Answer:
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Assume θ with a value and substitute with it.
Let θ = 45°
So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2
R.H.S = cot θ = cot 45 = 1
So, L.H.S ≠ R.H.S
So, sin θ cos θ = cot θ is not a trigonometric identity.
The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.
<h3>How to find the sum of terms using Arithmetic sequence formula</h3>
aₙ = a + (n - 1)d
where
Therefore, let's find a and d
a₁₀ = a + (10 - 1)d
a₃₅ = a + (35 - 1)d
Hence,
16 = a + 9d
66 = a + 34d
25d = 50
d = 50 / 25
d = 2
16 - 9(2) = a
a = 16 - 18
a = -2
Therefore, let's find the sum of 75 terms of the arithmetic sequence
Sₙ = n / 2 (2a + (n - 1)d)
S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)
S₇₅ = 37.5 (-4 + 148)
S₇₅ = 37.5(144)
S₇₅ = 5400
learn more on arithmetic sequence here: brainly.com/question/1687271
2(-2y+8)
-4y+16
Therefore the answer is:
-4y+16
The scale factor of the dilation of figure A to figure B is 3/2 based on the given parameters
<h3>What is dilation?</h3>
Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
<h3>How to determine the
scale factor of the
dilation of figure A to figure B?</h3>
From the figure, we have the following corresponding sides in figure A and figure B
- Side length on figure A = 8 cm
- Corresponding side length on figure B = 12 cm
The scale factor of the dilation of figure A to figure B is calculated using the following scale factor formula
Scale factor = Figure B / Figure A
Substitute the known values in the above equation
Scale factor = 12/8
Divide 12 by 4 and then divide 8 by 4
Scale factor = 3/2
Based on the given parameters, the scale factor of the dilation of figure A to figure B is 3/2
Read more about scale factor at
brainly.com/question/15891755
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Scalene triangle is a triangle with no congruent sides
isosceles triangle is a triangle with at least 2 congruent sides (i.e. 2 or 3 congruent sides)
equilateral triangle is a triangle with exactly 3 congruent sides.
Graph 15 is an isosceles triangle
