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Alenkinab [10]
3 years ago
6

Two row boats start at the same location, and start traveling apart along straight lines which meet at an angle of π3. Boat A is

traveling at a rate of 5 miles per hour directly east, and boat B is traveling at a rate of 10 miles per hour going both north and east. How fast is the distance between the rowboats increasing 3 hours into the journey?
Mathematics
1 answer:
alina1380 [7]3 years ago
5 0

Answer:

  5√3 miles per hour

Step-by-step explanation:

Throughout their journey, the component of velocity of rowboat B to the east is the same as that of rowboat A:

  (10 mph)(cos(π/3)) = 5 mph

Meanwhile, the component of velocity of rowboat B to the north is ...

  (10 mph)(sin(π/3)) = 5√3 mph

Since rowboat A is always traveling in a direction that is at right angles to the direction between the boats, it contributes nothing to their relative speed. Since rowboat B is always directly north of rowboat A, its speed to the north is their relative speed.

The distance between the rowboats is increasing at 5√3 mph ≈ 8.66 mph.

You might be interested in
X^2-2x+15 in quadratic equation​
Arturiano [62]

Answer:

No solution

Step-by-step explanation:

There is not a real nor an imaginary solution to this equation. You can use a radical calculator to verify.

3 0
2 years ago
A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0
3 years ago
If 19 represents 228 gallons, what is the value of 6 units
levacccp [35]

Answer:

72 gallons

Step-by-step explanation:

we know that

19 units represent 228 gallons

so

using proportion

Find out how many gallons represent 6 units

Let

x ---> the number of gallons for 6 units

\frac{228}{19}\ \frac{gallons}{units} =\frac{x}{6}\ \frac{gallons}{units}\\\\x=228(6)/19\\\\x=72\ gallons

7 0
3 years ago
Find the solution set of this equation.<br> y^2-11y=0 <br> separate the two values with a comma.
Tanya [424]

Answer:

0,11

Step-by-step explanation:

y^2-11y=0

y(y-11)=0 we have transformed the equation into a product

a product can be zero only if one of the factors is 0

so the two solutions are

y=0

and y-11=0  y=11

6 0
3 years ago
A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduc
Snezhnost [94]

Answer:

The test statistic value is, <em>t</em> = -5.245.

The effect size using estimated Cohen's d is 2.35.

Step-by-step explanation:

A paired <em>t</em>-test would be used to determine whether the remedial tutoring has been effective for the statistics tutor's five students.

The hypothesis can be defined as follows:

<em>H</em>₀: The remedial tutoring has not been effective, i.e. <em>d</em> = 0.

<em>Hₐ</em>: The remedial tutoring has been effective, i.e. <em>d</em> > 0.

Use Excel to perform the Paired <em>t</em> test.

Go to Data → Data Analysis → t-test: Paired Two Sample Means

A dialog box will open.

Select the values of the variables accordingly.

The Excel output is attached below.

The test statistic value is, <em>t</em> = -5.245.

Compute the effect size using estimated Cohen's d as follows:

\text{Cohen's d}=\frac{Mean_{d}}{SD_{d}}

                =\frac{0.54}{0.23022}\\\\=2.34558\\\\\approx 2.35

Thus, the effect size using estimated Cohen's d is 2.35.

8 0
3 years ago
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