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2 years ago

Solve for a. 4(a 3)=12 4a a. no solution b. all real numbers c. −3 d. −1

Mathematics

2 answers:

vfiekz [6]2 years ago

8 0

Answer:

b.) All real numbers.

Step-by-step explanation:

4 (a + 3) = 12 + 4a

4a + 12 = 12 + 4a

4a + 12 - 12 = 12 + 4a - 12

4a = 4a

4a/4 = 4a/4

0 = 0

All possibilities of other real number can fit into the equation. Hence, the answer is b.) All real numbers.

Vladimir79 [104]2 years ago

5 0

4(a + 3) = 12 + 4a
4a + 12 = 12 + 4a
0 = 0

Therefore, the solution to the equation is all real numbers.

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2 years ago

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jeka57 [31]

Answer:

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

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We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

$f(\theta) = 12sin(\theta) - 9 sin^2(\theta)$

Taking the first derivative of this with respect to $\theta$ and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of $f(\theta)$ w.r.t $\theta$ is

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)$

And setting this = 0 gives

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0$

Eliminating $cos(\theta)$ on both sides and solving for $sin(\theta)$ gives us

$sin(\theta) = \frac{12}{18} = \frac{2}{3}$

Plugging this value of $sin(\theta)$ into the original equation gives us

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Answer:

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