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DIA [1.3K]
3 years ago
13

Using a Table to find the Constant of Proportionality

Mathematics
1 answer:
muminat3 years ago
4 0

Answer:

k = 12

Step-by-step explanation:

The constant of proportionality k is the ratio

k = \frac{laps}{swimmers}

Use any ordered pair from the table to find k

Using number of laps = 240, number of swimmers = 20 , then

k = \frac{240}{20} = 12

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A raft and a motorboat simultaneously leave from the same point and move down the river. After 2 hours the motorboat turns aroun
lesya692 [45]

Answer:

2 hours

Step-by-step explanation:

Let x mph be the speed of motorboat in still water and y mph be the speed of current.

A raft and a motorboat simultaneously leave from the same point and move down the river, then speeds down the river are:

        motorboat =  x + y mph

        raft = y mph

In two hours they will cover:

        motorboat = 2(x+y) miles

        raft = 2y miles

After 2 hours the motorboat turns around and starts moving towards the raft (against the current), so its speed is now x - y mph.

Let t be the time they move towards each other. In t hours, they cover

        motorboat = t(x - y) miles

        raft = ty miles

The distance from the starting point to the turning point is the same as the sum of the distances the raft covers and the motorboat covers after turning around, so

2(x+y)=2y+t(x-y)+ty \\ \\2x+2y=2y+tx-ty+ty\\ \\2x=tx\\ \\t=2\ hours

6 0
3 years ago
Find the standard equation of the parabola that satisfies the given conditions. Also, find the length of the latus rectum of eac
lakkis [162]

Answer:

The standard parabola

                                y² = -18 x +27

Length of Latus rectum = 4 a = 18

                         

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given focus : (-3 ,0) ,directrix  : x=6

Let P(x₁ , y₁) be the point on parabola

PM perpendicular to the the directrix L

                          SP² = PM²

                (x₁ +3)²+(y₁-0)²  = (\frac{x_{1}-6 }{\sqrt{1} } )^{2}

              x₁²+6 x₁ +9 + y₁² = x₁²-12 x₁ +36

                          y₁² = -18 x₁ +36 -9

                           y₁² = -18 x₁ +27

The standard parabola

                                y² = -18 x +27

    Length of Latus rectum = 4 a = 4 (18/4) = 18

                         

5 0
3 years ago
Suppose that the candy machine holds exactly 650 skittles, and every time someone inserts a quarter, exactly 7 skittles come out
Lady bird [3.3K]

Answer:

510 skittles left in the machine

Step-by-step explanation:

7 skittles x 20 quaters = 140 skittles taken out

650 - 140 = 510

7 0
3 years ago
A sailboat rental company charges a fee of $78.75 plus $80.25 per hour to rent a sailboat. A second rental company charges custo
Varvara68 [4.7K]

Answer:

3.69 hours

Step-by-step explanation:

y = 80.25x + 78.75

y = 95.75 + 40

85.25x + 78.75 = 95.75 + 40

-85.25x   -40        -85.25x  -40

38.75/10.5 = 10.5x/10.5

3.690476190..... = x

rounding

3.69 = x

4 0
3 years ago
12. Phillip deposited $450 in an account that earns
Salsk061 [2.6K]
This is your genuine answer

7 0
3 years ago
Read 2 more answers
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