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3 years ago

Let f(x) = 3x+5 and g(x) = x^2. Find g(x)/f(x) and state its domain

Mathematics

2 answers:

lianna [129]3 years ago

7 0

Answer:

1/x-2; domain is the set of all real numbers except 2

Step-by-step explanation:

rodikova [14]3 years ago

3 0

Answer:

All real x except x = -5/3.

Step-by-step explanation:

g(x) / f(x)

= x^2/ (3x + 5)

We can't have a zero denominator so the domain is

All real x except x = -5/3.

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3 years ago

Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k

valkas [14]

Answer:

$\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\$

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k, the vector projection of B unto a is expressed as $proj_ab = \dfrac{b.a}{||a||^2} * a$

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||² = 130

$proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\$

<em>Hence the projection of b unto a is expressed as </em> $\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\$ <em></em>

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3 years ago