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2 years ago

Simplify the express (3x² – 2x – 1) – (3x² + 2x - 2)

Mathematics

1 answer:

ludmilkaskok [199]2 years ago

5 0

Answer:

-4x+1

Step-by-step explanation:

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

faltersainse [42]

Answer:

V = 34,13*π cubic units

Step-by-step explanation: See Annex

We find the common points of the two curves, solving the system of equations:

y² = 2*x x = 2*y ⇒ y = x/2

(x/2)² = 2*x

x²/4 = 2*x

x = 2*4 x = 8 and y = 8/2 y = 4

Then point P ( 8 ; 4 )

The other point Q is Q ( 0; 0)

From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.

Now with the help of geogebra we have: In the annex segment ABCD is dy then

V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy

V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴

V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )

V = π * [256/3 - 51,20]

V = 34,13*π cubic units

3 0

2 years ago

Multiply (x + 1)^3

Shalnov [3]

<h3>Answer: x3 +2 +x+x+</h3>

Step-by-step explanation:

6 0

2 years ago

A tree is 12 feet tall. A wire runs from the top of the tree to a point of 6 feet from its base. The wire is square root 180 fee

Artyom0805 [142]

13.42 is how long the wire is to the nearest hundredth of a foot

8 0

3 years ago

"find the reduction formula for the integral" sin^n(18x)

dexar [7]

Let

$I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx$
For demonstration on how to tackle this sort of problem, I'll only work through the case where $n$ is odd. We can write

$\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx$
$\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$

For the remaining integral, we can integrate by parts, taking

$u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx$ $\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax$

$\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx$

For this next integral, we rewrite the integrand

$\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax$
$\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)$

So putting everything together, we found

$I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$
$I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)$
$I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$
$\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$

$\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax$

7 0

2 years ago

The slope of a line is -3. Find the slope of a line that is perpendicular to this line.

nataly862011 [7]

<span>The slope of a line is -3
</span><span>perpendicular lines, slope is opposite and reciprocal
so </span><span>the slope of a line that is perpendicular to this line will be 1/3

answer
</span><span>C.1/3</span>

8 0

2 years ago