<h2>2.</h2><h3>Given</h3>
<h3>Find</h3>
- y·y'' +x·y' -16 in simplest form
<h3>Solution</h3>
It is convenient to expand the expression for y to ease determination of derivatives.
... y = 4x -6x²
... y' = 4 -12x
... y'' = -12
Then the differential expression can be written as
... (4x -6x²)(-12) +x(4 -12x) -16
... = -48x +72x² +4x -12x² -16
... = 60x² -44x -16
<h2>3.</h2><h3>Given</h3>
<h3>Find</h3>
- the turning points
- the extreme(s)
<h3>Solution</h3>
The derivative is
... y' = -16x^-2 + x^2
This is zero at the turning points, so
... -16/x^2 +x^2 = 0
... x^4 = 16 . . . . . . . . . multiply by x^2, add 16
... x^2 = ±√16 = ±4
We're only interested in the real values of x, so
... x = ±√4 = ±2 . . . . . . . x-values at the turning points
Then the turning points are
... y = 16/-2 +(-2)³/3 = -8 +-8/3 = -32/3 . . . . for x = -2
... y = 16/2 + 2³/3 = 8 +8/3 = 32/3 . . . . . . . for x = 2
The maximum is (-2, -10 2/3); the minimum is (2, 10 2/3).
cosθ = cotθ/cscθ is a true statement. The answer is option B
<h3>How to determine which of the trigonometric statements are true?</h3>
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles
A. tan²θ = 1 - sec²θ
tan²θ = 1 - sec²θ
tan²θ = 1 - 1/cos²θ (Note: sec²θ = 1/cos²θ)
tan²θ = (cos²θ- 1)/cos²θ
tan²θ = -sin²θ/cos²θ (Note: cos²θ- 1 = -sin²θ)
tan²θ = -tan²θ
This statement is not true
B. cosθ = cotθ/cscθ
cosθ = cotθ/cscθ
cosθ = (1/tanθ) / (1/sinθ)
cosθ = (cosθ/sinθ).sinθ
cosθ = cosθ
This statement is true
C. 1/sec²θ = sin²θ + 1
1/sec²θ = 1/(1/cos²θ)
1/sec²θ = cos²θ
1/sec²θ = 1 - sin²θ
This statement is not true
D. sec²θ - 1 = 1/cot²θ
sec²θ - 1 = 1/cos²θ - 1
sec²θ - 1 = (1-cos²θ)/cos²θ
sec²θ - 1 = sin²θ/cos²θ
sec²θ - 1 = tan²θ
This statement is not true
E. sinθ cscθ = tan θ
sinθ cscθ = tan θ
sinθ cscθ = sinθ (1/sinθ)
sinθ cscθ = 1
This statement is not true
Therefore, the true statement is cosθ = cotθ/cscθ
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4/7 is the answer to your question
The answer is the 4th or 119
Answer:
The solution is (3, -3)
Step-by-step explanation:
5x + 2y = 9
2x - 3y = 15
Use elimination by addition/subtraction. Multiply the first equation by 3 and the second by 2, obtaining:
15x + 6y = 27
4x - 6y = 30
----------------------
19x = 57
This yields x = 3.
Substituting 3 for x into 5x + 2y = 9, we get 5(3) + 2y = 9, or
15 + 2y = 9, or
2y = -6
This yields y = -3.
The solution is (3, -3)