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OLEGan [10]
2 years ago
15

The number of daily sales of a product was found to be given by S = 600xe−x2 + 600 x days after the start of an advertising camp

aign for this product. (Round your answers to one decimal place.) (a) Find the average daily sales during the first 30 days of the campaign—that is, from x = 0 to x = 30. (b) If no new advertising campaign is begun, what is the average number of sales per day for the next 20 days (from x = 30 to x = 50)?
Mathematics
1 answer:
Elena-2011 [213]2 years ago
4 0

Answer:

a. 20520

b. 12600

Step-by-step explanation:

Given the function S = 600xe^-x² + 600.

a. To find the average, we have to find the definite integral of the function because average, as it is known, is the sum of data points divided by the size of its dataset, this can be used for discrete data. Integral formula is just the continuous form of average, so we are using integral because we were given an interval of x= 0 to X = 30.

Let's integrate 100xe^x² first. Let –x² = u, this means –2xdx = du and we have dx = –du/2x. Also, when x = 0, u = –(0)² = –0 and when x = 30, u = –(30)² = –900. When we make our substitutions we have:

–600(xe^udu)/2x = –600(e^udu)/2 upon integrating that we have –600(e^u)/2. Applying our interval we have

–600[(e^900)/2 – (e^0)/2] ≈ – [– 3.7 – (1/2)] = –600 (–4.2) = 600 x 4.2 = 2520

Now let's integrate 600, with the interval x = 0 to x = 30 (we are using this interval here because the substitution we made didn't affect this).

We have, upon integrating:

600x.

Substituting our intervals we have:

600(30 – 0) = 600 x 30 = 18000.

Adding that up we have: 2520 + 18000 = 20520.

b. The same method is needed, just difference of interval.

Therefore, after integrating the first component with intervals u = 900 to u = 2500 (from x² = u) we have:

–600[(e^2500)/2 – (e^900)/2] ≈ –600[2.7 – 3.7] = –600(–1) = 600.

Then for the second component:

600x using x = 30 to x = 50

600(50 – 30) = 600 x 20 = 12000.

Adding that up we have:

12000 + 600 = 12600.

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Answer:

1

O nome de um polígono é um nome que se deve ao número de lados que o polígono possui.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 °

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a) agudo

4) 2240

5) 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

Step-by-step explanation:

1) Liste o nome dos polígonos de acordo com o número total de lados.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 ° b) 180 ° c) 270 ° d) 360 °

= a) 90°

Um triângulo ângulo reto pode ser definido como um triângulo onde um de seus 3 ângulos é equivalente a 90 graus (90°).

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a ) agudo b) raso c) reto d) obtuso.

Um ângulo maior que 0 ° e menor que 90 ° pode ser definido como um ângulo agudo.

= a) agudo

4) Um teatro com 64 filas de assentos e cada fila tem 35 assentos. Qual é a capacidade deste teatro?

No teatro, cada fila tem 35 lugares.

Temos 64 linhas

O número total de licenças que temos é calculado como:

1 fila = 35 assentos

64 linhas =

Multiplicação cruzada

64 filas × 35 assentos

= 2.240 assentos.

Portanto, a capacidade do teatro é de 2240.

5) André e Federico confeccionaram 28 embalagens contendo 180 bandeiras cada embalagem. Quantas bandeiras os meninos fizeram?

O número de bandeiras que os meninos fizeram é calculado como:

28 pacotes × 180 bandeiras

= 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

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