Solve the proportion and REDUCE

Mathematics

1 answer:

professor190 [17]4 years ago

3 0

Answer:

x = 58/3

Step-by-step explanation:

We can use cross products to solve this problem

6 7

---------- = -----------

14 x-3

6 * (x-3) = 7 * 14

Divide each side by 6

6 /6* (x-3) = 7 * 14/6

x-3 = 98/6

Add 3 to each side

x-3+3 = 98/6 +3

x = 98/6 +18/6

x = 116/6

Divide the top and bottom by 2

x =58/3

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3 years ago

The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by: P(x)=-12x^2+1

ra1l [238]

Answer:

A current of 5 amperes will produce the maximum power.

Step-by-step explanation:

Let be $p(x) = -12\cdot x^{2}+120\cdot x$ , where $p(x)$ is measured in watts and $x$ in amperes. At first we must obtain the first and second derivatives of the function to determine the current associated with maximum power. That is:

First derivative

$p'(x) = -24\cdot x + 120$

Second derivative

$p''(x) = -24\cdot x$

Now, we equalize the first derivative to zero and solve it afterwards: (First Derivative Test)

$-24\cdot x + 120 = 0$

$x = 5\,A$

The only critical point is $x = 5\,A$ .

As next step we need to assure that critical point leads to an absolute maximum by evaluating the critical point found above in the second derivative: (Second Derivative Test)

$p(5)'' = -24\cdot (5)$