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quester [9]
3 years ago
8

A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost.

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
7 0

Answer:

a)

We know that the total cost for the 150 shirts (plus a flat-rate of $25) is $1,825.

First, let's find how much costs each shirt.

First, the total cost of the shirts alone (neglecting the flat-rate) is:

$1,825 - $25 = $1,800

Then each shirt costs equal to the quotient of the cost and the number of shirts:

$1,800/150 = $12

Each shirt costs $12.

Then if you order T shirts, the total cost will be the flat-rate of $25 plus T times $12. The equation is:

C(T) = $25 + T*$12

b) C represents the cost

   T represents the number of shirts ordered.

c) The initial value is the constant value, in this case, is $25

The rate of change is the coefficient that multiplies the independent variable (T), in the equation the rate of change is $12.

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The function h(t) = 300 – 16t represents the height of a ball (in feet) dropped from 300 feet after t seconds. What will be the
Vaselesa [24]
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Hope this answers the question. Have a nice day.
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4 years ago
Read 2 more answers
Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.
fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)

f'(y)=0\implies f(y)=C

\implies F(x,y)=x^2y^3+\ln(x+y^2)=C

With y(1)=2, we have

8+\ln9=C

so

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3 years ago
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