Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y; 2x2 + 4y2 = 12 step 1 we need to optimize f(x, y) = 2x2y subject to the constraint g(x, y) = 2x2 + 4y2 = 12. to find the possible extreme value points, we must use ∇f = λ∇g. we have ∇f = 4xy, $$ correct: your answer is correct. 2x^2 and ∇g = $$ correct: your answer is correct. 4x, $$ correct: your answer is correct. 8y . step 2 ∇f = λ∇g gives us the equations 4xy = 4λx, 2x2 = 8λy. the first equation implies that x = incorrect: your answer is incorrect. or λ = correct: your answer is correct.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

answer: simile

step-by-step explanation: the difference between simile and metaphor is a simile describes with "as" and "like"

c. product line extension.