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3 years ago

G(x)=x^3+6x^2+12x+8 determine

Mathematics

2 answers:

TEA [102]3 years ago

3 0

G(-1) = 1

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

g(-1) = 1

Lyrx [107]3 years ago

3 0

Answer:

g(-1) = 1

Step-by-step explanation:

g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

g(-1) = 1

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slamgirl [31]

Answer:

The height of the jumping hill x = 189.3 m

Step-by-step explanation:

From Δ ABC

AB = x = height of the hill

∠A = 36° , ∠B = 90°

Thus ∠C = 180 - ∠A - ∠B

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Use the shell method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions

Marina CMI [18]

Answer:

44.18 cubic unit

Step-by-step explanation:

The intersection of the curve $y = x^2$ and $y = 8-x^2$ is

$x^2 = 8 - x^2$

$2x^2 = 8$

$x^2 = 4$

$x = \pm 2$

Since we are rotating the region where $x \geq 0.5$ we will use the intersection x = 2 and y = 4

Using the shell method with x ranges from 0.5 to 2. The volume of the shell would be

$V = \int\limits^2_{0.5} {2\pi x h} \, dx$

where h is the difference between the y-coordinates of the curves, in other words

$h = 8 - x^2 - x^2 = 8 - 2x^2$

Plug h into the V integral and we have

$V = \int\limits^2_{0.5} {2\pi x (8 - 2x^2)} \, dx\\V = 4\pi\int\limits^2_{0.5} {(4x - x^3)} \, dx\\V = 4\pi[2x^2 - x^4/4]^2_{0.5}\\V = 4\pi(2*2^2 - 2^4/4 - 2*0.5^2 + 0.5^4/4)\\V = 4\pi(8 - 4 - 0.5 + 0.015625) \approx 44.18$

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