Mathematics: Write (6,0) and (0,4) in standard form show all work

144Step-by-step explanation:First, find the x-values where the equations intersect:2x² = -2x² - 8x + 324x² + 8x - 32 = 04(x² + 2x - 8) = 0 (x + 4)(x - 2) = 0 x = -4 and x = 2 (see graph to confirm these values)Now, find the area under the curve: 4.5Step-by-step explanation:First, find the x-values where the equations intersect:x+3 = x² + 1 0 = x² - x - 20 = (x - 2)(x + 1)x = 2 and x = -1 (see graph to confirm these values)Now find the area under the curve:...

Write (6,0) and (0,4) in standard form show all

Ответ:

Angel1107

13.04.2023

Mathematics

144

Step-by-step explanation:

First, find the x-values where the equations intersect:

2x² = -2x² - 8x + 32

4x² + 8x - 32 = 0

4(x² + 2x - 8) = 0

(x + 4)(x - 2) = 0

x = -4 and x = 2 (see graph to confirm these values)

Now, find the area under the curve:

$\int\limits^{2}_{-4} [(-2x^2-8x+32)-(2x^2)]dx\\\\\\=\int\limits^{2}_{-4} (-4x^2-8x+32)dx\\\\\\=\bigg(-\dfrac{4}{3}x^3-\dfrac{8}{2}x^2+32x\bigg)\bigg|\limits^2_{-4}\\\\\\=\bigg(-\dfrac{4}{3}(2)^3-4(2)^2+32(2)\bigg)-\bigg(-\dfrac{4}{3}(-4)^3-4(-4)^2+32(-4)\bigg)\\\\\\=\bigg(-\dfrac{32}{3}-16+64\bigg)-\bigg(\dfrac{256}{3}-64-128\bigg)\\\\\\=\bigg(\dfrac{112}{3}\bigg)-\bigg(-\dfrac{320}{3}\bigg)\\\\\\=\dfrac{432}{3}\\\\\\=\large\boxed{144}$

4.5

Step-by-step explanation:

First, find the x-values where the equations intersect:

x+3 = x² + 1

0 = x² - x - 2

0 = (x - 2)(x + 1)

x = 2 and x = -1 (see graph to confirm these values)

Now find the area under the curve:

$\int\limits^{2}_{-1} [(x+3)-(x^2+1)]dx\\\\\\=\int\limits^{2}_{-1} (-x^2+x+2)dx\\\\\\=\bigg(-\dfrac{x^3}{3}+\dfrac{x^2}{2}+2x\bigg)\bigg|\limits^2_{-1}\\\\\\=\bigg(-\dfrac{2^3}{3}+\dfrac{2^2}{2}+2(2)\bigg)-\bigg(-\dfrac{(-1)^3}{3}+\dfrac{(-1)^2}{2}+2(-1)\bigg)\\\\\\=\bigg(-\dfrac{8}{3}+2+4\bigg)-\bigg(\dfrac{1}{3}+\dfrac{1}{2}-2\bigg)\\\\\\=\bigg(\dfrac{10}{3}\bigg)-\bigg(-\dfrac{7}{6}\bigg)\\\\\\=\dfrac{9}{2}\\\\\\=\large\boxed{4.5}$

Hello there! can i get some with this calculus practice problem? i don't think my answer is righ

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Write (6,0) and (0,4) in standard form show all work

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