A runner’s resultant velocity is 8 miles per hour due west running with a wind of 3 miles per hour N 28° W. What is the runner’s speed, to the nearest mile per hour, without the effect of the wind.
Answers
Answer:
7.07 miles/hour W 22° S.
Step-by-step explanation:
Given that the resultant velocity of the runner, [tex]v_r = 8[/tex] miles/hour due west.
Wind speed, [tex]v_w= 3[/tex] miles/hour N 28° W.
Assuming that the absolute velocity of the runner, [tex]v_a= x[/tex] miles/ hour W \alpha S as shown in the figure.
By using vector addition, [tex]\vec{v_r} = \vec {v_w} + \vec {v_a}[/tex] .
Now, from the figure,
[tex]|\vec {v_r}|=|\vec {v_w} |\sin{28°} + |\vec {v_a}| \cos \alpha \\\\\Rightarrow 8 = 3\sin{28°} + |\vec {v_a}| \cos \alpha \\\\\Rightarrow |\vec {v_a}| \cos \alpha =8-3\sin{28°} \cdots(i)[/tex]
And [tex]AC= |\vec {v_w} |\cos{28°} = |\vec {v_a}| \sin \alpha \\\\[/tex]
[tex]\Rightarrow |\vec {v_a}| \sin \alpha= 3\cos{28°} \cdots(ii)[/tex]
Dividing equation (ii) by equation (i), we have
[tex]\frac {|\vec {v_a}| \sin \alpha}{|\vec {v_a}| \cos \alpha}=\frac {3\cos{28°}}{8-3\sin{28°}} \\\\\Rightarrow \tan \alpha = 0.402 \\\\\Rightarrow \alpha = \tan ^{-1} (0.402)=22^{\circ} \\\\[/tex]
Putting the value of \alpha in equation (ii), we have
[tex]|\vec {v_a}| \sin {22^{\circ}}= 3\cos{28^{\circ}} \\\\\Rightarrow |\vec {v_a}| =(3\cos{28^{\circ}})/\sin {22^{\circ}} \\\\[/tex]
[tex]\Rightarrow |\vec {v_a}| = 7.07[/tex] miles/hour
Hence, the runner speed, without the effect of the wind, is 7.07 miles/hour W 22° S.
Related Questions
The government of a foreign country has recently decided to give a tax rebate to each of its adult citizens. The total amount the government can spend on the program is the equivalent of $5 × 1011. If the adult population of the country is approximately 2.29 × 108, what is a good estimate of the amount of money each person will receive (in dollars)?
Answers
Given :
The government of a foreign country has recently decided to give a tax rebate to each of its adult citizens.
The total amount the government can spend on the program is the equivalent of [tex]\$(5 \times 10^{11})[/tex]. If the adult population of the country is approximately [tex]2.29 \times 10^8[/tex].
To Find :
A good estimate of the amount of money each person will receive (in dollars).
Solution :
[tex]\text{Amount per person}= \dfrac{\text{Total amount}}{\text{Number of people}}\\\\A =\dfrac{5\times 10^{11}}{2.29\times 10^8}\\\\A = \$2183.406[/tex]
Hence, this is the required solution.
Please help me, What is the slope??
Answers
Answer:
-0.5
Step-by-step explanation:
this is the right picture can you help me
Answers
Answer:
Yeah i am pretty sure you are right
Step-by-step explanation:
HELPPPPPPP ASAPPPPPPPPPpp 25 POINTS
Answers
Answer:
A, the y intercept is 15
Step-by-step explanation:
This function is in standard form and is the only one where you can simply substitute 0 in for x and find the y- intercept.
Katya is traveling by train to visit her relatives in another state. The equation y=60x+20 represents the total distance she is from her home (y) after x hours of traveling on the train
Answers
Step-by-step explanation:
Step one:
Given
The expression for Katya's distance away from home is given by the expression
[tex]y=60x+20[/tex]
y represents her total distance away from home
x= represent the time of travel in hours
Step two:
60 represents the rate at which the train is traveling in km per hour
20 represents the initial distance from home
we predict her distance away at a given time
say 4 hours, that is x=4hours
substituting in the expression
y=60x+20
y=60(4)+20
y=240+20
y=260km
Answer:
y=260km
Step-by-step explanation:
Solve the equation: 7^n=343
Answers
Answer is
7^n = 7^3
N=3
Answer:
n=3
Step-by-step explanation:
7
n
=343
Use the rules of exponents and logarithms to solve the equation.
7
n
=343
Take the logarithm of both sides of the equation.
log(7
n
)=log(343)
The logarithm of a number raised to a power is the power times the logarithm of the number.
nlog(7)=log(343)
Divide both sides by log(7).
n=
log(7)
log(343)
By the change-of-base formula
log(b)
log(a)
=log
b
(a).
n=log
7
(343)
PLEASE HELP GUYSS I NEED IT
Answers
Answer:
To solve an area of a rectangle the formula is LxW. Right now we only know the width. Lx2 = 112 So, you would do 112 divided by 2 which equals 56.
LxW = 56x2
which is 112
Step-by-step explanation:
Calculate the slope between the points (2,0) and (6, 7)
Answers
Answer:
slope = 1.75
Step-by-step explanation:
slope = Y2-Y1/X2-X1
= 7/4
= 1.75
help asap help show work
Answers
A company offers courses to prepare students for the Graduate Management Admission Test (GMAT) has the following information about its customers: 20% are currently undergraduate students in business; 15% are undergraduate students in other fields of study; 60% are college graduates who are currently employes; and 5% are college graduates who are unemployeed. Choose a customer at random. If a student is not an undergraduate business student, what is the robability they are an undergraduate student in other feilds of study? Ok
Answers
Answer:
OK aaaaaaaa. What is it
If a student is not an undergraduate business student, what is the probability they are an undergraduate student in other fields of study = 0.08
What is Probability?It deals with the occurrence of a random event.
Given that a company offers courses to prepare students for the Graduate Management Admission Test (GMAT) has the following information about its customers: 20% are currently undergraduate students in business; 15% are undergraduate students in other fields of study; 60% are college graduates who are currently employed; and 5% are college graduates who are unemployed.
P(undergraduate in business) = 0.20
P(undergraduate in other subjects) = 0.15
P(employed graduates) = 0.60
P(unemployed graduates) = 0.05
We know, P(A') = 1 - P(A)
Therefore, P(not undergraduate business) = 1 - P(undergraduate business) = 1 - 0.20 = 0.80
Hence, probability they are an undergraduate student in other fields of study = 0.08
For more references on probability, click;
https://brainly.com/question/11234923
#SPJ2
What is 3+1?
Can somebody please explain? I've been trying to figure this out for hours and I need to know soon because it's for my homework. I think it might be 7 but I'm not sure.
Answers
How do I rewrite a mixed fraction as a sum?
Answers
Answer:
turn it into a decimal first
Step-by-step explanation:
If you spend two hours playing sports after school, what percent of your day is devoted to sports? Use 24 hours as the length of a day.
A. about 2%
B. about 8%
C. about 20%
D. about 12%
Answers
Answer:
The answer is B. about 8%
Step-by-step explanation:
The answer is B. because the actual answer would be 8.3333% but rounded it is about 8%
Question 14
A company paid $391 for 15 bushes and 8 bonsai trees. They had to purchase 9 more bushes and 5 more bonsai trees for $241. What is the cost of each bush and bonsai tree? Enter your answers in the
boxes below.
Bushes:
Bonsai Tree:
Answers
Answer:
The cost of each bushes is $9.00
The cost of each bonsai trees is $32.00
Step-by-step explanation:
The given parameters are
The amount the company paid for 15 bushes and 8 bonsai trees = $391
The amount for which the company purchased 9 more bushes and 5 more bonsai trees = $241
Let x represent the cost of each bushes and let y represent the cost of each Bonsai Trees, we have;
15 × x + 8 × y = 391...(1)
9 × x + 5 × y = 241...(2)
We make y the subject of both equations to get;
For equation (1), we have;
15·x + 8·y = 391
15·x + 8·y = 391
8·y = 391 - 15·x
y = 391/8 - 15/8·x
For equation (2), we have;
9 × x + 5 × y = 241
5·y = 241 - 9·x
y = 241/5 - 9/5·x
Equating both equations, gives;
391/8 - 15/8·x = 241/5 - 9/5·x
391/8 - 241/5 = 15/8·x - 9/5·x = 0.075·x
0.675 = 0.075·x
x = 0.675/0.075 = 9
x = 9
Therefore, the cost of each bushes = x = $9.00
From, y = 241/5 - 9/5·x, we have;
y = 241/5 - 9/5×9 = 32
y = 32
Therefore, the cost of each bonsai trees = y = $32.00
Planet Fitness charges a $10 per month plus
a one-time membership fee of $55.
a.) Write a linear equation for the situation
where x is the number of months and y
is the total cost.
b.) How many months have passed if you
paid $107? SHOW ALL WORK.
Answers
b)5.2 months
A. 10x+55=y
B. 5.2 months or 5 months
Which equation can be used to find the solution of (1/4)^y+1=64?
−y−1=3
y + 1 = 3
−y+1=3
y−1=3
Answers
Answer:
−y−1=3
Step-by-step explanation:
Which equation can be used to find the solution of (1/4)^y+1=64?
This can be solved by power of indices
(1/4)^(y+1)=64
(4^-1)^(y + 1)= 4^3
Note
(x^a)^b = x^ab
Hence:
4^(-1)(y + 1)= 4^3
4^-y - 1 = 4^3
Divide both sides by 4
−y−1=3
Hence, the equation that can be used to find the solution of (1/4)^y+1=64 is
−y−1=3
Answer:
-y-1=3
Step-by-step explanation:
took the test and got it correct
Can somebody solve this I don’t understand this.
Answers
Answer:
The third one!
Step-by-step explanation: 5 5 5 5 its 5!
How many times will you roll a number less than 4 on a number cube if you rolled it 250 times ?
A) 100
B) 90
C) 125
D) 85
Answers
Answer:
C. 125
Step-by-step explanation:
The ratio for one time is 3:6. It is 3:6 because there are 3 numbers less than 4 on a number cube. You can now compare the two ratios.
3:6 = x/250.
This is a ratio, so both numbers would have to be multiplied by the same number. 6 * 41 = 250.
3 * 41 = 123.
(41 was rounded from 41.6666667. This is why it comes out to 123.)
Determine the type of triangle that is drawn below.
Pls help asap!!!!
Answers
Answer:
right triangle
Step-by-step explanation:
Answer:
It is an scalene triangle.
Step-by-step explanation:
A scalene triangle is a triangle that's lines aren't equal. So in this case, this is a scalene triangle.
Mary bought a car priced at $23,500. If the value of the car decreases every year by 9%, approximately what will be the value of the car after 10 years?
Answers
Answer:
$4626.548
Step-by-step explanation:
Given that :
Cost of car = $23,500
Value of car decreases by 9% every year
Value of car after 10 years =?
Using the formula :
A = p(1 + r/n)^nt
A = final amount
P = cost of car = principal
r = Depreciation = - 15%
t = number of years
A = 23500(1 + - 0.15/1)^10
A = 23500(0.85)^10
A = $4626.548
Plssss help I will give all my points and give brain things pls help
Answers
answer for y: 180 - 76 = 104
answer for z: 180 - 117 = 63
1. Dennis made a 500 km trip in five hours. For the first two hours, Dennis had an average speed of 150 km/h. For the last two hours, Dennis had an average speed of 100 km/h. Which of the following is true about Dennis' trip? (25 Points) Dennis must have maintained a constant velocity throughout his trip. Dennis must have maintained a constant speed throughout his trip. O Dennis must have stopped for an hour in the middle of this trip Wich statemeent correctly discribes the locaton and Dennis must have driven without stopping during his trip
Answers
Answer:
The correct option is;
Dennis must have stopped for an hour in the middle of this trip
Step-by-step explanation:
The given parameters are;
The distance Dennis covered in 5 hours = 500 km
Dennis's average speed in the first two hours = 150 km/h
Dennis's average speed in the last two hours = 100 km/h
Therefore;
Dennis traveled 150 km/h × 2 h = 300 km in the first two hours
Dennis traveled 100 km/h × 2 h = 200 km in the last two hours
Which gives, Dennis traveled 300 km + 200 km in 2h + 2h = 4h
Therefore, Dennis traveled 500 km in 4 hours and Dennis must have stopped for an hour in the middle of this trip.
Which statement is true? Millimeters are larger than centimeters. Millimeters are larger than centimeters. Meters are larger than kilometers. Meters are larger than kilometers. Milliliters are larger than kiloliters. Milliliters are larger than kiloliters. Kilograms are larger than grams.
Answers
Given :
Conditions :
1) Millimetres are larger than centimetres.
2) Meters are larger than kilometres.
3) Millilitres are larger than kilolitres.
4) Kilograms are larger than grams.
To Find :
Which conditions are correct.
Solution :
1) Millimetre is 0.001 m and cm is 0.01 m .
So, option 1 is correct.
2) Kilometer is 1000 m .
So, option 2 is also correct.
3) Millilitres is 0.001 L and kilolitres is 1000 L .
Therefore, this is not correct.
4) Kilogram is 1000 g .
Therefore, this is also correct.
Therefore, option 1 , 2 and 4 are correct.
Hence, this the required solution.
Which set of ordered pairs does not represent a function?
O {(5,-2),(-6,-4), (-2,3), (-1,-4)}
O{(-3,4), (-8,0), (3,-8), (-3,-4)}
O {(6,3), (-1,5), (-7,3), (3,0)}
O {(3,9), (2,7), (9,9), (4, -3)}
Answers
Answer:
The second choices is the answer
O{(-3,4), (-8,0), (3,-8), (-3,-4)} as you can see there's a repeating domain or value of x which is the -3
what is 22/55 in simplest form
Answers
Answer:
2/5
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
because the highest number you can divide them both by is 11
Mr. Jackson lengthened the fence along the back of his yard. Before he added 130 feet, the fence was 300 feet long. He divided the fence into 5-foot sections. How many 5-foot sections does he have now?
A.430 B.26 C.86 D.60
Answers
Enter numbers to write 4.23×10^3 in standard notation.
Answers
The answer is 4230. I used mathmay to answer this question if you have anymore question like this I would suggest you go there it is a really good math answering site. Hope this helps!!
3р + 3 = 18 I need the answer now!
Answers
Answer:
3p + 3 = 18
3p = 18 -3
3p = 15
p = 15/3
p= 5
Step-by-step explanation:
Explanation: Start off by taking away 3 from both sides. After doing this you’ll be left with 3p=15 you want to divide by what’s next to the variable so that would be 3. 3p/3 equals p and 15/3 equals 5 so P=5
Will give BRAINLY. Complete the table using the equation y=4×+7
Answers
Answer: you would just do y= 4x (4•1 would be 4) plus 7. hope this helps!!
Step-by-step explanation:
Answer:
Is your computer cracked anywise
Step-by-step explanation:
At a dry cleaning store, it costs $1.79 to clean a man’s dress shirt and 6 times as much to clean a suit. Choose the answer that correctly completes the statement.
It would cost_________to dry clean one shirt and one suit.
Answers
You have to multiply 1.79 times 6 then add 1.79
Answer:
Step-by-anation: