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3 years ago

Find the GCF of the numbers 45 and 76 using lists of factors.

Mathematics

1 answer:

Marina86 [1]3 years ago

5 0

Answer:

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factors of 76 are: 1, 2, 4, 19, 38, 76

Then the greatest common factor is 1.

Step-by-step explanation:

There are no common factors other than 1

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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

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

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3 years ago

What is the blood type of the unknown parent?

Vinil7 [7]

Answer:

IBi0

Step-by-step explanation:

We look at the child's genotype (lAi0).

We know that the blood type's genotype has 2 genes, one from the mother and one from the father.

If the genotype is lAi0 and one gene is, let's say, from mother (lA), we know exactly that the other gene is from father (i0).

So, father's genotype is lBi0 (a).

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3 years ago

6. Dina is moving and he is going to rent a moving van. She will need it for one day. The cost of renting the van $145 for the d

Marat540 [252]

Answer:

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Step-by-step explanation:

we can write the following equation

.75m+145=price

we just need to plug in 345 for m

.75*345+145=price

put this into a calculator and get 403.75

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