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3 years ago

(33 points!!) Please help me!!

Mathematics

1 answer:

ella [17]3 years ago

7 0

Parallel means the same direction and they don't cross each other.

There are 2 parallel streets to Golden Gate, they are Turk and McAllister.

Intersect means lines that cross through or touch.

Those are: Howard, Mission, MArket, Golden Gate and Taylor.

C. Skew lines are not parallel or do not intersect.

So find pairs of lines that are not parallel to each other and do not touch each other at all.

Example of those would be: 7th and Golden Gate and 7th and Turk.

Using those two examples you could list the other ones.

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3 years ago

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3 years ago

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3 years ago

Write a polynomial of degree 5 with zero x=0,i square root 7, -2i

professor190 [17]

Answer:

$P(x)=x^5+11x^3+28x$

Step-by-step explanation:

<u>Roots of a polynomial</u>

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

$P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)$

Where a is an arbitrary constant.

We know three of the roots of the degree-5 polynomial are:

$x_1=0;\ x_2=\sqrt{7}\boldsymbol{i}:\ x_3=-2\boldsymbol{i}$

We can complete the two remaining roots by knowing the complex roots in a polynomial with real coefficients, always come paired with their conjugates. This means that the fourth and fifth roots are:

$x_4=-\sqrt{7}\boldsymbol{i}:\ x_3=+2\boldsymbol{i}$

Let's build up the polynomial, assuming a=1:

$P(x)=(x-0)(x-\sqrt{7}\boldsymbol{i})(x+\sqrt{7}\boldsymbol{i})(x-2\boldsymbol{i})(x+2\boldsymbol{i})$

Since:

$(a+b\boldsymbol{i})\cdot (a-b\boldsymbol{i})=a^2+b^2$

$P(x)=(x)(x^2+7)(x^2+4)$

Operating the last two factors:

$P(x)=(x)(x^4+11x^2+28)$

Operating, we have the required polynomial:

$\boxed{P(x)=x^5+11x^3+28x}$

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3 years ago