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3 years ago

Can someone explain please

Mathematics

1 answer:

blondinia [14]3 years ago

3 0

Answer:

$\large\boxed{B.\ \dfrac{7}{4}}$

Step-by-step explanation:

$\dfrac{\Delta y}{\Delta x}=\dfrac{14}{8}=\dfrac{14:2}{8:2}=\dfrac{7}{4}$

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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

3 years ago

What is the zero of the following function, f(x) = –(2/7) x − 10?

Stels [109]

Answer:

Step-by-step explanation:

the zeros of a function f are found by solving the equation f(x) = 0. Example 1. Find the zero of the linear function f is given by. f(x) = -2 x + 4 I hope this helps.

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4 years ago

Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius round to the nearest hundr

patriot [66]

volume for cylinder = pi x r^2 x h

radius = half the diameter = 8/2 =4

height = 3 times the radius = 3*4 =12

using 3.14 for pi

volume = 3.14 x 4^2 x 12 = 602.88 cubic inches

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3 years ago

There are 3/4 as many boys as girls in a class of fifth graders. If there are 35 students in the class, how many are girls?

OLEGan [10]

Answer:

20 There are 15 boys and 20 girls.

4 0

3 years ago

P + 46 = 94, what is p?

Natalka [10]

<h2>P is equal to:</h2>

48.

Because 46+48 equals 94.

You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.

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2 years ago

Can someone explain please​

Can someone explain please