A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?

Answers

Answer 1

The speed of the wind and the speed of the dragon in still air are respectively;  142.5 mph and 7.5 mph

How to calculate the speed?

The dragon flew 300 miles with the wind in two hours.

After flying against the wind for two hours, he had made 270 miles of the return trip.

Let s be the speed in still air

Let w be the speed of the wind

Thus;

(s - w) = effective speed against the wind

and

(s + w) = effective speed with the wind

We know that;

distance = time * effective speed

Thus;

2(s + w) = 300

2(s - w) = 270

This can be simplified to get;

s + w = 150   -----(1)

s - w = 135   -----(2)

Add both equations to get;

2s = 285

s = 285/2

s = 142.5 mph.

Then, plane speed in still air is;

142.5 + w = 150

w = 150 - 142.5

w = 7.5 mph is the speed of the wind

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Related Questions

A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.​

Answers

Answer: He have to pay $172.5 if he buys 150 such articles.

72 articles for --> $82.80
1 article for - - - > 82.80/72

150 articles for --> (82.80/72)*150
                           = $172.5

Answer:

$172.5

Step-by-step explanation:

Given:

Shopkeeper buys = 72 articles

Price = $ 82.8

To Find:

The amount he'll need to pay If he buys 150 articles.

Solution:

Amount if he buys 150 articles

[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]

[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]

[tex]= \$ (150* 1.15)[/tex]

[tex] = \$172.5[/tex]

So we can conclude that:

$172.5 he will have to pay if he buys 150 such articles.

Help pls ???????????

Answers

The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.

The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)

How to find the second derivative?

1)  We are given the function;

s(x) = 4/(1 + 2e^(-0.2x)

First derivative is;

ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²

Second Derivative is;

d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³

At x = 0;

d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³

d²s/dx² = 8/675

B) We are given the function;

k(t) = e^(-3t²)

The first derivative is;

dk/dt = -6te^(-3t²)

The second derivative is;

k''(t) = (36t² - 6)e^(-3t²)

At t = 1, we have;

k''(t) = (36(1)² - 6)e^(-3(1²))

k"(t) = 1.494

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The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?

Answers

The number of cars that have passed through the intersection is 245.

How many cars passed through the intersection?

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is; c = wk

Where:

c = number of carsw = number of wrecks k = constant of proportionality

1085 = k31

k = 1085 / 31

k = 35

c = 7 x 35

c = 245

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How do you round 56.053 to the nearest whole number

Answers

Answer:

56

Step-by-step explanation:

all your doing is removing the .053 to get your whole number

What is the domain of the function shown on the graph?

Answers

The asnwer is C

for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity

Please give brainliest

Assume the domain of the function is {1,2,3,...}. Determine the theta notation for the function f(n)=7n^2+4n+2

Answers

We have that O(n²) is the theta notation for 7n² + 4n + 2.

Let's give big-Oh a formal definition:

O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}

To show this

We need to find c and n₀ such that:

7n² + 4n + 2 <= cn² for all n >= n₀ .

Divide both sides by n², getting:

7 + 4/n + 2/(n²) <= c for all n >= n₀ .

If we choose n₀ equal to 1, then we need a value of c such that:

7 + 4 + 2 <= c

We can set c equal to 13. Now we have:

7n² + 4n + 2 <= 13n² for all n >= 1 .

Hence, 7n² + 4n + 2=O(n²)

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As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.

Answers

The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

What are the null hypothesis and alternative hypothesis?

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

Average x = 24375

u = 24230

SD = 523

n = 105

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is overpaid.

u > 24230

Assume significance level = 0.05

From the Z-table:

Z(critical) = 1.645

Now,

Z = (x-u)/(SD/√n)

Z = (24375-24230)/(523/√105)

Z = 2.84

Z > Z(critical)

So, reject the null hypothesis.

The average salary of sanitation workers in the city of Euonymus is overpaid.

Now, from the two-tail test:

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is 24230

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is not 24230

u ≠ 24230

Assume significance level = 0.05

From the Z-table for the two-tail test:

Z(critical) = ±1.96

Now,

Z = 2.84

Z > z(critical)

The average salary of sanitation workers in the city of Euonymus is not 24230.

Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

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Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.

What is the area of Maria’s circle?

6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared

Answers

The area of Maria’s circle is 18π square units option fourth is correct.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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? Question
Write an expression to represent the perimeter of Melissa's garden in terms of x.
Type the correct answer in each box. Use numerals instead of words.
Perimeter:
Question 3
? Question
x +

Answers

The expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

The linear equation is the equation where the highest degree of the variables is 1.

Here given that the garden is rectangular in shape and the tomato patch is square in shape.

the length of the side of the square tomato patch is x.

Asuume the length of the rectangle garden is l

and the breadth of the rectangle garden is b.

Given that

the length of the garden is greater than the 3 times of the length of the rectangular garden by 2 feet.

3 times of the length of the rectangular garden is 3x

2 feet greater than 3 times of the length of the rectangular garden= 3x+2

so from above, it is clear that l=3x+2

similarly, the breadth of the garden is greater than the length of the rectangular garden by 5 feet.

then the breadth of the garden = b= x+5

Therefore the expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

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Describe the graph of a function g by observing the graph of the base function ƒ.
A. g(x) = 2ƒ(–x) g(x)
B. g(x)= -1/2f(x)
C. g(x)= 1/2f(-x)
D. g(x)= f(-1/2x)

Answers

The correct answer is option B which is g(x)= 1/2f(-x).

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-

[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]

The value of the function f(x) will be:-

[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]

So g(x) = ( -1/2) f(x)

Therefore the correct answer is option B which is g(x)= 1/2f(-x).

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I need help with this question

Answers

Which of the following smallest values

The table shows the heights of three different plants.

Answers

Answer:

7/4 meters

Step-by-step explanation:

the tallest plant is 19/8

since they have all the same denominaters we can just compare the top numbers

so

the smallestp lant is 5/8

19/8 - 5/8 = 14/8

7/4 is your final answer after simplifying

Please help I’m confused

Answers

Answer:

Step-by-step explanation:

Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. The doctor recommends rest if the patient has the flu. The doctor recommends rest. not possible The patient does not have the flu. If the doctor recommends rest, the patient has the flu. The patient has the flu.

Answers

The doctor recommends rest if the patient has the flu. Then the correct option is A.

What is decision-making?

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Read the following two statements.

Then, if possible, use the Law of Detachment to draw a conclusion.

Then the correct option is A.

The doctor recommends rest if the patient has the flu.

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Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. ​

Answers

Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Part B

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

Suppose the derivative of a function is ′()=(−7)^7(−2)^2(+13)^10. Then the function is increasing on the interval _____.

Answers

The function is increasing on an interval if for every point on that interval the first derivative is positive.

Write 31/8 as a mixed number.
Reward: Mark as brainlist.

Answers

Answer:

[tex]3 \frac{7}{8}[/tex]

Step-by-step explanation:

Translate this sentence into an equation. Craig's savings decreased by 23 is .55

Answers

Answer:

x-23=.55

Step-by-step explanation:

Answer: 0.55 = x - 23

Step-by-step explanation:

let his savings = x


What is the vertex of the parabola defined by the equation
(x-2)² =-12(y-2)?
A (-12, 2)
B.
(2, 2)
C. (6,2)
D. (2,-2)

Answers

Answer: B. (2,2)

Step-by-step explanation:

The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).

Complete the coordinate proof of the theorem.

Answers

The coordinate of C( a+c , b) ,  AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)

What are Coordinates ?

Coordinates is the value assigned to a point in a x-y graph to determine its location.

The coordinates of parallelogram is

A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)

The y coordinate is same as D as b

and the x coordinate will be a+c

C( a+c , b)

The coordinate of the mid point of AC are ((a+c)/2 , b/2)

The coordinate of the mid point of BD are ((a+c)/2 , b/2)

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identify the percentage in 15 is 25% of 60

Answers

Answer:

25%

Step-by-step explanation:

In the sentence "15 is 25% of 60.", 25% is the percentage.

15 is the partial amount and 60 is the total amount.

15/60 = .25

convert a decimal to a percentage by multiplying by 100

.25 × 100 = 25

Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.

15/60 is 25%

Help me with this question please!! :)

Answers

Answer: 9516793/9765625

Step-by-step explanation:

We can subtract the probability none of them have been vaccinated from 1.

If 52% of people are vaccinated, then 48% of people are not vaccinated.

Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]

X: 4x^2+16 -20=0
What is x

Answers

the answer to X: 4x^2+16 -20=0 is that d equals 5
X=5

Answer:

[tex]\boxed{\sf x = 1, \ x = -5}[/tex]

Explanation:

[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]

[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]

[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]

[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]

[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]

[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]

[tex]\rightarrow \sf x = 1, \ x = -5[/tex]

Let (-7,3) be a point of terminal side of 0
Find Cos Sec Cot

Answers

The trigonometry ratios are cos(θ) = -7/√58, sec(θ) = -√58/7 and cot(θ) = -7/3

How to determine the trigonometry ratios?

The point on the terminal side is given as:

(x, y) = (-7, 3)

Start by calculating the hypotenuse using:

[tex]h= \sqrt{x^2 + y^2[/tex]

So, we have:

[tex]h= \sqrt{(-7)^2 + 3^2[/tex]

Evaluate

[tex]h= \sqrt{58[/tex]

The cosine is then calculated using:

cos(θ) = x/h

This gives

cos(θ) = -7/√58

The secant is then calculated using:

sec(θ) = 1/cos(θ)

This gives

sec(θ) = -√58/7

The cotangent is then calculated using:

cot(θ) = cos(θ)/sin(θ)

Where

sin(θ) = y/h

So, we have:

sin(θ) = 3/√58

So, we have:

cot(θ) = (-7/√58)/(3/√58)

This gives

cot(θ) = -7/3

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helppp im stuck :(
Hope you guys help me

Answers

Answer:

[tex]y=-\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

Define two points on the line:

  [tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]

  [tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]

Use the slope formula and the defined points to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]

Substitute the found slope and one of the points into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]

Simplify:

[tex]\implies y-2=-\dfrac{1}{2}x[/tex]

[tex]\implies y=-\dfrac{1}{2}x+2[/tex]

A horse was galloping at average speed of 50km/hr for the first 12 minutes. For the next x minutes, the horse slowed down and it’s average speed decreases to 30km/hr. The average speed of the horse for the whole journey is 45km/h. Find its total distance travelled in kilometres

Answers

The total distance travelled is 1075.91 km.

What is average speed?

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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what is the domain of the ordered pair shown in the graph?

Answers

Answer:

D.

Step-by-step explanation:

It is the only one that contains all the x-values of the points. (Domain is the set of x-values).

Which is the best description for the graph below?

Answers

Uh, there’s no graph.

boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.

Answers

Answer:

7.5mph

Step-by-step explanation:

Let the average speed of the boat to be x mph.

Total Distance = Avg. Speed x Total Time

60 = ((x+6) + (x-6))(4)

60 = (x+6+x-6)(4)

(2x)(4)=60

2x=60/4

2x = 15

x = 15 /2

x = 7.5mph

Answer:

  15 +√261 ≈ 31.155 mph

Step-by-step explanation:

The time for the trip can be found by dividing the distance by the speed.

__

setup

The relation between time, speed, and distance is ...

  time = distance/speed

The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...

  4 = 60/(b +6) +60/(b -6) . . . total  time is the sum of the times for the legs

__

solution

Multiplying by the product of the denominators, we have ...

  4(b +6)(b -6) = 60(b -6) +60(b +6)

  b² -36 = 30b . . . . divide by 4 and simplify

  b² -30b = 36 . . . . put in a form useful for completing the square

  (b -15)² = 36 +15² . . . . . complete the square

  b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)

  b = 15 +√261 ≈ 31.155 . . . . add 15

The average speed of the boat was about 31.155 mph.

4/3 - 1/2 What is the answer

Answers

Answer:

5/6

Step-by-step explanation:

4/3-1/2

1) make the denominators the same on both fractions

8/6-3/6=?

2) subtract numerators

5/6

3) simplify

cannot simplify

Answer:

5/6

Step-by-step explanation:

4/3  -1/2

The first step is to get a common denominator of 6

4/3 *2/2 = 8/6

1/2 * 3/3 = 3/6

8/6  -3/6

5/6

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