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AfilCa [17]
4 years ago
13

The expression ax - 8x² + bx + 6 is exactly divisible by

Mathematics
1 answer:
NARA [144]4 years ago
5 0

Answer:

a = 3;  b = -5

Step-by-step explanation:

x² -2x-3=(x-3)(x+1)

As  it divides p(x); P(3) = 0 and P(-1) =0

P(x)= ax³ - 8x² + bx + 6

P(3) = 3³a - 8*9 + 3b + 6 =0

27a - 72 + 3b + 6 = 0

27a + 3b -66 =0

27a + 3b = 66 ------------------(i)

P(-1) = -a -8*(-1)² + b* (-1) + 6 = 0

-a - 8 -b + 6 = 0

-a - b -2 = 0

-a -b = 2    --------(ii)

(i) -------    27a + 3b = 66

(ii)*3          -3a  -3b = 6

Add            24a      = 72

                       a = 72/24

                       a = 3

Substitute a value in (ii)

-3 - b= 2

 -b = 2+3

-b= 5

b = -5

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3 years ago
Your engineering firm is asked to specify the maximum load for the elevators in a new building: Each elevator has mass 490 kg wh
steposvetlana [31]

Answer:

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Step-by-step explanation:

The first step is to calculate the maximum load after safety considerations (T_{max}

Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate (T_{max} we multiply this value by \frac{2}{3} (as per the given safety consideration.

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a) Now to find the maximum load in kgs, we use the following formula

(m_{0} + m)(g + a) = T_{max}

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m = maximum load

g = acceleration due to gravity

a = maximum acceleration of elevator

Inputting the values and solving

m_{0} + m)(g + a) = T_{max}\\ (490 + m)(9.8 + 2.24) = 13000\\ 12.04m = 7100.4\\ m = 589.734kg

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