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2 years ago

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A train leaves at 12.13 and arrives at its destination at 13.03. If the train travelled 83 km, what was it's average speed in km

/h? Give your answer rounded to 1 dp

1 answer:

Mama L [17]2 years ago

3 0

Answer:

1.7km/h

Step-by-step explanation:

speed is distance over time,the time difference is 50 min and the distance is 83,you divide 83 by 50 to give you the answer

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Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

2 years ago

Which is f(-3) for the quadratic function graphed?<br> -9<br> -3<br> 0<br> 9

KATRIN_1 [288]

Answer:

9

Step-by-step explanation:

4 0

2 years ago

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If your car can travel 20 miles on 1 gallon of fuel how many litres were used to travel 130 miles? Step by step

Bezzdna [24]

Answer:2600 Gallons

Step-by-step explanation: You first have to take 130 and times it by 20 then times it by 1. make sure you add labels

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2 years ago

What is 2/5 plus 1/3

leva [86]

First, you need to get the denominators (the bottom number) the same. The smallest number to get them to is 15.

So, what you need to do is take 2/5 and multiply the bottom by 3 to get 15, and since you did it to the bottom, you need to do it to the top too. So you would get, 6/15.

Then, for 1/3, take the bottom number and multiply it by 5. Then, since you did it to the bottom, do it to the top as well. You would get 5/15.

Then, you need to put them side by side. You don't add the bottom, so your denominator would remain 15, but your numerator (top) would get added.

<u> 6</u> + <u>5</u> = <u>11</u>
15 15 15

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2 years ago

Y is inversely proportional to x, when Y = 2, x = 4.<br><br>Find the value of x when Y = 4.

ratelena [41]

The value of x when y =4 is 2

<h3>How to solve for x?</h3>

An inverse proportion is represented as:

k = yx

Where

k represents the constant of proportion

When y = 2, x = 4.

So, we have:

k =2 * 4

k = 8

Substitute k = 8 in k = yx

So, we have:

yx = 8

When y = 4, we have:

4x = 8

Divide by 4

x = 2

Hence, the value of x when y =4 is 2

Read more about variation at:

brainly.com/question/14254277

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8 0

1 year ago