3 years ago

Select all factors of the following polynomial: 5p3 + 45p2 + 40p

Mathematics

1 answer:

madam [21]3 years ago

7 0

Answer:

$\huge\boxed{5p;\ (p+1)}$

Step-by-step explanation:

$5p^3+45p^2+40p=5p(p^2+9p+8)=5p(p^2+p+8p+8)\\\\=5p\bigg[p(p+1)+8(p+1)\bigg]=5p(p+1)(p+8)\\\Downarrow\\\boxed{5p};\ \boxed{(p+1)};\ \boxed{(p+8)}$

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Find the area of the circle x^2+y^2=16 by the method of intregration

zhuklara [117]

Answer:

Hello,

$16\pi$

Step-by-step explanation:

$I=\dfrac{Area}{4} =\int\limits^4_0 {\sqrt{16-x^2} } \, dx \\\\Let\ say\ x=4*sin(t),\ dx=4*cos(t) dt\\\\\displaystyle I=\int\limits^\frac{\pi }{2} _0 {4*\sqrt{1-sin^2(t)} }*4*cos(t) \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {cos^2(t)} \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {\frac{1-cos(2t)}{2}} \, dt \\\\=8*[t]^\frac{\pi }{2} _0-[\frac{sin(2t)}{2} ]^\frac{\pi }{2} _0\\\\=4\pi -0\\\\=4\pi\\\\\boxed{Area=4*I=16\pi}\\$