If f(x) = 2 sin(x) and g(x) = sin(2x), which of the following statements is true? A
The graph of g(x) and the graph of f(x) are identical
The amplitude of g(x) is greater than the amplitude of f(x)
The amplitude of f(x) is greater than the amplitude of g(2)
D
O
The period of f(x) is half of the period of g(x)

The correct options are;

The amplitude of f(x) is greater than the amplitude of g(x)

Step-by-step explanation;

The given functions are plotted

From the graphs, we have;

The amplitude of f(x) is larger than the amplitude of g(x)

The graphs of g(x) and f(x) are not identical

The period (the time taken to complete one cycle) of g(x) is half the period of f(x)

The observed properties are due to the fact that the maximum value of the sine function are ±1, and the period of the sine function is 2·π or 360°.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

answer:   expression= p+p*d%

price reduction + sale price = $625

sale price: $p+$p*d%

where d% is the percentage of discount

step-by-step explanation:

original price = p

price went down by $150 price reduction $p*d%

sale price= $ 475

therefore the price before sale is: $625

and the expression that shows the price before sale is: p+p*d%