$sin^2 \ x + sin ^2 \ x + 2cos^ 2\ x = 2\\\\2sin^2 \ x + 2 cos^2 \ x = 2\\\\2 ( sin^2 \ x + cos^2 \ x ) = 2 \\\\2 \times 1 = 2 \\\\2 = 2 \\\\LHS = RHS \\\\Hence \ proved.$

5 0

3 years ago

Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separat

Dmitry [639]

Answer:

Step-by-step explanation:

Hello, dividing by 0 is not defined. so

$\dfrac{2x^2}{6x}$

is defined for x different from 0

This being said, we can simplify by 2x

$\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x$

and this last expression is defined for any real number x.

Thank you

4 0

3 years ago

Exponential growth/decay problem 1

RUDIKE [14]

Answer:

a) growth

b) $500

c) 6% = 0.06

d) $f(x)=500(1.06)^x$

e) $595.51

Step-by-step explanation:

Part (a)

Exponential GROWTH, since interest is applied to the account each year.

Part (b)

Initial amount = $500

Part (c)

Growth factor = 6% = 0.06 (in decimal form)

Part (d)

General form of exponential growth function:

$f(x)=a(1+r)^x$

where:

a = initial amount
r = rate of growth (in decimal form)
x = time (in years)

Given:

a = 500
r = 0.06

$\implies f(x)=500(1+0.06)^x$

$\implies f(x)=500(1.06)^x$

Part (e)

when x = 3

$\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}$

5 0

2 years ago