The function g(x) = 4sin(4x - π) - 3 is a transformation of the parent function f(x) = sin(x) involving a horizontal compression, phase shift, vertical stretch, and vertical shift.
How does the function g(x) differ from the parent function f(x) = sin(x)?The given function g(x) is a modification of the parent function f(x) = sin(x). By comparing the two functions, we can observe several transformations applied to the parent function.
First, coefficient 4 in front of the sin function indicates a horizontal compression of the graph. It means that the graph of g(x) oscillates more rapidly than the graph of f(x).
Second, the term 4x - π within the sin function represents a phase shift to the right by π/4 units. This means that the graph of g(x) is shifted horizontally to the right compared to the graph of f(x).
Next, coefficient 4 outside the sin function indicates a vertical stretch of the graph. It means that the amplitude of the oscillations in g(x) is four times greater than in f(x), resulting in a more pronounced wave pattern.
Finally, the constant term -3 outside the sin function represents a vertical shift downward by three units. This means that the graph of g(x) is shifted vertically downward compared to the graph of f(x).
Overall, the function g(x) = 4sin(4x - π) - 3 combines horizontal compression, phase shift, vertical stretch, and vertical shift to transform the parent function f(x) = sin(x) into a new function with distinct characteristics.
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Hazel is saving her allowance to buy a new handbag to match her favorite dress. The handbag is shaped like a trapezoid with one base that is 23 centimeters long and another base that is 17 centimeters long. The trapezoid has an area of 260 square centimeters. What is the height of the trapezoid? Write your answer as a whole number or decimal. Do not round.
The height of the trapezoid is 13cm.
What is the height of the trapezoid?A trapezoid is a convex quadrilateral with at least one pair of parallel sides.
Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Height = area / (0.5 x sum of lengths)
Sum of lengths = 23 + 17 = 40 cm
= 260 / (0.5 x 40) = 13 cm
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light with a wavelength of 694 nmnm passes through a slit 7.90 μmμm wide and falls on a screen 1.95 mm away.
Using the given values, we can calculate the angle of diffraction (θ) and the distance between adjacent bright fringes (y).
How to analyze the diffraction of light passing through a narrow slit?To analyze the diffraction of light passing through a narrow slit, we can use the concept of the single-slit diffraction equation:
sin(θ) = (m * λ) / w
Where:
- θ is the angle of diffraction
- m is the order of the bright fringe
- λ is the wavelength of light
- w is the width of the slit
Given:
- Wavelength (λ) = 694 nm = 694 × 10^(-9) m
- Slit width (w) = 7.90 μm = 7.90 × 10^(-6) m
- Distance to the screen (D) = 1.95 mm = 1.95 × 10^(-3) m
First, let's calculate the angle of diffraction (θ):
θ = sin^(-1)((m * λ) / w)
Now, let's calculate the distance between adjacent bright fringes (y):
y = (m * λ * D) / w
Using the given values, we can calculate the angle of diffraction (θ) and the distance between adjacent bright fringes (y).
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help i cant solve this
Answer:
[tex]\huge\boxed{\sf 44\ units}[/tex]
Step-by-step explanation:
Perimeter:Sum of all sides of a figure is known as perimeter of that figure.Solution:
So,
Perimeter of this figure:= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4
= 44 units[tex]\rule[225]{225}{2}[/tex]
Answer:
8-4=4
therefore 6+4=10
then perimeter =2(5)+10+6+2(3)+8+4=44units
Please help me I only have 3 days to get it done and if I don’t I won’t pass