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drek231 [11]
3 years ago
12

Niko is looking at two different options for a new cell phone plan. Plan A has a fee of $40 plus an additional fee of $0.04 per

minute. With this plan, the first 500 minutes are free. Plan B has a fee of $60 plus an additional fee of $0.02 per minute. With this plan, the first 800 minutes are free. After how many minutes would both options cost the same amount?
Mathematics
1 answer:
Afina-wow [57]3 years ago
7 0
5 the answer is 5 the answer is always 5
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Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti
Vikki [24]

Answer:

General Solution is y=x^{3}+cx^{2} and the particular solution is  y=x^{3}-\frac{1}{2}x^{2}

Step-by-step explanation:

x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}

This is a linear diffrential equation of type

\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)..................(i)

here p(x)=\frac{-2}{x}

q(x)=x^{2}

The solution of equation i is given by

y\times e^{\int p(x)dx}=\int  e^{\int p(x)dx}\times q(x)dx

we have e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}

Thus the solution becomes

\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+cy=x^{3}+cx^{2

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have 6=8+4c

Thus solving for c we get c = -1/2

Thus particular solution becomes

y=x^{3}-\frac{1}{2}x^{2}

5 0
3 years ago
What is the distance between -10 and six on a number line
Mkey [24]

Answer:

10+6=16

Step-by-step explanation:

3 0
2 years ago
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Pleaseeeeeeeeeeeeee helppppppppppp
sergeinik [125]

Answer:

Step-by-step explanation:

8) (5x + 23) + (17x - 41) = 180

                             22x = 198

                                  x = 9

      arc JK    5(9) + 23 = 68°

     arc MJ    17(9) - 41 = 112°

     arc LMK  360 - 112 = 248

9) 8x + (21x - 12) + (10x + 9) + 90 = 360

                                             39x = 273

                                                  x = 7

                    arc WX    21(7) - 12 = 135°

                    arc YW    90 + 8(7) = 146°

                      arc YX    10(7) + 9 = 79°

                  arc VXW  360 - 8(7) = 304°

6 0
2 years ago
What is the total cost of a $44.55 meal at a restaurant after including a 17% tip? SHOW WORK!
mrs_skeptik [129]

You can solve this in 2 easy steps: 1, multiply 44.55 by .17 (44.55 * .17 = 7.57) then adding the number you get to 44.55 (44.55 + 7.57 = 52.12). Your answer is D.

3 0
3 years ago
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I am sus lol so here is some points​
Masja [62]

Hello.

Have a beautiful and joyful day ahead

Thanks for points..

3 0
3 years ago
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