(a+b)^3 what if it is was a plus

Mathematics

2 answers:

bixtya [17]2 years ago

8 0

$(a + b)^{3} = {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3}$

Also do not get mixed between

${a}^{3} + {b}^{3}$

They both are not the same.

$(a + b)^{3} ≠ {a}^{3} + {b}^{3}$

ankoles [38]2 years ago

7 0

Answer:

Step-by-step explanation:

(a+b)³

a³+a²b+ab²+b³

a³+b³+ab(a+b)

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Pentagon JKLMN is similar to pentagon UVWXY.

marusya05 [52]

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Answer:

C. 12

Step-by-step explanation:

Corresponding sides are proportional. Sides with the same mark are the same length.

WX/XY = LM/MN = LM/KJ

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WX = 180/15 . . . . multiply by 10

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2 years ago

Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$

Anna [14]

Answer:

$\large\boxed{1\dfrac{1}{3}\ u^2}$

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

$x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1$

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

$\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}$