At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?

Step 1

Find the slope of the given line

Let

[tex]M(-3,5)\ N(2,0)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{0-5}{2+3}[/tex]

[tex]m=\frac{-5}{5}[/tex]

[tex]m=-1[/tex]

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have  

[tex]m=-1[/tex]

point N [tex](2,0)[/tex]

substitute the values

[tex]y-0=-1(x-2)[/tex]

[tex]y=-x+2[/tex]

therefore

the answer is

[tex]y=-x+2[/tex]

Final Answer:

Word done = 31 units

Explanation:

To find the work done by a force field [tex]$\mathbf{F}(x, y, z)$[/tex] on a particle moving along a path, we can use the line integral of the force field along that path.

First, we need to define the force field [tex]$\mathbf{F}(x, y, z)$[/tex] and the parametric equations for the line segment.

Given the force field

[tex]$$\mathbf{F}(x, y, z) = \langle y + z, x + z, x + y \rangle,$$[/tex]
we have the following components:

[tex]F_x &= y + z, \\\\F_y &= x + z, \\\\F_z &= x + y.[/tex]

Now, let's find the parametrization of the line segment from the point (1,0,0) to the point (5,3,2). We can define a vector [tex]$\mathbf{r}(t)$[/tex] that describes this line segment by

[tex]$$\mathbf{r}(t) = \mathbf{r_0} + t(\mathbf{r_1} - \mathbf{r_0}),$$[/tex]

where [tex]$\mathbf{r_0} = \langle 1, 0, 0 \rangle$[/tex] is the starting point, [tex]$\mathbf{r_1} = \langle 5, 3, 2 \rangle$[/tex] is the ending point, and t is a parameter that goes from 0 to 1.

So we have

[tex]\mathbf{r}(t) &= \langle 1, 0, 0 \rangle + t(\langle 5, 3, 2 \rangle - \langle 1, 0, 0 \rangle) \\\\ &= \langle 1, 0, 0 \rangle + t\langle 4, 3, 2 \rangle \\\\ &= \langle 1 + 4t, 3t, 2t \rangle.[/tex]

From the parametric equation, we have the components:

[tex]x(t) &= 1 + 4t, \\\\y(t) &= 3t, \\\\z(t) &= 2t.[/tex]

The line integral of the force field along the path can be computed by

[tex]$$W = \int_C \mathbf{F} \cdot d\mathbf{r},$$[/tex]

where [tex]$d\mathbf{r}$[/tex] is the differential element along the path C, and the dot product represents the scalar product of the force field and the differential path element.

We can express [tex]$d\mathbf{r}$[/tex] in terms of t as

[tex]$$d\mathbf{r} = \mathbf{r}'(t) dt = \langle \frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt} \rangle dt = \langle 4, 3, 2 \rangle dt.$$[/tex]

Then the work done is

[tex]W &= \int_{t=0}^{t=1} \mathbf{F}(x(t), y(t), z(t)) \cdot \mathbf{r}'(t) dt \\\\ &= \int_{0}^{1} \langle 3t + 2t, 1 + 4t + 2t, 1 + 4t + 3t \rangle \cdot \langle 4, 3, 2 \rangle dt \\\\ &= \int_{0}^{1} [(5t)(4) + (6t + 1)(3) + (7t + 1)(2)] dt \\\\ &= \int_{0}^{1} [20t + 18t + 3 + 14t + 2] dt \\\\ &= \int_{0}^{1} [52t + 5] dt \\\\ &= [26t^2 + 5t]_{0}^{1} \\\\ &= 26(1)^2 + 5(1) - (26(0)^2 + 5(0)) \\\\ &= 26 + 5 \\\\ &= 31.[/tex]


So, the work done by the force field [tex]$\mathbf{F}(x, y, z)$[/tex] on the particle as it moves along the line segment from (1, 0, 0) to (5, 3, 2) is 31 units of work.

compare the 5 and 10 dimension then the 7 and 14 dimensions

10/5 =2

14/7 =2

 they both are the same ratio/factor

 the factor is 2

Answer:

2:1

Step-by-step explanation:

it asks for the scale since 5 x 2 = 10 and 7 x 2 = 14

the scale is 2 : 1

Answer:

17

Step-by-step explanation:

Eliminating parentheses, we have ...

... 1 - 5q +2·2.5q +2·8

... = 1 -5q +5q +16 . . . . . carry out the multiplication

... = q(-5+5) +(1 +16) . . . . group like terms

... = q·0 +17 . . . . . . . . . . . combine like terms

... = 17

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given that Mark earns $135 for selling a $1500 refrigerator.

Since proportions states that two fractions are equal , so we will use proportions to find the same commission rate with the listed price from our given choices.

We can set proportion for commission and listed price as:

[tex]\frac{\text{Commission}}{\text{Listed price}}=\frac{135}{1500}[/tex]

Let us compare our given choices one by one.

A. $36 commission on a $400 dryer.

[tex]\frac{36}{400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{9}{100}=\frac{9}{100}[/tex]

[tex]0.09=0.09[/tex]

We can see that commission rates for both items are equal, therefore, option A is the correct choice.

B. $40 commission on a $500 dryer sale.

[tex]\frac{40}{500}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{2}{25}=\frac{9}{100}[/tex]

[tex]0.08\neq 0.09[/tex]

We can see that both commission rates are different, therefore, option B is not a correct choice.

C. $210 commission on $1400 oven sale.

[tex]\frac{210}{1400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{3}{20}=\frac{9}{100}[/tex]

[tex]0.15\neq 0.09[/tex]  

Since the commission rates are different, therefore, option C is not a correct choice.

D.  $30 commission on a $600 freezer sale.

[tex]\frac{30}{1400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{3}{140}=\frac{9}{100}[/tex]

[tex]0.0214\neq 0.09[/tex]  

Since the commission rates are different, therefore, option D is not a correct choice.

Answer:

The correct answers are options B and C.                            

Step-by-step explanation:                      

B It has four right angles.

C It has two pairs of parallel opposite sides.

All angles are right angles by definition of a rectangle. The rectangle has 2 pairs of parallel opposite sides.              

Option A is wrong as its a square whose all 4 sides have equal length.

Answer:

The correct answers are

(-2,1)

(-4,2)

(1,-1)

Step-by-step explanation:

hope dis help u guys, habe a good rest of ya day!

Answer:

(2.2, 0.5, 1.1)

Step-by-step explanation:

The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...

... L = (2, 0, 1) + t(2, 5, 1)

We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.

... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane

... 5 + 30t = 8 . . . . . simplify

... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)

For this value of t, L is ...

... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)

Answer:

462.25

Step-by-step explanation:

At an automobile factory, the number of parts are made in 4 hours = 1849.

We have to calculate the average rate of production per hour.

We will divide the production of parts in 4 hours by 4 to get the number of parts made per hour.

The average rate of production in one hour = [tex]\frac{1849}{4}[/tex]

                                                                         = 462.25/hour

462.25 parts are made per hour.

The likelihood that the flight will be no more than 5 minutes late would be equal to a flight that arrives between 2 hours and 2 hours and 10 minutes.

So the answer would be:

P (5 late or less) = 10 * 1/20 = 0.5

The answer is 0.5

But if we are looking for the probability of the flight that would be 10 minutes late, the likelihood of that event would be 0.25.

Final answer:

The probability that a Delta airlines flight from Cincinnati to Tampa will be no more than 5 minutes late, given that the actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes, is 0.50.

Explanation:

The question deals with the uniform distribution of flight times and calculating the probability that a flight will be no more than 5 minutes late. Assuming flight times are uniformly distributed between 2 hours (120 minutes) and 2 hours, 20 minutes (140 minutes), the total range of flight times is 20 minutes (140 minutes - 120 minutes).

Delta airlines quotes a flight time of 2 hours, 5 minutes, which is 125 minutes. Therefore, a flight being no more than 5 minutes late means the flight time would be at most 130 minutes. To find the probability that the flight time is 130 minutes or less, we calculate the proportion of the distribution that falls within this range.

The probability that the flight will be no more than 5 minutes late is the length of the interval from 120 minutes to 130 minutes divided by the total range (20 minutes), which is (130 - 120) / 20 = 10 / 20 = 0.5. Thus, the probability is 0.50 to two decimal places.

Final answer:

Three people can share fifths by dividing one pie into five slices and each taking three, or dividing three pies into fifteen slices and each person getting one slice from each pie. Both methods ensure each person receives three-fifths of a pie.

Explanation:

Two ways that three people can share fifths involve division and allocation of pie (or any other divisible whole). One way is to take a single pie, divide it into five equal slices, and each person takes three slices. However, since we need to divide these among three people and a pie has only five slices, we'll end up with a fraction of a slice per person. The second way is to start with three pies, divide them so that there are a total of fifteen slices (five slices per pie), and then each person gets one slice from each pie, totaling three slices per person.

Here are two arithmetic representations of the scenarios:

Whether we are dealing with one pie or three, each person ends up with the same fraction of the total available pie: three-fifths.

Answer:

Third option:

[tex]A(x)\approx 2,000(1.065)^x[/tex]

Step-by-step explanation:

Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:

2,000(1+0.004) = 2,000(1.004)

I just applied the simple interest formula.

Then after the second month we will have:

[tex]2,000(1.004)(1.004) = 2,000(1.004)^2[/tex]

And so on each month.

So at the end of the first year (12 months) we have:

[tex]2,000(1.004)^{12}[/tex]

But we also earn an additional 1.5% in the year, so we will have:

[tex]2,000(1.004)^{12}(1.015)[/tex]

At the end of the second year we will have:

[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]

At the end of the third year:

[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]

And so on,

So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:

[tex]2,000[(1.004)^{12}(1.015)]^x[/tex]

We use our calculator to simplify that inside the brackets:

[tex](1.004)^{12}(1.015)=1.06481[/tex]

Rounding  to the third decimal place we get: 1.065

So notice the amount in the savings after x years will be:

[tex]2,000(1.065)^x[/tex]

Since they want it in function notation we just write the A(x) that denotes the amount in the savings:

[tex]A(x)\approx 2,000(1.065)^x[/tex]

Julianna will earn $22,579.20 if she works for 46 weeks, which is closest to the option D) $22,500.

To calculate the amount of money Julianna will earn if she works for 46 weeks, we need to multiply the number of work hours per week (32) by the hourly wage ($14.15), and then multiply that result by the number of weeks worked (46). This can be calculated as follows:

Total earnings = (32 hours/week) × ($14.15/hour) × (46 weeks)

Total earnings = $22,579.20

Therefore, the closest amount of money Julianna will earn if she works for 46 weeks is $22,579.20, which is closest to option D) $22,500.

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