A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
Answers
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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Related Questions
A cube has an A on 3 sides and a B on 3 sides. Rolling it 50 times results in 17 A's and 33 B's.
Using this observed probability, how many A's would be rolled in 750 tries?
Answers
present ages of two children are 2 and 5 years the rspectively. After how long will the sum of their square ages be 45.
Answers
Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.
Calculating the duration to get the sum to 45Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.
Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;
let x represent the number of years from now when the sum of square of their respective age will be
45.(x + 2)² + (x + 5)² = 45
Expanding the brackets;
x² + 4x + 4 + x² + 10x + 25 = 45
2x² + 14x + 29 = 45
2x² + 14x + 29 - 45 = 0
2x² + 14x - 16 = 0
Solving the quadratic equation for x;
x = 1, x = -8
Taking the positive value, the value of x is 1
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HELP PLEASE
hhahsjdbrinejs eje did sis ieneieneiebenebeidbjebebejdne
Answers
You speak my language :0
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4. There are 36 units in a case. You have 90 loose units of stock in the store. The store manager has requested a stock count in CASES. How many cases of stock will 90 units fill? CALCULATION:
Answers
There are 36 pieces in one case. The store has 90 loose storage units. The store manager requested an inventory count where 2.5 units would fill her 90 units.
What is the inventory process like?Typically, this process involves the retailer (or team of employees) walking through the retailer's warehouse and storefront, counting each item. Information is captured manually using pen and paper or electronically using a mobile device.
Create a storage location map showing each shelf, bin, drawer, receiving dock, and return area. Place geographic divisions, not product lines, between each storage area. Let's start counting! After each counter completes a certain range, allow a manager or someone else to check the count.
90/36 = 2.5
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Factor f(a) = 7a²– 16a + 4
Answers
Factor this expression means to find two numbers x and y such that we can write f(a) = (a+x)(a+y).
To do this, we use the quadratic formula
\(\begin{gathered} a=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(7)(4)}}{2(7)} \\ a=\frac{16\pm\sqrt[]{256-112}}{14} \\ a=\frac{16\pm\sqrt[]{144}}{14} \\ a=\frac{16\pm12}{14} \end{gathered}\)so, one answer is
\(a=\frac{16+12}{14}=\frac{28}{14}=2\)and the other one
\(a=\frac{16-12}{14}=\frac{4}{14}=\frac{2}{7}\)To find the factors we use the solutions
\(\begin{gathered} a=2\text{ then a-2=0} \\ a-2\text{ is a factor} \end{gathered}\)\(\begin{gathered} a=\frac{2}{7}\text{ then 7a-2=0} \\ 7a-2\text{ is a factor} \end{gathered}\)Then, the factorization is
\(7a^2-16a+4=(7a-2)(a-2)\)3x + 3 = x - 5
Solve for x
Answers
Answer:
x = -4
Step-by-step explanation:
plz vote brainliest :)
-4
Explanation:
3(-4)+3=-4-5
^ ^
-12 -9
-12+3=-9
^
-9 =-9
consider the following :
\( f(x) = {x }^{2} - x + 2 \div x - 2 = x + 1 + 4 \div x - 2\)
which polynomials do you think we should call the divisor,dividend,quotient and remainder?
Answers
Answer:
X+1 +4 \ div x \)
Step-by-step explanation:
If wrong report and if correct brainless plss
You are comparing apples and oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2? Explain
Answers
Answer:
no
Step-by-step explanation:
because 3;2 is more the 2;3 as you know if you do it as a fraction it would be 3 over 2 and 2 over 3 the 3 over 2 whould be a whole and the 2 over 3 would be 3 forths of a whole and the 3 over 2 would be more
5/12x6/15=30/180
How do I simplify?
Answers
Answer:
0.167
Step-by-step explanation:
if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6
technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167
that should end up being your answer if i did the math right
Answer:
Step-by-step explanation:
5/12 * 6/15 =30/180
1/6=1/6
which is true, Right-hand side is equal to left-hand side
please helpjjjjjjjjjjjjjjjj
Answers
Answer:
Diverge i think.
Step-by-step explanation:
See the photo
If A={A,15,E,17,18, B,20} and B={ X,22, F,42, Y,62,72}, then what is n(A∪B)?
Answers
Answer:
14
Step-by-step explanation:
There are 7 elements in each set, and no elements are shared. The number of elements in the union of the sets is then ...
n(A∪B) = 7+7 = 14
Convert to an improper fraction.
2 1/5
Answers
Answer:
11/5
Step-by-step explanation:
2 x 5 = 10
10 + 1 = 11
11/5
To the nearest millimeter, a cell phone is 105 mm long and 66 mm wide. What is the ratio of the width to the length?
Answers
Answer:
22:35
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 66 and 105 is 3
Divide both the numerator and denominator by the GCD
66 ÷ 3/105 ÷ 3
Reduced fraction:
22/35
therefore the ratio will be 22:35
Please please help me please please
Answers
Answer:
4.1: y = 4
4.2: y = -1/2x + 4
4.3: x = -4
4.4: y = x-1
Step-by-step explanation:
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Answers
Answer:
C
Step-by-step explanation:
Beacuse
10/5=2 it
5 is also a factor
please very soon I offer the crown !!! + 10 points urgently !!!
Answers
Answer
a - 6 in each row, 12 altogethor
b - 5 in each row, 15 altogethor
c - 4 in each row, 16 altogethor
d - 2 in each row, 8 altogethor
color each row a diffrent color
sketch the region y=sqrtx, y=0, x=4
Answers
Answer:
see attached for a sketch
area = 5 1/3 square units
Step-by-step explanation:
You want the area under the square root curve, above y=0, from x=0 to x=4.
AreaThe area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...
dA = (√x)dx
A = ∫(√x)dx
The power rule can be used for the integration:
\(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)
The area of the region is 5 1/3 square units.
__
Additional comment
You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.
This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.
#95141404393
order the following decimals from least to greatest 3.21, 3.021, 3.12, 2.121
Answers
Answer:
2.121 , 3.021 , 3.12 , 3.21
Step-by-step explanation:
They're in ascending order, aka least to greatest. Just list the lowest number to the highest.
Answer:
2.121,3.021,3.12,3.21
Step-by-step explanation:
321/100, 3021/1000, 312/100, 2121/1000
3210, 3021, 3120, 2121
= 2.121, 3.021, 3.12, 3.21
If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
(f + g)(x 3 for all values of x
(f + g)(x) 3 for all values of x
(f + g)(x)6 for all values of x
(f + g)(x)for all values of x
Answers
The range of values of (f + g)(x) is for all values of x -infinity to + infinity
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
We are Given f(x) = |x| + 9 and g(x) = –6,
Required the range of (f + g)(x)
First, calculate
(f + g)(x) = f(x) + g(x)
Substitute values for f(x) and g(x)
(f + g)(x) = |x| + 9 - 6
(f + g)(x) = |x| + 3
The above expression shows that (f + g)(x) ≥3
Range = (f + g)(x) ≥3 for all values of x
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The odds in favor of an event are given. Compute the probability of the event. (Enter the probability as a fraction.)
4 to 7
Answers
The probability of the event for the given odds in favor (4 to 7) is found as 4/11.
How do you calculate the probability?The inquiry provides the unusual parameters shown below: Odd = 4 to 7First, we must translate the odd into a ratio.Thus, we have the depiction shown below: odds of 4 to 7To continue solving, we must represent the ratio as a fraction.
Thus, we have the depiction shown below.
Odds ratio equals 4/7
We use the following equation to translate the aforementioned odd's expression into a probability expression.
This is displayed as
P = (Odds + 1)/(Odds).
Replace the unknown values in the equation above.
The following equation is what we have.
P = (4/7)/(4/7 + 1)
Analyze the amount
This results
P = (4/7)/(11/7)
Put the quotient in product form.
P = (4/7) * (7/11)
Evaluate
P = 4/11
Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 20 mi/h faster than the other. If the two buses are 576 miles apart after 4 hours, what is the rate of each bus?
Answers
0.007 is 1/10 of what?
Answers
Answer:
0.007 × 10 = 0.07
Step-by-step explanation:
cant do step by step
Answer:
0.070
Step-by-step explanation:
Write your question as an equation, then solve.
0.007 = 1/10 × what
The inverse of the coefficient of "what" is 10/1, so multiply both sides of the equation by that.
10 × 0.007 = 10 × 1/10 × what
0.070 = what
0.007 is 1/10 of 0.070
sara used a total of 1 cup of liquid for a recipe. She used 2/5 cup of vinegar, and the rest of the liquid she used was milk.
How much milk, in cups, did sara use for the recipe?
A) 2/5
B)3/5
C)5/5
D) 1 2/5
Answers
Answer:
B 3/5
Step-by-step explanation:
To celebrate getting a new job, Marco went out for a dinner that cost $100. If the local sales tax is 6% and Marco left a 15% tip on $100, what was the total cost of his meal?
Answers
9514 1404 393
Answer:
$121.00
Step-by-step explanation:
Together, the tax and tip were 6% and 15% of $100, or 21% of $100. That means the total cost of Marco's mean was ...
(1 +21%) × $100 = 1.21×$100 = $121.00
Find the price of one marker if three markers cost $18. A.) $6
B.) $54
C.) $4
D.) $3
Answers
You take $18/3 markers which gives you $6 for each marker.
A rectangular field is four times as long as it is wide. If the perimeter of the field is 560 yards, what are the field’s dimensions?
Answers
Answer:
Width=56 yards
length=224 yards
Step-by-step explanation:
let:
Width=x
length= x*4= 4x
perimeter = 2*x + 2*4x
working
\((x \times 2) + (4x \times 2) = 560\)
\(2x + 8x = 560\)
\(10x = 560\)
\( \frac{10x}{10} = \frac{560}{10} \)
\(x = 56\)
\(4x = 56 \times 4 = 224\)
width =56 yards
length = 224 yards
What is the answer pleaseee
Answers
Answer: 803.84cm3
Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.
To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.
4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.
Now, we have the area of the circle. 50.24cm squared!
The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,
16cm x 50.24cm squared = 803.84cm cubed.
The volume of the can of soup is 803.84cm cubed.
Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation. If y varies inversely as the square of x, and y=7/4 when x=1, find y when x=3
Answers
Answer:
y=7/36
Step-by-step explanation:
Since y varies inversely to the square of x, we can say
\(y = z/x^2\)
where z is the constant of variation.
Then, from knowing that y=7/4 when x=1, we plug them in to find z.
\(7/4=z/(1^2)\\z=7/4\)
Now we have the full equation,
\(y=7/4x^2\)
Plug x=3 in and we get,
\(y=7/4(3^2) = 7/36\)
Please read the question
Answers
\(\frac{2}{7}= \frac{3.5}{x} => 2x=3.5(7)= 24.5 => x=\frac{24.5}{2} = 12.25\)
ok done. Thank to me :>
Apply Thales theorem
7/2=x/3.53.5=x/3.5x=3.5²x=12.25What is greater 1.0275 or 1.029
Answers
Answer:
1.029 is greater than 1.0275
Step-by-step explanation:
Answer:
1.029
Step-by-step explanation:
What is greater 1.0275 or 1.029
.027 < .029
So, 1.029 is greater.