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Anna [14]
2 years ago
6

Please help i’m so stuck i can’t do calc for the life of me

Mathematics
1 answer:
KATRIN_1 [288]2 years ago
5 0

Answer:

-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}  is the answer. See steps below.

Step-by-step explanation:

\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}\\\\-3x^5+11x^4+33x^3-26x^2-36x-6\\\\\mathrm{and\:the\:divisor\:}x^3+6x^2-3x-5:\\\\\mathrm{Quotient}=\frac{-3x^5}{x^3}=-3x^2\\\\\mathrm{Multiply\:}x^3+6x^2-3x-5\mathrm{\:by\:}-3x^2\:\:\rightarrow\:\:-3x^5-18x^4+9x^3+15x^2\\\\\mathrm{Subtract\:}-3x^5-18x^4+9x^3+15x^2\mathrm{\:from\:}-3x^5+11x^4+33x^3-26x^2-36x-6\mathrm{\:to\:get\:new\:remainder}.\\\\\mathrm{Remainder}=29x^4+24x^3-41x^2-36x-6

=-3x^2+\frac{29x^4+24x^3-41x^2-36x-6}{x^3+6x^2-3x-5}

Repeat the steps and you will reach a point where no further division is possible.

<u />

<u />=-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}<u />

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Please help! Area of part of a circle!!!
Helga [31]

The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°)   ⇒   b = 96√3 cm

Call b the base of this triangle.

The vertex angle is 120°, so the other two angles have measure θ such that

120° + 2θ = 180°

since the interior angles of any triangle sum to 180°. Solve for θ :

2θ = 60°

θ = 30°

Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

tan(30°) = h / (b/2)   ⇒   h = 48 cm

Then the area of the triangle is

1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

3072π cm² - 2304√3 cm² ≈ 5660.3 cm²

7 0
2 years ago
What are the center and radius of the circle described by the equation x2 + y2 + 6x + 10y + 18 = 0?
frosja888 [35]

Answer:

Step-by-step explanation:

What are the center and radius of the circle described by the equation x2 + y2 + 6x + 10y + 18 = 0?

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O Center (3,5); Radius 16

O Center (3.5); Radius 10

x² + y²+ 6x + 10y + 18 = 0

x² + 6x + y² + 10y = -18

x² + 6x + 9 + y² + 10y + 25 = -18 + 6 + 9

x² + 3x + 3x + 9 + y² + 5y + 5y + 25 = -3

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3 years ago
Jake's family is moving to a new home. They pack 22 boxes in 1 5/6 hours. What is the average number of boxes per hour? Explain.
lbvjy [14]
12 boxes per hour is the answer
7 0
2 years ago
The sum 4/7+ -1/3 is rational or inrational
lora16 [44]

Answer:

it is rational

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
In rectangular form, 6(cos120°, isin120°)
anastassius [24]

Answer:

  (-3, 3√3)

Step-by-step explanation:

Evaluate each of the coordinates. Keep or drop the "i" as your convention requires.

  6(cos(120°), i·sin(120°)) = (6·cos(120°), i·6·sin(120°)) = (6(-0.5), i·6·√3/2)

  = (-3, 3√3 i)

You may want the (x, y) coordinates written as (-3, 3√3).

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In the complex plane, this is -3+i·3√3.

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