3 years ago

Plz solve this question mhanifa

Mathematics

1 answer:

IrinaK [193]3 years ago

7 0

Answer:

Option D

Step-by-step explanation:

Given:

f(x) = 1/ (x - 3)
g(x) = $\sqrt{x+5}$

The composite function f · g(x) is:

f(g(x)) = 1 / ( $\sqrt{x+5} - 3$ )

Restrictions are:

x + 5 ≥ 0 ⇒ x ≥ - 5

and

$\sqrt{x+5}$ ≠ 3 ⇒ x + 5 ≠ 9 ⇒ x ≠ 4

Combination of the above gives us the domain:

x ∈ [ - 5, 4) ∪ (4, +∞)

Correct choice is D

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1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is t

natta225 [31]

The area of the surface given by $\vec r_1(u,v)$ is 1. In terms of a surface integral, we have

$1=\displaystyle\int_{-4}^4\int_{-4}^4\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

By multiplying each component in $\vec r_1$ by 5, we have

$\dfrac{\partial\vec r_2(u,v)}{\partial u}=5\dfrac{\partial\vec r_1(u,v)}{\partial u}$

and the same goes for the derivative with respect to $v$ . Then the area of the surface given by $\vec r_2(u,v)$ is

$\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}$