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3 years ago

Here is part of a timetable for the Paris to Montpellier express train service.

Mathematics

1 answer:

evablogger [386]3 years ago

3 0

Answer:

772.8 km

Step-by-step explanation:

Speed is the rate of change of distance. Speed is the ratio of distance travelled to time taken. Average speed is the ratio of the total distance travelled to the total time taken, it is given by:

Average speed = Total distance / total time

The 20 07 train leaves Paris at 20:07 and reaches Montpellier at 23:34. This means that the total time taken is 3 hours 27 minutes, that is 3.45 hours.

Given that average speed is 224 km/h, hence:

Average speed = total distance / total time

224 km/h = total distance / 3.45 h

total distance = 224 * 3.45 = 772.8 km

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Textbook: Please write as an expression involving functions of Θ alone.

Setler [38]

Step-by-step explanation:

tan(Θ + 30°)

Use angle sum formula:

tan(A + B) = (tan A + tan B) / (1 − tan A tan B)

So we can write this as:

(tan Θ + tan 30°) / (1 − tan Θ tan 30°)

tan 30° = 1/√3, so:

(tan Θ + 1/√3) / (1 − 1/√3 tan Θ)

Multiply top and bottom by √3:

(√3 tan Θ + 1) / (√3 − tan Θ)

6 0

4 years ago

Let v1=(3,5) and v2=(-4,7).

Nat2105 [25]

PART A

The given vectors are,

$v_1 = \: < \: 3 , \: 5 \: >$

$v_2 = \: < \: - 4 , \: 7 \: >$

The magnitude of the vector

$v= \: < \: x , \: y \: > \:$

is given by:

$|v| = \sqrt{ {x}^{2} + {y}^{2} }$

This implies that,

$|v_1| = \sqrt{ {3}^{2} + {5}^{2} }$

$|v_1| = \sqrt{9 + 25}$

$|v_1| = \sqrt{34}$

$|v_2| = \sqrt{ {( - 4)}^{2} + {7}^{2} }$

$|v_2| = \sqrt{ 16+ 49}$

$|v_2| = \sqrt{65}$

PART B

To find the unit vector in the direction of a given vector, we divide by the magnitude of that vector.

$^{ - } _{v_1} = \: < \: \frac{3}{ \sqrt{34} } , \: \frac{5}{ \sqrt{34} } \: >$

Rationalize the denominator.

$^{ - } _{v_1} = \: < \: \frac{3\sqrt{34}}{ 34 } , \: \frac{5\sqrt{34}}{ 34 } \: >$

Also,

$^{ - } _{v_2} = \: < \: \frac{ - 4}{ \sqrt{65} } , \: \frac{7}{ \sqrt{65} } \: >$

$^{ - } _{v_2} = \: < \: \frac{ - 4\sqrt{65}}{ 65 } , \: \frac{7\sqrt{65}}{ 65 } \: >$

PART C

The sketch of the given vectors as well as their unit vectors are shown in the attachment.

3 0

3 years ago

Please help this is due very soon show the steps in how you found the answer

meriva

Answer:

4x-6

Step-by-step explanation:

this is correct ans

4 0

3 years ago

Find the quotient. Write in simplest form: 1/16 ÷ 3/4

Sav [38]

The answer would be 1/12.

1/16 * 4/3

1* 4 over 16 * 3

4 over 16 * 3

4/48

1/12.

3 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through the point

Dimas [21]

Answer:

y=-5x-4

Step-by-step explanation:

y=mx+b

-5=-5m+b

-5=-1+b

b=-4

y=-5x-4

7 0

3 years ago