:

1. First, let's solve the inequality.

Step 1: Simplify both sides of the inequality.

$-6x + 2 < 8$

Step 2: Subtract 2 from both sides.

$-6x + 2 - 2 < 8 - 2$
$-6x < 6$

Step 3: Divide both sides by -6 and flip the sign.

$\frac{-6x}{-6} < \frac{6}{-6}$
$x > -1$

2. Now that we solved the inequality and got x > -1, that means that all values of x are more than -1. It can be represented on the number-line as this:

7 0

3 years ago

According to the rational root theorem, which is not a possible rational root of x^3+8x-x-6?

iren [92.7K]

I don't know if this is what you were looking for because it doesn't have the options of your answers. Just in case it helps you get your answer here you go!

8 0

4 years ago