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3 years ago

Who wrote most definitive text on geometry

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

Euclid

Step-by-step explanation:

Euclid was a Greek geometer who wrote the Elements, the world's most definitive text on geometry. The book synthesized earlier knowledge about geometry and was used for centuries in Western Europe as a geometry textbook.

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Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

7 0

3 years ago

Can someone pls help me

yarga [219]

If I read the problem correctly, the answer should be D) 5.

The picture was blurry so I hope I read it right.

I hope this is correct and that it helps✨❤️

6 0

2 years ago

Read 2 more answers

Help me with this pls pls pls

Lemur [1.5K]

The answer would be the third one, p<319, because the auditorium can seat AT LEAST (<) 320 people, but it would be preferable to contain 319.

5 0

3 years ago

Read 2 more answers

Find the area of the parrellogram and the units

gavmur [86]

Answer:

1968

Step-by-step explanation:

A= basexheight

= 48x41

= 1968

Units: If base and height are given in metres, units of area will be m².

If they are in cm, them unit of area= cm².

7 0

3 years ago

Stephanie puts 30 cubes in a box. each cube is 1/2 an inch on each side. The box holds 2 layers of 15 cubes. what is the volume

Serhud [2]

Answer:

3.75 cubic inches

Step-by-step explanation:

Volume = length x breadth x height

since the box holds 2 layers of 15 cubes

length contains 5 cubes= 5x1/2 inches=2.5 inches

breadth contains 3 cubes=3x1/2inches=1.5 inches

height contains 2 cubes=2x1/2inches=1.0 inches

Volume=2.5x1.5x1.0=3.75 cubic inches

5 0

2 years ago