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tatiyna
3 years ago
14

Miguelito vende camisas de vestir . En el local le cobran $150 de alquiler; comprq cada camisa en $3.00 y la vende en $5.00. Cua

nto es el numero minimo de camisas que debe vender para tener ganancias.
Mathematics
1 answer:
lapo4ka [179]3 years ago
4 0

Answer:

x_{min} = 75\,camisas

Step-by-step explanation:

El número mínimo de camisas a vender es igual al costo de alquiler del local dividido por la diferencia entre los valores de venta y compra de cada camisa. (The minimum amount of shirts to be sold is equal to the rental cost of the retail space divided by the difference between sell and purchase cost per shirt):

x_{min} = \frac{\$ 150}{\$ 5 - \$ 3}

x_{min} = 75\,camisas

Miguelito debe vender un mínimo de 75 camisas para obtener ganacias. (Miguelito must sell a minimum of 75 shirts to make a profit.)

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3 years ago
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Read 2 more answers
A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.
irakobra [83]

Answer:

The integral is equal to 5\sec^2(2x)+C for an arbitrary constant C.

Step-by-step explanation:

a) If u=\tan(2x) then du=2\sec^2(2x)dx so the integral becomes \int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C. (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case u=\sec(2x) hence du=2\tan(2x)\sec(2x)dx. We rewrite the integral as \int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C.

c) We use the trigonometric identity \tan(2x)^2+1=\sec(2x)^2 is part b). The value of the integral is 5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C. which coincides with part a)

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