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maks197457 [2]
2 years ago
10

What is the domain of (cd)(x)?

Mathematics
1 answer:
viktelen [127]2 years ago
6 0

Answer:

Only option B is correct, i.e. all real values of x except x = 2.

Step-by-step explanation:

Given the functions are C(x) = 5/(x-2) and D(x) = (x+3)

Finding (C·D)(x) :-

(C·D)(x) = C(x) * D(x)

(C·D)(x) = 5/(x-2) * (x+3)

(C·D)(x) = 5(x+3) / (x-2)

(C·D)(x) = (5x+15) / (x-2)

Let y(x) = (C·D)(x) = (5x+15) / (x-2)

According to definition of functions, the rational functions are defined for all Real values except the one at which denominator is zero.

It means domain will be all Real values except (x-2)≠0 or x≠2.

Hence, only option B is correct, i.e. all real values of x except x = 2.

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C

Step-by-step explanation:

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4 side triangles

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now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

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