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Over [174]
3 years ago
11

Zak and Ryan earn $60 per week for dilevering pizzas. Zak worked for x weeks and earned an aditional total bonus of $25. Ryan wo

rked for y weeks. Which expression shows the total money, in dollars, that Zak and Ryan earned for delivering pizzas?
Mathematics
1 answer:
olga55 [171]3 years ago
6 0
60 times x plus 60 times y plus 25
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PLSSSS ASAPPP!!!!!!!!!!
konstantin123 [22]
The answer is 13, i got this by using the pythagorean theorem. a^2 + b^2 = c^2. in this case it would be 84^2 + b^2 = 85^2. then that would turn into 7056 + b^2 = 7225, subtract both sides by 7056 to get b^2 = 169, then square 169 to get 13 :)
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3 years ago
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1. Sheena and her friends want to form a team to play recreational soccer. They want a combination of males and females for the
Vikki [24]
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3 years ago
Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +
Veronika [31]

Answer:

Verified

y(x) = \frac{3Ln(x) + 3}{x}

y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

                           x^2y' +xy = 3

- A general solution to the above ODE is also given as:

                          y = \frac{3Ln(x) + C  }{x}

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

                          y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x)  }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

                          -\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3

- Therefore, the complete solution to the given ODE can be expressed as:

                        y ( x ) = \frac{3Ln(x) + 3 }{x}

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)

- Therefore, the complete solution to the given ODE can be expressed as:

                        y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}

                           

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6 0
3 years ago
How many times does 9 go into 67
OlgaM077 [116]
9 goes into 67, 7 times, with a remainder of 4. So we would get 7 \frac{4}{9}
5 0
3 years ago
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(6x + 3) + (3 + x^4)
olganol [36]

The answer is: x^4+6x+6

3 0
3 years ago
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