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aev [14]
3 years ago
12

The following graph represents the distance a commercial airplane travels over time, at cruising speed and an altitude of 35,000

feet. In fact, the distance the airplane travels at cruising speed is directly proportional to the time it travels. Using complete sentences, describe what the points (0, 0) and (4, 2268) represent.

Mathematics
1 answer:
ANEK [815]3 years ago
3 0

Answer:

see the explanation

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the time in hours

y ----> the distance in miles

<em>Find the value of k</em>

For the point (4,2268)

k=\frac{2,268}{4}=567\ mph

The slope represent the speed of the airplane

so

The linear equation is

y=567x

Part 1 :

The point (0,0) represents the starting point of the aircraft, when the time and distance are equal to zero. The cruising starts when time t = 0.

Part 2 :

The  point  (4, 2268) represents the plane after 4 hours of cruise , and shows it has traveled a distance of 2268 miles after 4 hours

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Find the nature of the root
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3) Real and distinct

4) Real and distinct

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Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

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If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

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3) \frac{2}{x} + \frac{3}{x} = x - 4

⇒ 5 = x² - 4x

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So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

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So, the roots will be real and distinct.

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Hence, the roots will be real and distinct.

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So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

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