two ships leave a harbor at
the same time. One ship travels
on a bearing S15°W at 10 miles per
hour. The other Ship travels on a
bearing N75°E at 10miles per hour.
bearing
How far apart will the ships be
after 3 hours?
Answers
Answer:
30√3 ≈ 51.96 miles
Step-by-step explanation:
The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.
__
Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.
The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.
The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.
_____
Additional comment
If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.
c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²
c = 30√3 . . . . . take the square root (miles)
Related Questions
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
294 inches squred
Step-by-step explanation:
3 x 10 = 30
3 x 9 = 27
10 x 9 = 90
2(30) + 2(27) + 2(90) = 294
Which expression is equivalent to 18x+8y?
Answers
Answer
2 (9 x + 4 y)
Hope this helps :)
How can I get 9th grade to add up to 500? You can only change summer and fall. Thank you
Answers
Answer:
8th fall- 203 9th fall-95
Step-by-step explanation:
the 9th total is 500
8th fall is 203
9th fall is 95
Factor the GCF 7x^2+21x-35
Answers
Answer:
(7)(x² + 3x - 5)
Step-by-step explanation:
To Find the GCF : Prime factorize each term
7x² = 7 × x²21x = 7 × 3 × x-35 = 7 x -5As seen above, we can conclude the GCF is 7.
Therefore, by factoring using the GCF :
(7)(x² + 3x - 5)What is the value of the expression (3/4)³
81/256
27/64
9/12
27/4
Answers
Answer:
9/12
Step-by-step explanation:
Answer:
The answer is
9 over 12
9/12
The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. A 2-column table with 5 rows. Column 1 is labeled number of tickets with entries 1, 2, 3, 4, 5. Column 2 is labeled Probability with entries 0.17, 0.55, 0.20, 0.06, 0.02. What is the probability that a randomly selected purchase has less than two tickets? 0.17 0.55 0.72 0.83
Answers
Answer:
0.17
Step-by-step explanation:
The probability for purchasing 2 tickets at a time can be given as 0.17. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Suppose X be the event to represent the number of tickets in purchase.
Then, as per the question distribution table can be formed as follows,
The number of tickets (X) P(X) Probability
1 0.17
2 0.55
3 0.20
4 0.06
5 0.02
Thus, the probability of selecting less than two tickets can be obtained as,
P(X < 2) = P(X = 1)
⇒ 0.17
Hence, the probability for a purchase to have less than two tickets is given as 0.17.
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Which mixed number is equivalent to
19/3
Answers
Answer:
6 1/3
Step-by-step explanation:
You just have to see how many times it goes into it
Five marbles labeled 1 through 5 are placed in a bag. A marble is randomly pulled and the number is recorded before the marble is
placed back in the bag. The results of the simulation of 20 marble pulls are shown in a dot plot.
Which dot plot models an unfair data-generating process?
Answers
Using the dot plot concept, it is found that the left plot on the bottom row shows an unfair data-generating process.
What does a dot plot show?The dot plot shows the number of times each measure appears in the data-set.
In this problem, each trial has 5 possible outcomes and there are 20 trials, hence each number should appear 20/5 = 4 times.
On the left plot of the bottom row, outcomes 1 and 5 appear 7 times, while outcomes 2, 3 and 4 appear 2 times, which are the furthest values from 5, hence it is an unfair data-generating process.
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Answer:
Step-by-step explanation:
(21*3+8)-17+(85-12+9-45)
Answers
Answer:
91
Step-by-step explanation:
(21)(3)+8−17+85−12+9−45
=63+8−17+85−12+9−45
=71−17+85−12+9−45
=54+85−12+9−45
=54+73+9−45
=54+82−45
=54+37
=91
A small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 8+x= rate going downstream and 8−x= rate going upstream.)(Round your answer to the nearest tenth.)
Answers
The rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Let's suppose the rate of the current = r
The time it takes to go downstream + 4 hours = time to go upstream
As we know the:
[tex]\rm Time = \dfrac{Distance}{ Rate }[/tex]
Now,
[tex]\rm \dfrac{44}{ (8 + r)} + 3 = \dfrac{44}{ (8 - r)}[/tex]
After solving:
[tex]\rm \dfrac{44}{ (8 - r)}-\dfrac{44}{ (8 + r)} =3[/tex]
After cross multiplication
44(8+r) - 44(8-r) = 3(8+r)(8-r)
88r = 3(64 - r²)
3r² + 88r - 192 = 0
After solving the above quadratic equation, we get:
r = 2.03 or
r=−31.37 (reject as it is negative)
So, the r =2.03 mph
Thus, the rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
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Find the area of a sector of the circle below. Express in terms of pie and as a decimal.
Answers
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=18\\ \theta =40 \end{cases}\implies \begin{array}{llll} A=\cfrac{(40)\pi (18)^2}{360}\implies A=36\pi \\\\\\ A\approx 113.097 ~m^2 \end{array}[/tex]
Answer:
36π (m²) or ≈ 113.14 m²
Step-by-step explanation:
[tex]A_{circle}[/tex] = [tex]\pi r^{2}[/tex]
[tex]A_{sector}[/tex] = x
[tex]\frac{360^o}{40^o}[/tex] = [tex]\frac{18^2 \pi }{x}[/tex]
9 = [tex]\frac{18^2 \pi }{x}[/tex]
x = 36π
or
x ≈ 36 × [tex]\frac{22}{7}[/tex] ≈ 113.14 m ²
This question is worth 20 points if someone answers it!
Answers
The maximum number of tourists in the third week will be maximum in the numberville city.The solution of f(x)=h(x) will be x(5,2).
What are equations?The equation is actually a relationship between the numbers and the variables.
To calculate the number of the tourists in the third week we will put the value 3 in every function:
[tex]f(x)=x^2+5x+10=(3)^2+(3\times 3)+10=29\\\\\\g(x)=3^x=3^3=27\\\\\\h(x)=10x=10\times 3=30[/tex]
So we can see that the function third h(x) numberville city is having a maximum number of tourists.
The solution of f(x)=h(x) will be calculated as:
[tex]x^2-3x+10=10x\\\\\\x^2-7x+10=0\\\\\\x^2-5x-2x+10=0\\\\\\x(x-5)-2(x-5)=0\\\\\\x=5,2[/tex]
Hence the solution of f(x)=h(x) will be x(5,2).
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please help thank you
Jack and Marcy are at an amusement park. Jack is standing 75 meters from a hot air balloon ride. He is recording Marcy with his cell phone as she gets into the basket of the balloon and the hot air balloon begins to rise.
Answers
Tan65°=h/75m
2.1445 × 75 = h
h = 160.83
Step-by-step explanation:
This is very very simple
Use the quadratic formula to solve x^2- 5x + 3 = 0.
Answers
Answer: Heyaa! ~
Your Answer is... x = 5 ± √ 13/ 2
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Hopefully this helps you!
-Matthew ^^
Which sport is required to have both male and female competitors?
A. Water polo
B. Swimming
C. Hockey
D. Mixed doubles tennis
Answers
Sand and gravel are mixed in the ratio 5:3 to form ballast.
How much sand is mixed with 750kg of gravel ?
Answers
Work Shown:
sand/gravel = 5/3
x/750 = 5/3
3x = 750*5
3x = 3750
x = 3750/3
x = 1250
Tell whether the system has one solution, infinitely many solutions, or no solution.
Answers
Answer:
Has infinite solutions
Explanation:
-x + 5y = -3..... eq1
2x - 10y = 6 .... eq2
===============
make x the subject in equation 1
-x + 5y = -3
-x = -3 - 5y
x = 5y + 3
========= insert this in equation 2
2(5y + 3) - 10y = 6
10y + 6 -10y = 6
6 = 6
So, Has infinite solutions as L.H.S = R.H.S
Label the scatterplot correctly
Answers
What is the volume of a cube with sides measuring 1.5 inches
Answers
Answer:
A cube with a side length of 3 inches has a volume of 27 cubic inches.
Step-by-step explanation:
yes
Write an equation for the translation of y =5/x
that has the asymptotes x= -7 and y= 7
Answers
The equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
What is hyperbola?
It is a curve in two-dimensional geometry having two parts, they both are symmetric. In other words, It can be defined as the number of points in the two-dimensional geometry that have a constant difference from that point to two fixed points in the plane.
We have:
[tex]\rm y = \dfrac{5}{x}[/tex]
Vertical asymptotes x= -7 and
Horizontal asymptotes y= 7
After translation:
[tex]\rm y = \dfrac{5}{x+7}+7[/tex]
Thus, the equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
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A survey of high schools offering honors classes to ninth graders reveals that 38% of the high schools offer no honors classes, 12% offer one honors class, 25% offer two honors classes, 20% offer three honors classes, and 5% offer four honors classes.
A high school is selected at random. What is the probability that it offers an even number of honors classes?
0.62
0.30
0.68
0.32
Answers
Using the discrete distribution, it is found that the probability that it offers an even number of honors classes is of 0.68.
What is the discrete probability distribution?The distribution for the number of honors classes the school offers is given by:
P(X = 0) = 0.38P(X = 1) = 0.12.P(X = 2) = 0.25.P(X = 3) = 0.2.P(X = 4) = 0.05.Hence the probability of an even number is given by:
P(even) = P(X = 0) + P(X = 2) + P(X = 4) = 0.38 + 0.25 + 0.05 = 0.68.
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PLEASE HELP ME, I GIVE 69 POINTS FOR CORRECT ANSWER
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
A: Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
B: Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
C: Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
D: Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
(PS: If you choose C, you're wrong.)
Answers
Answer:
D
Step-by-step explanation:
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
Evaluate: 2 • [(6 + 1)2 + 1]
Answers
Answer:
20
Step-by-step explanation:
2•[(6+1)2+1]
2•[(7)3]
2•10
• means times
2×10
20 answer
Answer:
p
Step-by-step explanation:
2 • [(6 + 1)2 + 1]
First The Brackets :
[(6 + 1)
->>> 6 + 1
= 7
But there's a bracket around 6 + 1 so now we multiply
-->>> [(7)2 + 1]
->>> 7 x 2
= 14
So now we add :
-->>> 14 + 1
= 15
And now we multiply:
->>> 15 • 2
--->>> 30
Hope it helps :))))
13. What is the distance between the y-intercept of the function f(x) = 2(3)* and the y-intercept of the function g(x) represented by the table below?
Answers
Answer:
the answer is letter C.
I hope this can help you!
only answer if you know!! no spams
Answers
Answer:
The answers would be D and C.
Hope this helps!
Evaluate the expression:
-a^2 + c(a-c) - n^2 a= -3 c= -2 n= 3
Answers
Answer: -a^2+c\left(a-c\right)-n^2a=3\quad :\quad c=-\frac{-a+\sqrt{-3a^2-4an^2-12}}{2},\:c=-\frac{-a-\sqrt{-3a^2-4an^2-12}}{2}
Step-by-step explanation: YW! plese mark branlest!
how to find 2 square root of 3
Answers
Answer:
sqrt12
Step-by-step explanation:
being given any problem like this, let's use the form y√x, y representint 2, and x is 3, but it's generalized
in order to find the unsimplified √ we would do 2(yx). Which in this case is 12
16) Graph g(x) = x + 3 + 2
Answers
Arun is caring for many yellow-spotted salamanders. He weighs each and
then counts the number of yellow spots on its back. Which trend line best fita
the data?
Answers
Answer:
The answer is B.
Step-by-step explanation:
Looking at the option, a trend line best fits the data within the plot. Seeing Answer B has the line that goes through the plot.
Order the numbers from greatest to least?
2/9, 21%, 5/20, 8%
Answers
Answer:
5/20, 2/9, 21%, 8%
Step-by-step explanation:
2/9 = 0.22
21% = 0.21
5/20 = 0.25
8% = 0.08
0.25>0.22>0.21>0.08
mark brainliest please!
