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2 years ago

Nathan ended round one of a quiz with 200 points. In round

Mathematics

1 answer:

pochemuha2 years ago

3 0

Answer:

100 points

Step-by-step explanation:

maths and more maths

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Expand & simplify

Wittaler [7]

Answer:

6(2a+4)-4(3a-4)= (12a+24) +(-12a+16) = 40

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1 year ago

What is the distance between 5,4 and -1,1

spayn [35]

Answer:

3 $\sqrt{5}$

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 1, 1)

d = $\sqrt{(-1-5)^2+(1-4)^2}$

= $\sqrt{(-6)^2+(-3)^2}$

= $\sqrt{36+9}$

= $\sqrt{45}$

= 3 $\sqrt{5}$ ← exact value

≈ 6.71 ( to 2 dec. places )

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2 years ago

Divide. write in smplest form 12÷2 2/7

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2 years ago

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2 years ago

Read 2 more answers

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

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2 years ago