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3 years ago

Christopher is choosing between two cell phone plans that offer the

Mathematics

1 answer:

Goryan [66]3 years ago

5 0

Answer:

39.99 + 0.45a = 44.99 + 0.40a you're welcome (:

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How do i solve this?

Nesterboy [21]

Answer:

$\large\boxed{-1}$

Step-by-step explanation:

$p(x)=x^3-2\ divided\ by\ (x-1)\\\\\text{We nedd only find the value of}\ p(1).\\\text{Put the x = 1 to the polynomial}\\\\p(1)=1^3-2=1-2=-1$

6 0

3 years ago

Two fractions are given. For each one, write its decimal equivalent and determine if the decimal is terminating or non terminati

ziro4ka [17]

Answer:

9/20 yes, 4/15 not. See below

Step-by-step explanation:

Pick 9/20 and multiply numerator and denominator by 5:

9/20 = 45/100

We know that if we divide a number by 100 we need to move the coma as two places left, so:

9/20 = 45/100 = 0.45

And this is a terminal decimal as we know where it ends.

On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):

4 |_ 15

we can divide 4 by 15, so we use 40 and begin with a comma

40 |_ 15

15 enters 2 times in 40 with a rest of 10, so:

40 |_ 15

30 0.2

100

100 divided by 15 is 6 and we have 10 as rest again, and again and again...

40 |_ 15

30 0.266.....

100

....

So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...

6 0

3 years ago

Shanay can swim the 100m race in 70.2seconds.Swapnil can swim the same in 70.06 seconds. Who is faster

ruslelena [56]

Swapnil is faster
70.06 < 70.2 s

4 0

3 years ago

Find a particular solution to the nonhomogeneous differential equation y'' + 4 y = cos(2x) + sin(2x).

alukav5142 [94]

The characteristic solution follows from solving the characteristic equation,

$r^2+4=0\implies r=\pm2i$

so that

$y_c=C_1\cos2x+C_2\sin2x$

A guess for the particular solution may be $a\cos2x+b\sin2x$ , but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to

$y_p=ax\cos2x+bx\sin2x$

which has second derivative

${y_p}''=(-4ax+4b)\cos2x+(-4bx-4a)\sin2x$

Substituting into the ODE, you have

$y''+4y=\cos2x+\sin2x$
$\implies4b\cos2x-4a\sin2x=\cos2x+\sin2x$
$\implies\begin{cases}4b=1\\-4a=1\end{cases}\implies a=-\dfrac14,b=\dfrac14$

Therefore the particular solution is

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

Note that you could have made a more precise guess of

$y_p=(a_1x+a_0)\cos2x+(b_1x+b_0)\sin2x$

but, of course, any solution of the form $a_0\cos2x+b_0\sin2x$ is already accounted for within $y_c$ .

6 0

3 years ago

Nalini is a real estate agent. She is paid

Vinvika [58]

I believe the commission is 7,511

5 0

3 years ago