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Stolb23 [73]
3 years ago
13

Juliet and Mercutio are moving at constant speeds in the xy-plane. They start moving at the same time. Juliet starts at the poin

t (0, −6) and heads in a straight line toward the point (10, 5), reaching it in 10 seconds. Mercutio starts at (7, −16) and moves in a straight line. Mercutio passes through the same point on the x-axis as Juliet, but 2 seconds after she does.How long does it take Mercutio to reach the y-axis?
Mathematics
1 answer:
juin [17]3 years ago
6 0

Answer:

  574/17 ≈ 33.765 seconds

Step-by-step explanation:

This problem begs to be solved using parametric equations for the lines of travel. Such an equation for position (P) can be written in terms of a starting point (A) and direction of travel (V) as ...

  P = A + tV

Here, the direction of travel between points A and B is V = B-A, and the time value (t) is scaled by the amount of time it takes to get there.

__

The position of Juliet as a function of time from point A to point B in 10 seconds can be written as ...

  J = A + (t/10)(B-A) = (0, -6) + (t/10)(10-0, 5-(-6))

  J = (t, 1.1t -6)

Juliet will reach the x-axis when her y-position is zero:

  1.1t -6 = 0

  t = 6/1.1 = 60/11

Her position at that point is J = (60/11, 0).

__

Mercutio's position can be described similarly. Starting at point C(7, -16), he reaches D(60/11, 0) after 60/11+2 = 82/11 seconds.

  M = C +(11t/82)(D -C) = (7, -16) +(11t/82)(60/11 -7, 0 -(-16))

  M = (7 -17/82t, 88/41t -16)

Mercutio will reach the y-axis when his x-position is zero:

  7 -17/82t = 0

  7 = 17/82t

  82/17×7 = t = 574/17 ≈ 33.765 . . . . seconds

It takes Mercutio about 33.765 seconds to reach the y-axis.

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AleksAgata [21]

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x

The table is:

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}

3 0
3 years ago
What is the area of a triangle with a<br> base of 6m and a height of 7m
Veronika [31]

Answer:

It is 21

Step-by-step explanation:

5 0
3 years ago
Please help! This is the third time I asked
Alexxx [7]
Hi,
To find K you will pick a value from the x and then the corresponding Y value. Then we will plug it into the equation that is given y=Kx

Here:
X=25 Y=160
160=k25
(Divide both sides by 25 to isolate K)
K=6.5

Then plug K value into equation
Y=6.5X

Then if you want to check if that is correct you can pick a different point on the table and plug that into the equation to see if you get the same value.

Check:
X=50

Y=6.5x50
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3 years ago
Mr.Williams physical education class lasts 7/8 hour if instruciton is 1/5 how many minutes are not spent on instruction?
g100num [7]
= 7/8 − 1/5

= ((7 × 5) − (1 × 8)) / (8 × 5)

= (35 - 8) / 40

= 27/40


SO, 27/40 minutes are NOT spend on instructions.
Hope I was able to help! :)
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3 years ago
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Answer:

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Step-by-step explanation:

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