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a port and a radar station are 2 mi apart on a straight shore running east and west. a ship leaves the port at noon traveling no

Rom4ik [11]

Answer:

The rate of change of the tracking angle is 0.05599 rad/sec

Step-by-step explanation:

Here the ship is traveling at 15 mi/hr north east and

Port to Radar station = 2 miles

Distance traveled by the ship in 30 minutes = 0.5 * 15 = 7.5 miles

Therefore the ship, port and radar makes a triangle with sides

2, 7.5 and x

The value of x is gotten from cosine rule as follows

x² = 2² + 7.5² - 2*2*7.5*cos(45) = 39.04

x = 6.25 miles

By sine rule we have

$\frac{sin A}{a} = \frac{sin B}{b}$

Therefore,

$\frac{sin 45}{6.25} = \frac{sin \alpha }{7.5}$

α = Angle between radar and ship α

∴ α = 58.052

Where we put

$\frac{sin 45}{6.25} = \frac{sin \alpha }{x}$ to get

$\frac{x}{6.25} = \frac{sin \alpha }{sin 45}$ and differentiate to get

$\frac{\frac{dx}{dt} }{6.25} = cos\alpha\frac{\frac{d\alpha }{dt} }{sin 45}$

$\frac{15sin45 }{6.25cos\alpha } =\frac{d\alpha }{dt} }$ = 3.208 degrees/second = 0.05599 rad/sec.

6 0

3 years ago

________________________

xenn [34]

✩ Answer:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

$\bold{Hello!}\\\bold{Your~answer~is~below!}$

✩ Step-by-step explanation:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

✺ Divide both sides by −3. Since −3 is negative, the inequality direction is changed:

-3 ÷ -3 = Cancels Out
Turns into: $\frac{-9}{-3} >5x-2$

✺ Divide −9 by −3 to get 3. Since they are both negatives it turns into a positive:

-9 ÷ -3 = 3
Turns into: $3 > 5x - 2$

✺ Swap sides so that all variable terms are on the left hand side. This changes the sign direction once more:

Turns into: $5x-2$

✺ Add 2 to both sides:

Turns into: $5x$

✺ Add 3 and 2 to get 5:

3 + 2 = 5
Turns into: $5x$

✺ Divide both sides by 5. Since 5 is positive, the inequality direction remains the same:

5 ÷ 5 = Cancels Out
Turns into: $x$

✺ Divide 5 by 5 to get 1:

5 ÷ 5 = 1

✺ So your answer is B, $\boxed{x$ .

(Number line is below.)

$Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex$

5 0

3 years ago

Read 2 more answers

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose

Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)

Step-by-step explanation:

Notation and definitions

n=50 represent the sample size

$\bar X= 27.2$ represent the sample mean

$s=5.83$ represent the sample standard deviation

m represent the margin of error

Confidence =88% or 0.88

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by $\alpha=1-0.88=0.12$ and $\alpha/2 =0.06$ . The degrees of freedom are given by:

$df=n-1=50-1=49$

We can find the critical values in R using the following formulas:

qt(0.06,49)

[1] -1.582366

qt(1-0.06,49)

[1] 1.582366

The critical value $tc=\pm 1.582366$

Calculate the margin of error (m)

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=1.582366 \frac{5.83}{\sqrt{50}}=14.613$

With R we can do this:

m=1.582366*(5.83/sqrt(50))

m

[1] 1.304639

Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$27.02 - 1.582366 \frac{5.83}{\sqrt{50}}=25.715$

$27.02 + 1.582366 \frac{5.83}{\sqrt{50}}=28.325$

Using R the code is:

lower=27.02-m;lower

[1] 25.71536

upper=27.02+m;upper

[1] 28.32464

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)

6 0

3 years ago

Please Help ASAP!!! I'm Timed!!! Will give brainliest to first correct answer!!! Hurry!!

Inessa05 [86]

Answer: If you are reflecting the triangle(or coordinate points in general) off of the x or y axis on the upper quadrants, then the reflection would be negative for x.

If you are reflecting the triangle(or coordinate points in general) off of the x or y axis on the lower quadrants, then the reflection would be negative for y.

This is because the lower quadrants are usually negative and the upper quadrants are usually positive according to the x axis. The same thing vice verse with y.

These are the rules that I’m guessing your trying to find. Hope this helps!

3 0

3 years ago

PLS HELP I WILL GIVE BRAINLY THINGY

VashaNatasha [74]

Answer: The y is going to be 7

Explanation: Because 5y/35 divide 5 both sides cancel the both 5's and y stays by itself and 35/5 equals 7. 7*5= 35

8 0

3 years ago