The inequality 6-2/3x

Mathematics

1 answer:

densk [106]2 years ago

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Answer:

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Step-by-step explanation:

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Given that f(x) = x2 + 2x + 3 and g(x) = quantity of x plus four, over three , solve for f(g(x)) when x = 2.

Sidana [21]

$f(x)=x^2+2x+3$
$g(x)=\frac{x+4}{3}$
$f(g(x))=(\frac{x+4}{3})^2+2(\frac{x+4}{3})+3$
$f(g(x))=\frac{x^2+8x+16}{9}+\frac{2x+8}{3}+3$
$f(g(2))=\frac{2^2+8(2)+16}{9}+\frac{2(2)+8}{3}+3$
$f(g(2))+\frac{4+16+16}{9}+\frac{4+8}{3}+3$
$f(g(2))=\frac{36}{9}+\frac{12}{3}+3$
$f(g(2))=4+4+3$
$f(g(2)=11$

Check:
g(2)=(2+4)/3=2
f(2)=2^2+2(2)+3=4+4+3=11 Checks.

4 0

2 years ago

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A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t

xz_007 [3.2K]

Full Question

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

Determine the spring constant k.

Answer:

Spring Constant = 1000Nm^-1

Step-by-step explanation:

Given

Mass = 10kg

Spring Extension = 9.8cm

Spring Constant K = Force/Extension

Force = Mass * Acceleration

Force = 10 * 9.8 = 9.8N

Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m

Spring constant = 98 / 0.098