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katrin [286]
3 years ago
12

A clown is juggling at a circus. The path of the ball is given by the parametric equations x=2 cos t+2 and y=3 sin t+3. In what

direction is the ball moving?
A. up and to the right
B. counterclockwise
C. down and to the right
D. clockwise

Mathematics
1 answer:
Masja [62]3 years ago
3 0
We need to find the direction the ball is moving, so wee have this parametric equation, namely:

\left \{ {{x=2cost+2} \atop {y=3sint+3}} \right.

The graph of this equation is given in figure below. So, we well substitute some values of t in the equation:

If t = 0
x = 4 and y = 3
P0(4, 3)

if t = 1
x = 3.08 and y = 5.52
P1(3.08, 5.52)

if t = 2
x = 1.16 and y = 5.72
P2(1.16, 5.72)

So, as shown in the figure, the answer is B. <span>counterclockwise </span>

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Step-by-step explanation:

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Write the equation of the line in slope-intercept form.
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Answer:

y = 1/40x + 20

Step-by-step explanation:

Slope-intercept equation format:

y = mx + b

m = slope/ gradient/ constant of variation/ rate of change

b = y-intercept

To find the slope, use the formula:

\frac{y_2-y_1}{x_2-x_1}

Find  two random points:

1 - (0.5, 40) , 2 - (1, 60)

Plug in:

\frac{60-40}{1-0.5}

Solve:

\frac{20}{0.5}

Divide:

\frac{1}{40}

The y-intercept is when the x-coordinate is equal to 0.

The y-intercept is always the beginning.

So observing the graph, the first point is (0, 20)

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8 0
1 year ago
How do you work out this problem, step by step please I am so lost. Year Average Household Income (before taxes) Food Housing Tr
Hitman42 [59]

Answer:

(a)Food-12%

9b)Transportation-17%

Step-by-step explanation:

In the Year 2000

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  • Amount Spent on Transportation=$7,417

Therefore:

(a)Percentage of the average household income in 2000 was spent on food

=\dfrac{5158}{44649} \times 100\\\\=11.55\%\\\\\approx 12\% $(to the nearest percent.)

(b)Percentage of the average household income in 2000 was spent on transportation

=\dfrac{7,417}{44649} \times 100\\\\=16.6\%\\\\\approx 17\% $(to the nearest percent.)

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