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2 years ago

Any figure that has line symmetry must also have rotational symmetry. true or false

Mathematics

1 answer:

ozzi2 years ago

4 0

A figure that has line symmetry MUST also have a rotational symmetry.

Answer is TRUE.

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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

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

8 0

2 years ago

ASAP! Due tomorrow! 25 points! Read the word problem. Write an equation to represent the word problem. Solve the equation. Durin

Marrrta [24]

What you gotta take from this problem:

What Joe got during break = $2t+2$

What his sister gave him = $3t$

What he has total = 10 tadpoles.

Now to assemble this equation:

$2t+2+3t=10$

Now combine like terms to get $5t+2=10$

Subtract 2 on each side of the equation to get $5t=8$

Now you would divide 5 on each side and get $t=1.6$ , however since you can't have a .6 of a tadpole, you would have to round it up to 2.

7 0

3 years ago

Which of these is the first step in constructing an angle congruent to a given angle?

Salsk061 [2.6K]

Do u have answers to choice from

3 0

3 years ago

Explain two ways to find the LCM

svp [43]

Answer:

1. List the first several multiples of each number.

Look for multiples common to both lists. ...

Look for the smallest number that is common to both lists.

This number is the LCM.

Find the GCF for the two numbers.

Divide that GCF into the either number; it doesn't matter which one you choose, so choose the one that's easier to divide.

Take that answer and multiply it by the other number.

Step-by-step explanation:

Hope this helps!

4 0

3 years ago

If(X+1)and(3x+2)are factors of 3x^3+2x^2-3x-2, find the third factor

Lelechka [254]

Answer:

$3 {x}^{3} + 2 {x}^{2} - 3x - 2 = \\ {x}^{2} (3x + 2) - 1 \times (3x + 2) = \\ (3x + 2)( {x}^{2} - 1) = (3x + 2)(x - 1)(x + 1)$

6 0

2 years ago