P(x)=5x^4+7x^3-2x^2-3x+c

Mathematics

1 answer:

Tatiana [17]3 years ago

4 0

Answer:

Positive roots- 3 or 1

Negative roots - 2 or 0

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If the difference (3x2 - 2x + 5) – (x2 + 3x - 2) is multiplied by 1/2x^2,

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Answer in photo below
4x^4-10x^3+14x^2

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3 years ago

Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.

lora16 [44]

First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.

The sum $x^2+y^2$ can be written as: $x^2+y^2=(x+y)^2-2xy$ ,

from the binomial expansion formula: $(x+y)^2=x^2+2xy+y^2$ .

Thus, substituting y=-3x+18 and simplifying we have

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This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.

At x=5.4, the expression $10x^2-108x+18^2$ , which is equivalent to $x^2+y^2$ , takes it smallest value.

Substituting, we would find $10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324$ =32.4 This is the smallest value of the expression.

For x=5.4, y=-3x+18=-3(5.4)+18=1.8.

Answer: (5.4, 1.8)

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3 years ago

What are the coordinates of the orthocenter of △XYZ with vertices at X(−3, 3) , Y(1, 3) , and Z(−3, 0) ?

klemol [59]

Orthocenter is at (-3,3) The orthocenter of a triangle is the intersection of the three heights of the triangle (a line passing through a vertex of the triangle that's perpendicular to the opposite side from the vertex. Those 3 lines should intersect at the same point and that point may be either inside or outside of the triangle. So, let's calculate the 3 lines (we could get by with just 2 of them, but the 3rd line acts as a nice cross check to make certain we didn't do any mistakes.) Slope XY = (3 - 3)/(-3 - 1) = 0/-4 = 0 Ick. XY is a completely horizontal line and it's perpendicular will be a complete vertical line with a slope of infinity. But that's enough to tell us that the orthocenter will have the same x-coordinate value as vertex Z which is -3. Slope XZ = (3 - 0)/(-3 - (-3)) = 3/0 Another ick. This slope is completely vertical. So the perpendicular will be complete horizontal with a slope of 0 and will have the same y-coordinate value as vertex Y which is 3. So the orthocenter is at (-3,3).

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%7D%7Bx%20%7B%7D%5E%7B2%7D%20-%203x%20-%2010%20%7D%20%20-%20%20%5Cfrac%7B6x%7D%

Alex Ar [27]

$\bf \cfrac{3x}{x^2-3x-10}-\cfrac{6x}{x^2-7x+10}\implies \cfrac{3x}{(x-5)(x+2)}-\cfrac{6x}{(x-5)(x-2)}
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\textit{our LCD is clearly then }(x-5)(x+2)(x-2)
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\cfrac{(x-2)3x~~-~~[(x+2)6x]}{(x-5)(x+2)(x-2)}\implies \cfrac{3x^2-6x~~-~~[6x^2+12x]}{(x-5)(x+2)(x-2)}
\\\\\\
\cfrac{3x^2-6x-6x^2-12x}{(x-5)(x+2)(x-2)}\implies \cfrac{-3x^2-18x}{(x-5)(x+2)(x-2)}$

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3 years ago

ASAP!!!!!! SHOW WORK!!!! Thank you!!!!!!!!!

Delvig [45]

Its A trapezium

For Calculations Refer to the attachment

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3 years ago

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