Answer true or false for 1-10 (picture above)

Mathematics

1 answer:

Softa [21]3 years ago

3 0

$\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a+b}\leq\sqrt{a}+\sqrt{b}\\\\\sqrt{a-b}\geq\sqrt{a}-\sqrt{b}\\----------------------\\1)\ \sqrt{72}=\sqrt{9\cdot8}=\sqrt{9}\cdot\sqrt{8}\qquad TRUE\\\\2)\ \sqrt{13-5}=\sqrt{13}-\sqrt5\qquad FALSE\\\\3)\ \sqrt{9\cdot10}=\sqrt9+\sqrt{10}\qquad FALSE\\\\4)\ \sqrt{18bx}=\sqrt{18}\cdot\sqrt{b}\cdot\sqrt{x}\qquad TRUE\ if\ b\geq0\ and\ x\geq0\\\\5)\ \sqrt{8\cdot12}=\sqrt8\cdot\sqrt{12}\qquad TRUE\\\\6)\ \sqrt{m+x}=\sqrt{m}+\sqrt{x}\qquad FALSE$

$7)\ \sqrt{100+64}=\sqrt{100}+\sqrt{64}\qquad FALSE\\\\8)\ \sqrt{30}=\sqrt{5\cdot6}=\sqrt5\cdot\sqrt6\qquad TRUE\\\\9)\ \sqrt{44}=\sqrt{22+22}=\sqrt{22}+\sqrt{22}\qquad FALSE\\\\10)\ \sqrt{10\cdot10}=\sqrt{10}\cdot\sqrt{10}\qquad TRUE$

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sukhopar [10]

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Step-by-step explanation:

Given the mass is m =16kg, and 1N force will stretch the spring 1 m.

That is, F =1N,Z =1m. Now find the spring constant k:

F = kL = 1 = k(1) = k= 1N/m.

The damping force is 8times the instantaneous velocity, this means β = 8,

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The differential equation for a spring mass system with

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so, 16x"+ 8x' + x= 0, x(0} = -0.6, x'(0)= 2m/s.

Now solve the DE:

The auxilary equation for the homogeneous equation is 16x"+8x'+x=0

solving we get, 16r² + 8r + 1 = 0 => (4r + 1)² = 0 => r = - 1/4.

Then the general solution for the homogenous system is: $x(t)=c_1e^{-t/4} +c_2te^{-t\4}$ .

Use the initial conditions x (0) = -0.6, x'(0) = 2m/s:

$x(0)=c_1e^{0} +c_2(0)e^{0}=-0.6=c_1\\x'(t)=-\frac{1}{4}c_1e^{-t/4}+c_2e^{-t/4}-\frac{1}{4}c_2te^{-t/4}\\x'(0)=-\frac{1}{4}c_1e^0+c_2e^0-\frac{1}{4}c_2(0)e^0=2=-\frac{1}{4}(-0.6)+c_2=c_2=1.85$ .