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STatiana [176]
3 years ago
8

When the function f(x) = 2x^n + ax^2 - 6 is divided by (x - 1), the remainder is -7 and when divided by (x + 3), the remainder i

s 129.
Calculate the value of "a" and "n" and hence write the polynomial function completely.
Mathematics
2 answers:
hodyreva [135]3 years ago
5 0

Answer:

Step-by-step explanation:

From the fact that the remainder is -7 after we divide by x -1 , then we know that f(1) = -7. But f(1) = 2 + a - 6.

So 2 + a - 6 = -7

a - 4 = -7

a = 4 - 7

a = -3.

Also we know that when divided by x + 3 the remainder is 129. Hence f( -3) = 129

129 = f(-3) = 2 (-3)^ n + (-3)(-3)^2 -6

129 = 2 (-3)^n -27 - 6

129 = 2 (-3)^n -33

129 + 33 = 2(-3)^n

162 = 2 (-3)^n

81 = (-3)^n

Hence n =4 and therefore f(x) = 2x^4 -3x^2 - 6.

zhannawk [14.2K]3 years ago
3 0

Answer:

Step-by-step explanation:

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The function f(x)=-(x-3)^2 +9 can be used to represent the area of a rectangle with the perimeter of 12 units, as a function of
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Maximum area of the rectangle is 9cm^{2}

<u>Explanation:</u>

<u></u>

Considering the dimensions to be in cm

f(x) = -(x-3)^{2} +9\\f(x) = -(x^{2} +9 - 6x)+9\\f(x) = -x^{2} +6x\\f'(x) = -2x+6\\-2x+6 = 0\\2x=6\\x=3cm\\\\

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Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.

<h3>¿Cuántos boletos de adulto fueron vendidos?</h3>

Definamos las variables:

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  • y = boletos de estudiantes vendidos.

Se vendieron un total de 430 boletos, entonces:

x + y = 430

Y se vendieron 70 boletos de estudiante menos que boletos de adulto:

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Tenemos el sistema de ecuaciones:

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Para resolverlo, podemos reemplazar la segunda ecuación en la primera:

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