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Mariana [72]
3 years ago
15

At a pizza restaurant a large cheese pizza cost $8.99 plus $1.25 per topping if Laura paid $13.99 for a large pizza before taxes

how many toppings did Laura put on her pizza
Mathematics
2 answers:
pishuonlain [190]3 years ago
8 0

The answer would be 4 toppings.

First you must subtract $13.99 by $8.99 which gives you $5. Then you divide that by the price of a topping which is $1.25. When you divide you get 4.

Hope this helps

AlladinOne [14]3 years ago
5 0

Answer:

4 toppings

Step-by-step explanation:

13.99-8.99=5

5÷1.25= 4

Laura put 4 toppings on her pizza.

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For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.

y''+3y'=2t^4

Assume the ansatz solution,

{y_p}=at^5+bt^4+ct^3+dt^2+et

\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e

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(You could include a constant term <em>f</em> here, but it would get absorbed by the first solution C_1 anyway.)

Substitute these into the ODE:

(20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4

15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4

\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}

y''+3y'=t^2e^{-3t}

e^{-3t} is already accounted for, so assume an ansatz of the form

y_p=(at^3+bt^2+ct)e^{-3t}

\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}

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Substitute into the ODE:

(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}

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