Mathematics, 28.08.2019 16:30 Elephants12

Find the formula for each of the functions graphed below

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9) The period of this graph is 10 because the curve repeats every 10 units. The amplitude is 4 because that is the distance from the midline (y = 0) to the top/bottom of a curve. In order to find the equation, you need to start out with the most basic equation there is. This graph is more similar to a sin(x) graph, so we will use this:

f(x) = sin(x)

The amplitude is basically the the vertical stretch or shrink. Adding the amplitude to the function will make it:

f(x) = 4 sin(x)

To find the horizontal stretch or shrink, we have to apply the period, which is 10. The horizontal stretch/shrink is
(2pi)/(horizontal shrink or stretch) = period
--> 2pi / ? = 10
--> ? = pi/5
Therefore, the horizontal shrink/stretch is pi/5. Adding this to the equation:

f(x) = 4 sin(pi/5)(x)

Next, we use the phase shift. The graph is shifted over one to the left from a sin graph, so this is the new equation.

f(x) = 4 sin(pi/5)(x + 1) <--final equation

10) The period of this graph is 6. The amplitude is 3. The vertical stretch/shrink = amplitude, and the horizontal stretch/shrink = pi/3. The horizontal phase shift is 1 to the left.

f(x) = 3 sin(pi/3)(x + 1)

Answer from: Quest

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean = $\frac{2+3+4+5+6+7+8+9}{8}=\frac{44}{8}=5.5$

also, median= $\frac{5+6}{2}=\frac{11}{2}=5.5$ , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean = $\frac{2+3+4+5+6}{5}=\frac{20}{5}=4$

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

Answer from: Quest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

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