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4 years ago

Why did little tommy drop his ice cream cone? Any answers are welcome.

2 answers:

7 0

Because the bird hit the clock tower which made the bell ring that made the cups shake and fall onto little tommy's hand and made the ice cream cone fall on the ground. Then he got hit by a bus.

pashok25 [27]4 years ago

7 0

Because little Tommy realized he was lactose intolerant.

Because little Tommy tripped and the ice cream dropped out of his hand

There was an earthquake and the ice cream fell out of little Tommy's hand

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4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

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