Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other 52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?
Answers
Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]
So, we use the cosine rule , which states that
[tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Related Questions
if f(x)=2x and g(x)=x^2-1 which statement is true?
A. (f*g)(x)=2x^2 -1
B.(f*g)(x)=2x(x^2-1)
C.(g*f)(x)=4x-1
D.(g*f)(x)=4x^2-1
Answers
We have then:
f (x) = 2x
g (x) = x ^ 2-1
Multiplying we have:
(f * g) (x) = (2x) * (x ^ 2-1)
Answer:
The following statement is correct:
B. (f * g) (x) = 2x (x ^ 2-1)
(I will give the brainliest! Please answer quickly)
Leia cuts congruent triangular patches with an area of 21 square centimeters from a rectangular piece of fabric that is 14 centimeters long and 6 centimeters wide. How many of the patches can Leia cut from 31 pieces of the fabric?
Answers
In a certain state, license plates consist of three letters followed by three numbers.
a. how many
Answers
If there are no repeats then the answer is 11,232,000
i think this is correct im srry if it is not
The cover of a jacuzzi is a regular pentagon. If the side measures 2.5 feet and the apothem is 1.7 feet, find the area of the lid used to cover the Jacuzzi
Answers
[area of a regular pentagon]=5 *[Area of triangle with side 2.5 ft and height (apothem) 1.7 ft]
[area of a regular pentagon]=5 *[2.5*1.7/2]-------------> 5*[2.125]-----> 10.625 ft²
the answer is 10.625 ft²
When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?
5x + 2 – 3x2
Answers
First, we must define the words "leading coefficient" and "constant."
Take a look at the simple definitions...
Leading coefficient- the number behind the term with the highest exponent
Constant- the number without any variable in front of it
This means that for the polynomial
5x+2-3x^2 the leading coefficient is -3 because it is the number behind the term with the highest exponent! The constant is 2 because there are no variables behind it.
I really hope this helps!
Best wishes :)
According to these three facts, which statements are true?
Circle W has center (−3, 0) and radius 8.
Circle V is a translation of circle W, 2 units down.
Circle V is a dilation of circle W with a scale factor of 2.
Select each correct answer. (You can choose more than one).
A. Circle V and circle W are similar.
B. Circle V and circle W have the same center.
C. The radius of circle V is 16.
D. The center of circle V is (−5, 0).
Answers
1)Circle W has center (−3, 0) and radius 8
the equation of a circle W is
(x+3)²+(y)²=8²
2)Circle V is a translation of circle W, 2 units down.
the center of circle V--------> (-3,0-2)---------> (-3,-2)
3)Circle V is a dilation of circle W with a scale factor of 2.
then the radius circle V is 8*2------> 16 units
the equation of a circle V is
(x+3)²+(y+2)²=16²
therefore
case A. Circle V and circle W are similar.---------> is correct
because I can transform circle V to circle W using only translations, rotations and scaling (In the case of circles, no rotations are necessary).
case B. Circle V and circle W have the same center.-------> is not correct
case C. The radius of circle V is 16.-----------> is correct
case D. The center of circle V is (−5, 0).----------> is not correct
the answer is
case A. Circle V and circle W are similar.---------> is correct
case C. The radius of circle V is 16.-----------> is correct
Circle V and Circle W are similar and the radius of Circle V is 16; however, Circle V and Circle W do not have the same center, and the center of Circle V is not (-5, 0), but rather (-3, -2).
Given the information that Circle W has center (-3, 0) and radius 8, and Circle V is a translation of Circle W 2 units down and a dilation with a scale factor of 2, the following statements can be evaluated:
Circle V and Circle W are similar: This statement is true. Both circles maintain their shape after a translation and dilation.Circle V and Circle W have the same center: This statement is false. Translation moves the center of Circle V 2 units down, changing its coordinates.The radius of Circle V is 16: This statement is true. The radius is doubled through the dilation process.The center of Circle V is (-5, 0): This statement is false. The correct center after translation would be (-3, -2).A packet processed by an internet router carries either audio information with probability 7/10, video, with probability 2/10, or text with probability 1/10. the probability that the router processes 70 audio packets, 20 video packets, and 10 text packets in a sequence of 100 packets is:
Answers
Here we have three variables,
a=number of audio packets
v=number of video packets
t=number of text packets
we note that a+v+t=100 (as given)
and correspondingly,
A=number of audio packets in the pool
V=number of video packets in the pool
T=number of text packets in the pool
Here, the pool is from a population such that the probabilities of selecting each type are respectively 0.7, 0.2 and 0.1 (as given).
Defining C(n,r)=n!/(r!(n-r)!) as the number of combinations of r objects chosen out of n.
In a pool of 1000 packets, then A=700, V=200 and T=100.
The multivariate hypergeometric distribution gives
P(70,20,10,1000)
=C(700,70)*C(200,20)*C(100,10)/C(1000,100)
=0.0147526
In a pool of 100000 packets, then A=70000,V=20000,T=10000.
The multivariate hypergeometric distribution gives
P(70,20,10,1000)
=C(70000,70)*C(20000,20)*C(10000,10)/C(100000,100)
=0.0132925
Since the population has a size of infinite, we will try to approach the value by choosing an even larger population, say, 1000000,
P(70,20,10,1000000)=0.0132806
Next try
P(70,20,10,1000000000)=0.013279255
P(70,20,10,1000000000000)=0.013279254
...
So we can conclude that
P(70,20,10,population)=0.013279 with almost certainty.
which term best describes the statement given below?
if a = b and b = c then a= c
Answers
Answer:
Syllogism law
Step-by-step explanation:
Given:
a ⇒ b, and b ⇒ c, then a ⇒ c
This is a transitive property and it is also called syllogism law.
For example,
if it rains (a), then the cricket field will be wet (b), this means a ⇒b
If the cricket field wet(b), then the game will be cancelled(c), this means b ⇒c
if it rains (a), then the game will be cancelled(c), this means a ⇒ c
So it is a valid conclusion. This is called syllogism law.
Julie is going to a store to buy vases to use as centerpieces at her party. Small vases cost $2 and large vases cost $4. She needs to buy a minimum of 15 vases, and can spend a maximum of $50.
Which system of linear inequalities represents this situation? Let s represent the number of small vases and l represent the number of large vases.
A
s + l ≥ 15
2s + 4l ≤ 50
B
s + l ≤ 15
2s + 4l ≥ 50
C
s +l ≥ 50
2s + 4l ≤ 15
D
s + l ≥ 15
2s +4l ≥ 50
Answers
D: the second equation is wrong. She wants to be under 50
C: The system is confusing money with the number of vases
B: The answer is wrong. She wants to spend under or equal to 50 not over.
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning. Show all work!
Answers
ωωωωωωωωωωωωωω
Answer:
17
Step-by-step explanation:
what is the slope of the line that contains (-3, 4) and (7, 5)
Answers
5-4 1
m = --------- = ---------
7-(-3) 10
On a trip, you had to change your money from dollars to British pounds. You got 560560 pounds for 800800 dollars. How many pounds will you get for 300300 dollars?
Answers
800,800÷300,300= 2.66666.... (recurring)
If $300,300 goes into $800,800 2.66666 times, then the amount of pounds you want to find goes into £560,560 2.66666 times as well. Let's write this as an equation to solve for x (where x is the amount of pounds you will obtain for $560,560):
2.66666x = 560,560
Divide both sides by 2.66666
x = 210,210
Therefore, you will get £210,210 for $300,000
At Pizza Pi, 9% of the pizzas made last week had broccoli on them. If 27 pizzas had broccoli, on how many pizzas in all were made last week?
Answers
Given Information
----------------------------------------------------------
9% of pizza made had broccoli
27 pizza had broccoli
----------------------------------------------------------
Equation the information and find 1%
----------------------------------------------------------
9% = 27
1% = 27 ÷ 9
1% = 3
----------------------------------------------------------
Find 100%
----------------------------------------------------------
1% = 3
100% = 3 x 100
100% = 300 pizzas
----------------------------------------------------------
Answer: There were 300 pizzas made last week
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me n my dad share the cost of a meal the ratio of 2:3 i payed £52.20 whats the total cost of the meal
Answers
52.20 / 2 = 26.1
26.1 * 3 = 78.30 ( amount dad pays)
total = 78.30 + 52.20 = 130.50
A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inches. How far, to the nearest hundredth of an inch does each corner of the burger stick out from the bun? Explain.
Answers
.. 16 in^2 = πr^2
.. r = (4 in)/√π ≈ 2.25676 in
The distance from the corner to the center of the square hamburger is
.. d = 4 in/√2 = 2√2 in ≈ 2.82843 in
The burger will stick out
.. (2.82843 -2.25676) in ≈ 0.57 in
this math problem is hard
Answers
It is the only one that makes sense
The Voyager 2 space probe took 2 years to make its closest approach to Jupiter. How many months did it take Voyager 2 to reach Jupiter? (1 year = 12 months)
Answers
2 YEARS=24 MONTHS
Machine A makes 50 more than 4 times the number of parts that Machine B makes each day. If Machine A makes 450 parts each day, how many parts does Machine B make each day? 100 125 500 1850
Answers
Answer:
125 is NOT the right answer. read the question out completely. 100 is your answer.
Step-by-step explanation:
you're supposed to write an algebraic expression for 50 more than 4 times the number of parts that Machine B makes and set that equal to 450.
The graph of f(x) is shown below.
(First image below)
If g(x) and f(x) are inverse functions, which graph represents g(x)?
A. 2nd Graph below
B. 3rd Graph below
C. 4th Graph below
D. 5th Graph below
Answers
[tex]f(x) = \sqrt{x} [/tex]
to find the inverse, replace f(x) with y, switch the x and the y, then solve for y
[tex]f(x) = \sqrt{x} ... \: y = \sqrt{x} \\ x = \sqrt{y} \\ {( \sqrt{y})}^{2} = {x}^{2} \\ y = g(x) = {x}^{2} [/tex]
The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)
Given that we have the graph of f(x), we want to see which one is the graph of its inverse. The correct option is B, the third graph.
Remember that two functions f(x) and g(x) are inverses if:
f(g(x)) = g(f(x)) = x
This also means that if:
f(x) = y
then g(y) = x.
So we basically should have the exact same graph of f(x), but we just "interchange" the two axes.
From this, we can see that the correct option is the third graph (the one where the curve goes upwards. So the correct option is B.
If you want to learn more about inverse functions, you can read:
https://brainly.com/question/10300045
You are saving money to buy an electric guitar. You deposit $1000 in an account that earns interest compounded annually. The expression 1000(1+r)^2 represents the balance after 2 years where r is the annual interest rate in decimal form. Write a polynomial in standard form.
The interest rate is 3%. What is the balance of your account after 2 years.
The guitar costs $1100. Do you have enough money in your account after 3 years?
Answers
after 2 years?
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$1000\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &2 \end{cases} \\\\\\ A=1000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=1000(1.03)^2[/tex]
after 3 years?
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$1000\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &3 \end{cases} \\\\\\ A=1000\left(1+\frac{0.03}{1}\right)^{1\cdot 3}\implies A=1000(1.03)^3[/tex]
is that enough to pay the $1100?
now, let's write 1000(1+r)² in standard form
1000( 1² + 2r + r²)
1000(1 + 2r + r²)
1000 + 2000r + 1000r²
1000r² + 2000r + 1000 <---- standard form.
The balance of your account after 2 years is $1,060.90. You do not have enough money in your account after 3 years to buy the $1100 guitar.
Explanation:To write a polynomial in standard form for the balance after 2 years, we substitute the given interest rate of 3% (0.03 in decimal form) into the expression $1000(1+r)^2. This gives us $1000(1+0.03)^2. Simplifying this equation, we have:
$1000(1+0.03)^2
= $1000(1.03)^2
= $1000(1.0609)
= $1,060.90
Therefore, the balance of your account after 2 years is $1,060.90.
To determine if you have enough money in your account after 3 years to buy the $1100 guitar, we can substitute the values into the expression $1000(1+r)^3. Using the same interest rate of 3% (0.03 in decimal form) and solving the equation, we have:
$1000(1+0.03)^3
= $1000(1.03)^3
= $1000(1.0927)
= $1,092.70
Since $1,092.70 is less than the cost of the guitar, you do not have enough money in your account after 3 years to buy the guitar.
If 1 mile equal to 1.61 kilometers, how many kilometers are there in 50 miles
Answers
50m-x
There 50 x 1.61
80.5 km
Hi can someone please help me? If sin2A=cos 3A find the value of A. Can you please explain in full detail how you arrived at your answer? Also Find the exact value of (sec30)^2. Will I need to use a calculator in order to solve this prob?
Answers
sin(2A) = cos (90 - 2A)
=cos (3A)
90 - 2A = 3A
5A=90
A=18
if m 6 =50 then find m 11
Answers
The question about finding the value of m 11 based on m 6 cannot be answered with the information provided. Additional context or a specific formula is needed to make a calculation.
Explanation:It appears that there might be a misunderstanding in the question, as the provided information is not sufficient to determine the value of m 11 based on the value of m 6. The references provided deal with various scientific and mathematical concepts that do not seem directly related to one another and therefore do not give a clear method for calculating m 11 from m 6.
Additional context or information such as a specific formula, sequence, or relationship between m 6 and m 11 would be necessary to provide an accurate answer. Without this information, it's not possible to calculate m 11.
how many factors in the expression 8(x+4)(y+4)(z2+4z+7)have exactly two terms
Answers
- 8
- (x + 4)
- (y + 4)
- (z² + 4z + 7)
Terms are separated by "+" and "-" signs, so that eliminates the first factor, which only has one term. The fourth factor has two "+" signs, and as you can see, it has three terms; that one is out as well. The last two factors both have only one "+" sign, and they both have two terms. Therefore...
Answer:
Two factors in the expression 8(x + 4)(y + 4)(z² + 4z + 7) have exactly two terms.
carlos walked 2 miles on Monday and 5 miles on Saturday. the number of miles he walked on thise two days is 3 miles more than the number of miles he walked on Friday. write and solve an addition equation to find the number of miles Carlos walked on Friday.
Answers
Express the decimal as a percent. 0.24
Answers
Final answer:
To express the decimal 0.24 as a percent, you would multiply it by 100. The decimal 0.24 can be expressed as 24%.
Explanation:
To convert a decimal to a percent, you need to multiply it by 100. In this case, to express the decimal 0.24 as a percent, you would multiply it by 100.
0.24 * 100 = 24
So, the decimal 0.24 can be expressed as 24%.
A percent represents a part per hundred.
When you multiply a decimal such as 2.4 by 100 to find its percent equivalent, you move the decimal point two places to the right. If there are not enough decimal places, we use zeros as placeholders.
Therefore, 2.4 times 100 is 240, and 0.24 times 100 is 24, which gives us 24%.
Find an equation of the plane that contains the point p(5,1,4) and the line x = 2−t, y = 3 + t, t = 3−3t.
Answers
.. (5-2, 1-3, 4-3) = (3, -2, 1)
The cross product of this with the line's direction vector (-1, 1, -3) is (5, 8, 1). The dot product of that with any of the points in the problem statement is 37. Your plane equation can be written as
.. 5x +8y +z = 37
_____
A suitable vector calculator is very handy for this. I used an HP-48 app on my phone.
The main span of Bridge A (2300 feet) is _____ percent shorter than the main span of Bridge B (4700 feet).
Answers
To do this you divide the difference in lengths by the starting length. We start with the main bridge.
4700-2300=2400
2400/4700 is about 51.1% shorter.
The main span of bridge A is 51.1% shorter than the main span of bridge B.
Span of bridge A = 2300 feets
Span of bridge B = 4700 feets
Percentage difference in span length :
[(difference in span) / span of B] × 100%
Difference in span = 4700 - 2300 = 2400
Percentage difference = (2400 ÷ 4700) × 100%
Percentage difference = 0.5106 × 100% = 51.1%
Therefore, the main span of bridge A is 51.1% shorter than the main span of bridge B.
Learn more :https://brainly.com/question/13218948
Mauricio wants to fry 18 potatoes per hour for 3.5, point. He can fry 6 potatoes using each gallon of oil. How many gallons of oil does Mauricio need for frying potatoes? Choose 1 answer: A: 378 B:21 C:189 D:10.5
Answers
Answer:
The answer is option D.
Step-by-step explanation:
Mauricio wants to fry 18 potatoes per hour for 3.5 hours.
So, total becomes = [tex]18\times3.5=63[/tex]
As he can fry 6 potatoes using each gallon of oil.
So, for 63 potatoes, he will need = [tex]\frac{63}{6}=10.5[/tex] gallons.
Therefore, the correct answer is option D.
Ron needs paper for his class project. He buys 5 packs of paper and uses all but 3 pieces. If p stands for the amount of paper per pack, which expression can he use to find out the number of papers that he used?
Answers
1 pack = p pieces of paper
5 packs = 5p pieces of paper (multiply both sides by 5)
Ron uses 5 packs, so there are 5p pieces of paper total. He uses all but 3 pieces, meaning that he uses 5p-3 pieces of paper. So that's why 5p-3 is the answer
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Here's a more concrete example
Let's say p = 10. In other words, let's say there are 10 pieces of paper per pack.
If that's the case, then 5 packs yield 5*10 = 50 sheets total. This is the same as saying 5p = 5*10 = 50. All I've done is replace p with 10. The letter p is simply a placeholder.
If he uses all but three sheets of paper, then Ron uses 47 sheets since 50-3 = 47. A more longer way to see this is to plug p = 10 into the expression 5p-3 and we get
5p - 3 = 5*10-3 = 50 - 3 = 47
which helps us confirm we have the right expression. I recommend you try other values of p to generate more examples. Make sure p is a whole number and that it is a positive number.
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Once again the answer is 5p-3