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nika2105 [10]
3 years ago
9

Quick Computing Company produces

Mathematics
1 answer:
olganol [36]3 years ago
5 0

Answer:

c(x) = 2x^2 + 6x + 25

Completed question;

Quick Computing Company produces calculators. They have found that the cost, c(x), of making x calculators is a quadratic function in terms of x. The company also discovered that it costs $45 to produce 2 calculators, $81 to produce 4 calculators, and $285 to produce 10 calculators. Derive the function c(x).

Step-by-step explanation:

Given that;

the cost, c(x), of making x calculators is a quadratic function in terms of x.

c(x) = ax^2 + bx + c

Substituting the 3 case scenarios given;

it costs $45 to produce 2 calculators,

45 = a(2^2) + b(2) + c

45 = 4a + 2b +c .......1

$81 to produce 4 calculators,

81 = a(4^2) + b(4) + c

81 = 16a + 4b + c .......2

and $285 to produce 10 calculators.

285 = a(10^2) + b(10) + c

285 = 100a + 10b + c .......3

Solving the simultaneous equation;

Subtracting equation 1 from 2, we have;

36 = 12a + 2b ......4

Subtracting equation 1 from 3

240 = 96a + 8b .......5

Multiply equation 4 by 4

144 = 48a + 8b ......6

Subtracting equation 6 from 5, we have;

96 = 48a

a = 96/48

a = 2

Substituting a = 2 into equation 4;

36 = 12(2) + 2b

36 = 24 + 2b

2b = 36-24 = 12

b = 12/2 = 6

b = 6

Substituting a and b into equation 1;

45 = 4(2) + 2(6) +c

45 = 8 + 12 + c

c = 45 - (8+12)

c = 25

Since a = 2 , b = 6 and c = 25, the quadratic equation for c(x) is ;

c(x) = ax^2 + bx + c

c(x) = 2x^2 + 6x + 25

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Step-by-step explanation:

As a square with a perimeter of 40cm.

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P = 10+10+10+10

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and

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Calculating the Shaded Area:

As the upper length of shaded side of the shape inside square = 7 cm

so the non-shaded length of upper side of the square = 10-7 = 3cm

so

the area of left sided un-shaded triangle = 1/2 * b * h

                                                                    = (3 * 10)/2

                                                                   

Similarly, the right sided length of shaded side inside the square = 4 cm

so the non-shaded right sided-length of the square = 10-4 = 6cm

the area of right sided un-shaded triangle = 1/2 * b * h

                                                                    = (10 * 6)/2

Therefore, the area inside the square that is shaded is:

\left(10\:\times 10\right)\:-\:\frac{\left(3\:\times \:10\right)}{2}\:-\:\frac{\left(10\times \:6\right)}{2}

=\left(10\times \:10\right)-45            ∵ -\frac{3\times \:10}{2}-\frac{10\times \:6}{2}:\quad -45

=100-45

=55  cm²  

So,  the percentage of the total area inside the square

that is shaded = 55%.

And the percentage of the total area inside the square

that is non-shaded = 100 - 55 = 45 cm²   ∵ Total Area - shaded Area

Therefore, the percentage of the total area inside the square

that is shaded = 55%.                        

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