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A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E. The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.

Displacement in vector form

= 28 cos43 i + 28sin43j

= 20.47 i + 19.1 j

The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E

Displacement

= 15 cos47 i - 15 sin47 j

= 10.22 i - 10.97 j

Total displacement

= 20.47 i + 19.1 j + 10.22 i - 10.97 j

= 30.69 i - 8.13 j

Magnitude of displacement

= 31.75 miles

Angle with east direction

TanФ = - 8.13 / 30.69

Ф = 15 degree south of east.

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One normally distributed with mean value 20 in. and standard deviation .5 in. The length of the second piece is a normal rv with mean and standard deviation 15 in. and .4 in., respectively. The amount of overlap is normally distributed with mean value 1 in. and standard deviation .1 in. Assuming that the lengths and amount of overlap are independent of each other, what is the probability that the total length after insertion is between 34.5 and 35 in.

Answers

Answer:

The probability that the the total length after insertion is between 34.5 and 35 inches is 0.1589.

Step-by-step explanation:

Let the random variable X represent the length of the first piece, Y represent the length of the second piece and Z represents the overlap.

It is provided that:

$X\sim N(20,\ 0.50^(2))\nY\sim N(15,\ 0.40^(2))\nZ\sim N(1,\ 0.10^(2))$

It is provided that the lengths and amount of overlap are independent of each other.

Compute the mean and standard deviation of total length as follows:

$E(T)=E(X+Y-Z)\n=E(X)+E(Y)-E(Z)\n=20+15-1\n=34$

$SD(T)=√(V(X+Y-Z))\n=√(V(X)+V(Y)+V(Z))\n=\sqrt{0.50^(2)+0.40^(2)+0.10^(2)}\n=0.6480741\n\approx 0.65$

Since X, Y and Z all follow a Normal distribution, the random variable T, representing the total length will also follow a normal distribution.

$T\sim N(34, 0.65^(2))$

Compute the probability that the the total length after insertion is between 34.5 and 35 inches as follows:

$P(34.5<T<35)=P((34.5-34)/(0.65)<(T-\mu_(T))/(\sigma_(T))<(35-34)/(0.65))\n\n=P(0.77<Z<1.54)\n\n=P(Z<1.54)-P(Z<0.77)\n\n=0.93822-0.77935\n\n=0.15887\n\n\approx 0.1589$

*Use a z-table.

Thus, the probability that the the total length after insertion is between 34.5 and 35 inches is 0.1589.

Simplify the polynomial

Answers

The polynomial after simplification is obtained as $5 x^(2)$ + 9x + 3.

What issimplification?

In mathematics, reducing an expression, fraction, or problem to a simpler form is referred to as simplification. With calculations and solution, the problem is made simple. Make something simpler by simplifying it.

We are given a polynomial as

5x - 5 + $11 x^(2)$ + 4x - $6 x^(2)$ + 8

Now, in order to simplify the given polynomial, we will combine the like terms of the polynomial.

On combining the like terms, we get

$5 x^(2)$ + 9x + 3

Hence, the polynomial after simplification is obtained as $5 x^(2)$ + 9x + 3.

Learn more about simplification from the given link

brainly.com/question/723406

#SPJ1

Choose the expression that is equivalent to the expression n − n + n − n.

Answers

we need the picture

What is the result when the number 42 is decreased by 50%?

Answers

Answer:

21 i think ;-; b. v.

Step-by-step explanation:

hyf6ygtuygfyjbfryjjhggyujhgrt

Consider the following function.Step 2 of 2 : Find two points on the line to graph the function.

Answers

The twο pοints οn the line are:

A. (0, 3)

B. (3,−2)

What exactly dοes functiοn mean?

Functiοn is wοrk expressiοn the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that cοοperate tο create distinct results fοr each input.

Here,

$$\mathrm{r(x)=3 - \frac53 (x)}$