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Elan Coil [88]
3 years ago
9

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates

Mathematics
1 answer:
My name is Ann [436]3 years ago
4 0

Answer:

W(t) = 0.9cos(2πt/366) + 8.2  

Step-by-step explanation:

W(t) = a cos(bt) + d

1. Calculate the phase shift, b

At t= 0, the dog is at maximum weight, so the cosine function is also at a maximum.

The cosine function is not shifted, so b = 1.

W(t) = a cos t + d

2. Calculate d

The dog's average weight is 8.2 kg, so the mid-line d = 8.2.

W(t) = a cos t + 8.2  

3. Calculate a

The dog's maximum weight is 9.1 kg.

The deviation from the average (the amplitude, a) is 9.1 kg - 8.2 kg = 0.9 kg.

W(t) = 0.9cos t  + 8.2

3. Calculate t

The period p = 2π/b = 2π/1 = 2π

From t = 0 to t = 91.25 da is one-quarter of a period, so

p = 4 × 91.25 da = 365 da = 2π rad

The conversion factor is 1 da =2π/365 rad

The function with t in radians is

W(t) = 0.9cos(2πt/365) + 8.2

The figure below shows the graph of the function.

 

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Serhud [2]

Answer:

-315

Step-by-step explanation:

same terminal side

7 0
3 years ago
5x is equal to 8X raise to power - 1/3​
goldenfox [79]

Answer:

No solutions.

Step-by-step explanation:

5x = 8x^-1/3

Divide 8 into both sides.

5/8x = x^-1/3

Divide both sides by x.

5/8 = x^-4/3

Multiply both sides by the exponent -3/4.

5/8^-3/4 = x

1.422624 = x

Plug in 1.422624 for x to check.

It does not work. There are no real solutions.

7 0
2 years ago
For the function y = 3x^2 - 12x + 4, what is the mirror point for the y-intercept? Give your answer in (x,y) point form.
saveliy_v [14]

Answer:

Your in Pacyber aren't you? Mr. Breux class? Anyway the answer is (0,-4)

Step-by-step explanation:

The y intercept is (0,-4)

6 0
3 years ago
Complete the assignment on a separate sheet of paper<br><br> Please attach pictures of your work.
Irina18 [472]

Answer:

<u>TO FIND :-</u>

  • Length of all missing sides.

<u>FORMULAES TO KNOW BEFORE SOLVING :-</u>

  • \sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}
  • \cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}
  • \tan \theta = \frac{Side \: opposite \: to \: \theta}{Side \: adjacent \: to \: \theta}

<u>SOLUTION :-</u>

1) θ = 16°

Length of side opposite to θ = 7

Hypotenuse = x

=> \sin 16 = \frac{7}{x}

=> \frac{7}{x} = 0.27563......

=> x = \frac{7}{0.27563....} = 25.39568..... ≈ 25.3

2) θ = 29°

Length of side opposite to θ = 6

Hypotenuse = x

=> \sin 29 = \frac{6}{x}

=> \frac{6}{x} = 0.48480......

=> x = \frac{6}{0.48480....} = 12.37599..... ≈ 12.3

3) θ = 30°

Length of side opposite to θ = x

Hypotenuse = 11

=> \sin 30 = \frac{x}{11}

=> \frac{x}{11} = 0.5

=> x = 0.5 \times 11 = 5.5

4) θ = 43°

Length of side adjacent to θ = x

Hypotenuse = 12

=> \cos 43 = \frac{x}{12}

=> \frac{x}{12} = 0.73135......

=> x = 12 \times 0.73135.... = 8.77624.... ≈ 8.8

5) θ = 55°

Length of side adjacent to θ = x

Hypotenuse = 6

=> \cos 55 = \frac{x}{6}

=> \frac{x}{6} = 0.57357......

=> x = 6 \times 0.57357.... = 3.44145.... ≈ 3.4

6) θ = 73°

Length of side adjacent to θ = 8

Hypotenuse = x

=> \cos 73 = \frac{8}{x}

=> \frac{8}{x} = 0.29237......

=> x = \frac{8}{0.29237.....} = 27.36242..... ≈ 27.3

7) θ = 69°

Length of side opposite to θ = 12

Length of side adjacent to θ = x

=> \tan 69 = \frac{12}{x}

=> \frac{12}{x} = 2.60508......

=> x = \frac{12}{2.60508....}  = 4.60636.... ≈ 4.6

8) θ = 20°

Length of side opposite to θ = 11

Length of side adjacent to θ = x

=> \tan 20 = \frac{11}{x}

=> \frac{11}{x} = 0.36397......

=> x = \frac{11}{0.36397....}  =30.22225.... ≈ 30.2

5 0
2 years ago
los miembros de un club social se pueden agrupar en sin que ninguno quede suelto, por parejas, por trios y por grupos de 7. ¿ cu
mote1985 [20]

Answer:

El club tiene 84 miembros.

Step-by-step explanation:

El mínimo común múltiplo (mcm) es el número positivo más pequeño que es múltiplo de dos o más números. Es decir, el mínimo común múltiplo de dos números a y b es el número más pequeño que es múltiplo de a y múltiplo de b. Recordar que los múltiplos son el resultado de multiplicar un número por todos y cada uno de los números naturales.

Para calcular el mcm se descompone los números para escribirlos como un producto de números primos. Para descomponer un número se divide el número sucesivamente entre números primos hasta llegar a 1.  La descomposición es el producto de las potencias de los números primos, siendo sus exponentes el número de veces que se ha dividido por dicho primo.

El mínimo común múltiplo se obtiene escogiendo todos los factores (comunes y no comunes), elevados a la máxima potencia. Es decir eliges todos los factores, pero los que se repitan serán elevados a la máxima potencia.

En este caso, los miembros de un club social se pueden agrupar, sin que ninguno quede suelto, por parejas, por tríos y por grupos de 7. Para calcular la cantidad de miembros que tiene el club, entonces debes calcular el mcm entre los números 2,3 y 7

No podemos descomponer los números como producto de primos porque ya son números primos., por lo que el mínimo común múltiplo es el producto de comunes y no comunes al mayor exponente:

mcm (2,3,7)= 2*3*7= 42

Pero sabes que los miembros son más de 80 pero menos de 90, por lo que calculas un múltiplo del mcm obtenido.

Múltiplo de 42= 2*42= 84

<u><em>El club tiene 84 miembros.</em></u>

5 0
3 years ago
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