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2 years ago

Suppose f and g are continuous functions such that g(2) = 6 and lim x → 2 [3f(x) + f(x)g(x)] = 36. find f(2).

Mathematics

1 answer:

True [87]2 years ago

7 0

Answer: f(2) = 4

Step-by-step explanation:

F(x) and g(x) are said to be continuous functions

Lim x=2 [3f(x) + f(x)g(x)] = 36

g(x) = 2

Limit x=2

[3f(2) + f(2)g(2)] = 36

[3f(2) + f(2) . 6] = 36

[3f(2) + 6f(2)] = 36

9f(2) = 36

Divide both sides by 9

f(2) = 36/9

f(2) = 4

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3 years ago

3 A class has 6 boys and 15 girls. What is the ratio of boys to girls?

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Step-by-step explanation:

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2 years ago

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Factor the greatest common factor from the polynomial 3x^2 + 6x -9

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Answer:

$3(x+3)(x -1)$

Step-by-step explanation:

$3x^2 + 6x -9$

All the terms in this polynomial are divisible by 3. Factor 3 out of this polynomial:

$= 3(x^2 + 2x -3)$

Now, factor inside the parentheses by grouping:

$= 3(x^2 -1x+3x -3)$

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1 year ago

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Angelina_Jolie [31]

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3 years ago

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A carpenter is putting a skylight in a roof. If the roof measures 10 + 8 by 8 + 6 and the skylight measures + 5 by 3 + 4, what i

Usimov [2.4K]

Answer:

The area is: $77x^2 + 105x + 28$ , option b.

Step-by-step explanation:

Rectangular area:

The area of a rectangular space is given bt the multiplication of its measures.

Area of the roof:

Dimensions of 10x + 8 and 8x + 6. So

$A_{r} = (10x+8)(8x+6) = 80x^2 + 60x + 64x + 48 = 80x^2 + 124x + 48$

Area of the skylight:

Dimensions of x + 5 and 3x + 4. So

$A_{s} = (x+5)(3x+4) = 3x^2+4x+15x+20 = 3x^2 + 19x + 20$

What is the area of the remaining roof after the skylight is built?

Total subtracted by the skylight, which is a subtraction of a polynomial, in which we subtract the like terms. So

$A_{r} - A_{s} = 80x^2 + 124x + 48 - (3x^2 + 19x + 20) = 80x^2 - 3x^2 + 124x - 19x + 48 - 20 = 77x^2 + 105x + 28$

The area is: $77x^2 + 105x + 28$ , option b.

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2 years ago