All categories

2 years ago

Two planes are flying away from Toronto Pearson International Airport. The Air Canada

Mathematics

1 answer:

erica [24]2 years ago

5 0

Answer:

1832 miles

Step-by-step explanation:

First we need to find the angle between the routes of the planes.

If one is N30°W and the other is S45°W, we can find the angle between the routes with the following equation:

30 + angle + 45 = 180

angle = 105°

Then, we need to find the distance travelled by each plane, using the formula:

distance = speed * time

The time is 1.5 hours, so we have that:

distance1 = 800 * 1.5 = 1200 km

distance2 = 750 * 1.5 = 1125 km

Now, to find the distance between the planes, we can use the law of cosines:

distance^2 = 1200^2 + 1125^2 - 2*1200*1125*cos(105)

distance^2 = 3356214.43

distance = 1832 miles

You might be interested in

Three friends attended a carnival. John rode the rollercoaster twice, the bumper cars three times, and the Ferris wheel once. He

Paha777 [63]

Answer:

The system of equations is the option A

Step-by-step explanation:

Let

x ------> the number of tickets for the roller-coaster

y ------> the number of tickets for the bumper

z ------> the number of tickets for the Ferris wheel

we know that

The system of equations is equal to

John

2x+3y+z=42

Darren

3x+y+2z=36

Shelley

x+2y+3z=32

therefore

The system of equations is the option A

5 0

2 years ago

Alex wants to have $3000 in his bank account after 4 years. If the account earns 6% interest compounded 2 times per year, how mu

lesantik [10]

3000 = p( 1 + .06/2)^(4 * 2)

3000 = p(1.03)⁸ 

p = 3000/ 1.03⁸ 

p = 2368.2277029 

$2368.23 <-----

3 0

2 years ago

Read 2 more answers

Adding/Subtracting rational expressions

Leona [35]

7]
6/(x-1)-5x/4
subtracting the above we put the fraction under the same denominator:
6/(x-1)-5x/4
multiplying the denominators we get:
4(x-1)
thus subtracting we get:
6/(x-1)-5x/4
=(4*6-5x(x-1))/[4(x-1)]
=[24-5x^2+5x]/(4x-4)
Answer:
(-5x^2+5x+24)/(4x-4)

9]
3/(x+7)+4/(x-8)
the common denominator is:
(x+7)*(x-8)=(x+7)(x-8)
thus adding the fractions we put them under the same denominator as follows:
[3(x-8)+4(x+7)]/[(x+7)(x-8)]
=[3x-24+4x+28]/[(x+7)(x-8)]
=(7x+4)/[(x+7)(x-8)]

5 0

2 years ago

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the pro

lisov135 [29]

Answer:

0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.

The sketch is drawn at the end.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 0°C and a standard deviation of 1.00°C.

This means that $\mu = 0, \sigma = 1$