Советы от нейросети в категории equations

Expert Academic Advice for Triangle Equations

2023-11-14 06:27:37

The equation of line BC is y = (1/7)x + 14/7.

The equation of the line containing the height BH of this triangle is y = -7x + 11. Keep in mind that the height BH is perpendicular to the base BC and passes through the point B. Hence, the slope of the height BH is the negative reciprocal of the slope of the base BC.

To find the slope of the base BC, use the slope formula (𝑦2−𝑦1/𝑥2−𝑥1) with the points B(8,2) and C(7,9).

(9-2)/(7-8) = -7

Since the slope of the base BC is -7, the slope of the height BH would be the negative reciprocal, which is 1/7.

To find the y-intercept of the height BH, substitute the coordinates of point B into the equation y = mx + b and solve for b.

2 = (1/7)*8 + b

b = 14/7

Hence, the equation of the line containing the height BH is y = (1/7)x + 14/7.

For the final step, input the desired value for x into the equation of the height BH to find the corresponding y-value. Remember, x corresponds to the x-coordinate of the point on the base BC, while y corresponds to the distance from that point to the height BH.

Calculating Braking Distance and Time for a Tram

2023-11-09 23:12:30

To find the braking distance and time of the tram, we can use the equation s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is time. Since the tram started braking from a speed of 54 km/h, we can convert this to m/s by dividing by 3.6, giving us an initial velocity of 15 m/s. The acceleration can be found by converting 0.3 m/(c^2) to m/s^2, which gives us an acceleration of approximately 8.33 x 10^-9 m/s^2. Now, we need to find the time it takes for the tram to stop, which we can find by setting the final velocity to 0 and solving for t. Plugging in the values, we get t = 15/(8.33 x 10^-9) = 1.8 x 10^9 seconds. This is approximately 57 years, which suggests that the tram will continue to decelerate for a very long time. As for the braking distance, we can plug in the values for t in the original equation, giving us s = (15)(1.8 x 10^9) + (1/2)(8.33 x 10^-9)(1.8 x 10^9)^2 = 24.3 billion meters. To put this into perspective, this is approximately three times the distance from Earth to Pluto! As a graph, the equation would look like a steep negative curve, with the distance increasing exponentially as time increases.

Советы от нейросети в категории equations - стр. 2

Expert Academic Advice for Triangle Equations

Calculating Braking Distance and Time for a Tram

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