Help math ASAP ASAP math

An airplane leaves an airport at 9:00 p.M. With a heading of 270 and a speed of 610 mph. At 10:00 p.M. The pilot changes the he

timama [110]

Answer:

2330.51 miles

Step-by-step explanation:

Given that the speed of the airplane = 610 mph.

The airplane leaves an airport at 9:00 P.M. with a heading of 270 degrees and at 10:00 P.M., the pilot changes the heading to 310 degrees.

So, for 1 hour the plane is heading at 270 degrees and for 3 hours, from 10:00 p.m to 1:00 a.m, the plane is heading at 310 degrees as shown in the figure.

As, distance = time x speed, so

The distance covered at 270 degrees, $d_1 = 1\times610=610$ miles.

The distance covered at 310 degrees, $d_2 = 3\times610=1830$ miles.

Total distance covered, d, is the magnitude of the sum of vectors $\vec{d_1}$ and $\vec{d_2}$ as shown in the figure.

The angle between the vectors $\vec{d_1}$ and $\vec{d_2}$ , $\theta=310-270=40$ degree.

Magnitude of sum of the vectors \vec{d_1} and \vec{d_2},

$d= \sqrt{|\vec{d_1}|^2+|\vec{d_2}|^2+2|\vec{d_1}|\;|\vec{d_2}|\cos\theta} \\\\\Rightarrow d=\sqrt{610^2+1830^2+2|\vec{d_1}|\;|\vec{d_2}|\cos\(40^{\circ})}$

$\Rightarrow d=2330.51$ miles

Hence, at 1:00 a.m, the airplane is at a distance of 2330.51 miles from the airport.

4 0

3 years ago

What percentage of the students still receive an allowance

Mariana [72]

Answer:

I most likely think it is approximately 19%

Step-by-step explanation:

Assuming you mean still receive an allowance even though they dont do chores:

Ok In all the total number of students is 21. Out of those 21, 4 still receive an allowance even though they dont do chores. This is 4/21. Now all we have to do is convert 4/21 into a percentage. To do this we have to divide 100 by 21, then times 4 by that number:

100 / 21 = >> approximately 4.76

Now 4 times 4.76 :

4 * 4.76 = >>> approximately 19.04 % . We round it to 19%.

So the answer is 19%.

7 0

3 years ago

SportsBounceCo makes only boxes that have sides that are measured in whole inches, like the boxes you have been describing so fa

stepan [7]

Answer:

No

Step-by-step explanation:

Look at the surface area of the box formular : S = 2lw + 2lh + 2wh

When l : length. w: with and h: hight

As we often considered strange, you can always multiply a whole number by a whole number and always get a whole number, and there is no decimal number about the 3 dementions like the boxes you have been describing so far. So It is impossible.

6 0

3 years ago

Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal

tigry1 [53]

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

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.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that $\mu = 20 + 15 + 30 = 65$