There are 28 students in Mr. Connelly's Pre-Calculus class.
1 answer:
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Answer:
x = - 4 , x =
Step-by-step explanation:
given 2x² + 7x = 4
rearrange into standard form : ax² + bx + c = 0 : a ≠ 0
subtract 4 from both sides
2x² + 7x - 4 = 0 ← in standard form
Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term, that is
product = 2 × - 4 = - 8 and sum = + 7
The factors are + 8 and - 1
use these factors to split the middle term
2x² + 8x - x - 4 = 0 ( factor by grouping first/second and third/fourth terms )
2x(x + 4) - 1(x + 4) = 0 ( take out the common factor (x + 4) )
(x + 4)(2x - 1) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
Answer:
you're not doing anything wrong
Step-by-step explanation:
In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.
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Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.
As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.
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This is a good one to discuss with your teacher.
