HELP !! Show work also please !!

Mathematics

1 answer:

____ [38]3 years ago

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Answer:

1) The slope of a vertical line is not defined, therefore it is not possible to count it. Graphically the tangent never touches the vertical line, but it is believed that it would touch it at infinity (m=∞ )

2) It is not possible to write the equation of the given line in the slope point form, since for a vertical line the slope has an indefinite value (∞). This is because the angle of inclination of the line is 90 ° and the tangent line has no value at this point. Line formula is y = 2

Step-by-step explanation:

Hi! How are u?

1) As you may already know the slope of a line or element is the inclination of that element with respect to the horizontal axis (x axis). In this case, if we look at the graph, the line that passes through points (2,1) and (2,0) is a vertical line (that is, the angle of inclination is 90 °).

To count the slope we must calculate the tangent of the angle of inclination, in this case 90°, but if you use your calculator you will see that it will not give you an error.

m=tan⁡∝

m=tan⁡(90°)

m=∞

Conclusion: The slope of a vertical line is not defined, therefore it is not possible to count it. Graphically the tangent never touches the vertical line, but it is believed that it would touch it at infinity.

2) The Point-Slope form is:

y-y1=m∙(x-x1 )

To express the line in this way, you need to know the slope, for which you must use the following formula:

m=∆y/∆x=(y2-y1)/(x2-x1 )

Were:

x1=2, y1=1, x2=2, y2=0

If you replace these values in the equation, it is as follows:

m=(1-0)/(2-2)=1/0=∞

Remember that division by zero does not have a definite value, since for real numbers zero has no multiplicative inverse (no real number multiplied by 0 results in 1). However, if we calculate the limit of the slope equation, with x tending to 0, m tends to infinity.

Conclusion: It is not possible to write the equation of the given line in the slope point form, since for a vertical line the slope has an indefinite value (∞). This is because the angle of inclination of the line is 90 ° and the tangent line has no value at this point.

I hope I've been helpful!

Regards!

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Using the pattern, give the coefficients of (x + y)^5 and (x + y)^6

musickatia [10]

Answer:

$(x+y)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

$(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$

Step-by-step explanation:

In order to find the values of $(x+y)^5$ and $(x+y)^6$ , you need to apply the binomial theorem (high-level math you most likely don't need to worry about, it's easier than multiplying all the binomials together).

$(x+y)^5$ = $\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i$ = $\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$ = $x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$ .

$(x+y)^6$ = $\sum _{i=0}^6\binom{6}{i}x^{\left(6-i\right)}y^i$ = $\frac{6!}{0!\left(6-0\right)!}x^6y^0+\frac{6!}{1!\left(6-1\right)!}x^5y^1+\frac{6!}{2!\left(6-2\right)!}x^4y^2+\frac{6!}{3!\left(6-3\right)!}x^3y^3+\frac{6!}{4!\left(6-4\right)!}x^2y^4+\frac{6!}{5!\left(6-5\right)!}x^1y^5+\frac{6!}{6!\left(6-6\right)!}x^0y^6$ = $x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$ .